Journal
2014 | 2013 | 2012
Friday 15 August 2014
I stopped into the lab for a couple of hours this morning to finish up a few things, which included organizing the reimbursement submission copies, looking into how to use E-RAS vs. SBU Reporting (See 10 July 2014 journal entry), and tracking down an online pdf of the Nikon D3000 manual to figure out how to change the playback display mode back to the large preview (versus the overview data screen it’s been showing us).
I can’t believe the summer program’s over - but it was once again a rewarding experience for me. I really appreciated being able to return to the LTC, once again, to work with these exceptional students and guide them through the unique LTC research experience - what an invaluable opportunity for all of us!
Thursday 14 August 2014
This morning I prepared reimbursement forms for the summer expenses - after totaling everything (making sure to subtract tax this time), I organized the receipts into each expenditure category, filled out a cash voucher, and attached the Excel spreadsheet with details of each expense. I also finalized the overall list of 2014 expenses and sent off that spreadsheet to John. Chris and Eric from Eden’s group stopped by to have their pictures taken for the LTC website, which I then cropped to the usual 300 x 300 pixel squares.
I once again caught up with some of my web journals (see Art/Optics OPN article info below) and did some cleaning in the lab. I put away Ikaasa’s tape layers in a drawer labeled “quarter-wave plates / retarders / polarizers” (they’re in a small envelope with her name on it), packed up the spectrometer in its case and put it on the back room shelves (with the CMOS cameras), and wiped down the student desks.
Peter van der Straten, Hal’s collaborator from Utrecht who helped him co-author the book on Laser Cooling and Trapping, gave a talk this afternoon on "Spin drag in a Bose gas.” The physics was over my head, but definitely it was a good experience - and it was interesting that Hal remarked at the end that it created more questions than answers, which was a compliment to Peter and his research team.
I stumbled upon a very interesting OPN article the a while back and didn’t have a chance to write about it yet - Optical Insights into Renaissance Art (Falco and Hockney 2000), which investigated the use of optical aids by Renaissance painters. Charles M. Falco is an optics and physics professor at the University of Arizona in the College of Optical Sciences, and David Hockney is an English artist and photographer. (This paper was part of a long list of optics-art connections that Falco has researched).
They argued that some Renaissance artists could have used a concave mirror (or lens) to project their subject directly onto the canvas, making it easier to draw out the correct proportions etc. A good example is the painting Husband and Wife, by Lorenzo Lotto 1523. You can see where the pattern on the tablecloth goes out of focus and has two vanishing points, as if Lotto had been using an optical element and had to reposition it at some point in order to continue drawing past the depth of field.
Knowing the geometry of the original scene and the size of the canvas, they determined the focal length of the lens used (this is an exercise that I then tried with my students during one of our morning discussions!). With that and the depth of field (the total distance on either side of the focal point in which the image is “sharp”), they also figured out the diameter of the lens used. If there were discrepancies in the magnification or vanishing points of different sections of the painting, this probably attested to the fact that the lens was repositioned during the painting process. Distortions in the painting could have resulted from the lens’s optical aberrations.
There is a lot of controversy surrounding the Hockney-Falco thesis because of its implications, as if it were some sort of attack on the artist’s skill. I personally think this is a fascinating discovery that doesn’t belittle the artist’s talent, but rather shows their innovation and interest in using science to enhance their work. Falco suggests the artists learned about such possibilities from Alhazen’s book of optics, written in 1021. A good source that lays out the theory and evidence is this Brandeis website.
Wednesday 13 August 2014
This morning I caught up in detailing the lab’s summer expenses and created a requisition form for Libby’s housing expenses (This proved to be especially time-consuming… Since we previously established that the reason the Requisition Form wasn’t printing with a requisition number was because it’s often fickle with Macs and Safari. I decided to try to fill it out on John’s computer, but Internet Explorer crashed every time I tried to open the form online. So then I moved to the other Windows desktop computer in the lab, but Internet Explorer wouldn’t even open on this computer and Firefox wouldn’t let me fill-in any of the form boxes. Chrome appeared to be working okay, just incredibly slowly, until I tried printing/saving the form after finishing it - everything just froze… So finally I moved back to my own Mac and used Chrome - which I might not have actually tried other times - I filled out the form once again and when I hit “print” it prompted me to select a funding source (i.e. SBF) and gave me a requisition number, but deleted everything else I had typed in! Oh well. I handwrote it after printing - at least we got the number to generate, finally!
In the afternoon there were a couple of grad student talks - the first was Spencer Horton’s oral exam. The title of his talk was “Development of an 8eV Light Source for Measurements of Excited State Lifetimes and Direction Comparison of Weak and Strong Field Ionization.” He’s working in the ultrafast spectroscopy group with Prof. Weinacht. The second was Zakary Burkley’s masters thesis defense, titled “Towards Single Photon Nonlinearities using Cavity EIT (Electromagnetically Induced Transparency). He’s been working in the quantum information lab with Prof. Figueroa.
Marissa stopped by this afternoon for a little bit! It was great seeing her. Libby and I showed her the summer students’ projects and the laser light show.
I spent a lot of time organizing the photos I had uploaded yesterday - I’ve now updated the lab photos page and the summer calendar page. I also created a page for the Simons students’ LTC tour and for the Simons symposium. I still have the originals on my computer if anyone wants a higher-quality copy of any of the photos.
Tuesday 12 August 2014
This morning was the poster symposium in the Wang Center for the Simons summer program. It was great seeing our students’ posters up and to also have the opportunity to look at other students’ work. Afterwards, there was a short awards ceremony where each student was presented a certificate for completing the research program.
We then gathered our group and had a nice farewell lunch at the Simons center cafe - 16 of us in total! There was John, me, Libby, Andrea, Marty, Alex and his parents, Jonathan and his mom, Ikaasa and her parents and aunt, and Hal with his friend and collaborator visiting from Holland - Peter van der Straten. Before saying our goodbyes, we took a group photo out on the cafe deck.
Back in the lab, I spent a lot of time sorting through pictures from the tour yesterday and the poster event today, uploading them to my laser account, resizing them and shrinking their overall quality. Tomorrow I’ll put them on a couple of separate webpages.
Monday 11 August 2014
We started off the day with a final morning discussion at the white board - I wrote down a bunch of important equations that we had discussed together at various points during the summer program. But I didn’t label any of them! Instead, I asked the students to go through each equation and explain what it meant, where it comes from, what a sketch of it would look like, etc. These topics included the binomial and small angle approximations, single- and double-slit equations, circular aperture equations and Rayleigh criterion, derivatives and integrals, resonance, Law of Malus, Euler’s formula, the golden ratio and Fibonacci sequence, and of course the pig toy. We hit a few snags along the way, but in general the students were able to give a basic review of each topic.
We then did a lab clean up - putting away unused optics, tidying up optics tables, organizing demos, getting “mood-lighting” up and running (i.e. sodium lamp, UV light, christmas lights), vacuuming, and discussing once more the structure of the tour.
I caught up on some missing journal entries from the previous week - it’s especially hard to keep up during crunch time!
Our lab tour for the Simon’s students was at 3:30 pm - I think it went well! We started off with everyone in the conference room for some opening remarks from John, which included a description of the LTC, why it’s special, what’s expected of its students (i.e. webpages and lab notebooks - my regular lab notebook and mini notebook were passed around as examples), and how important optics is to all types of research. We then divided the students into 4 groups of about 6-8 students. While the first group moved into the lab, the other stayed behind in the conference room to do interactive demos with John.
Jonathan showed the interferometer and rubber band demo and then talked about his Airy beam project
Andrea talked about her single bubble sonoluminescence project
Alex showed his optical tweezers setup
Ikaasa talked about polarized light and the spectrometer
Libby ran the laser light show.
The beginning groups that finished first circled back to the conference room to see the demos they and missed. I made sure the whole event ran smoothly and took plenty of pictures! Overall, the tour ended up lasting about an hour and a half (3:30pm - 5pm), and I think that it worked well that we had it on the day before the symposium since everyone had basically finished their abstracts, posters, and research.
Tomorrow we’re planning to have a nice farewell lunch at the Simons Center Cafe with LTC students, parents, and mentors. For future reference - the number to call for reservations at the Cafe is 2-2881.
Friday 8 August 2014
I spent most of the morning discussing posters with Ikaasa and Jonathan and reviewing them with John and Marty.
I also talked a little bit with the group about responsibilities for the the upcoming lab tour - they’ll each be doing 5-10 mini demonstrations about their projects or other related demo. They’ll need to start off with some good background about the physics involved, since many of these Simons students are working in other fields and may not have a good understanding of optics. Then the idea is to try to involve the students - explain things to them, but not lecture them - give them the opportunity to learn by participating.
Last year we did parallel sessions, and that worked pretty well. But this summer John suggested we try doing it in series, with the laser light show as the grand finale, so I was trying to figure out the best way to organize that. I worked through a plan for the students will move through the lab from Jonathan, to Andrea, to Alex, to Ikaasa, then finally to Libby for the light show - while groups are waiting to enter the LTC, they’ll do general demos with John in the conference room.
We tidied up the lab a little bit in the afternoon - but the bulk of the clean-up will have to be done Monday morning.
We’ve reached the end of the summer crunch time! The last week is always a little hectic - everyone’s trying to finish last minute things with their projects while doing abstracts and posters, and they should also be keeping up with their web journals and lab notebooks. We’ve got the Simons students’ lab tour Monday afternoon and their poster symposium is Tuesday morning.
Thursday 7 August 2014
Rachel gave a great informational talk on spacial light modulators this morning - she started with a little background on liquid crystals, different types of SLMs (reflective vs. transmissive, VAN PAN and TN), their applications, advantages versus disadvantages, how to control them (either by means of an extended monitor with a Paint, Powerpoint, or Photoshop mask, or using a separate monitor with a Matlab or Mathematica generated mask), and how to encode a phase mask and optimize it with a blazed grating instead of a binary one (and the SLM sensitive area should be completely filled by the laser to avoid extra, undesired diffraction).
Libby, Ikaasa, John and I had a nice lunch at the Simons Center Cafe with Rachel and Niyati Desai (another Simons student working in the physics department) and discussed the Stony Brook Honors College versus the WISE program and choosing colleges in general.
In the afternoon, we worked with Jonathan for a little to help him model the theoretical expansion of a Gaussian whose beam waist starts at the same narrow width as his Airy beam to drive home the fact that the Airy beam is non-diffracting. I also talked with Ikaasa more about her project and the math behind it. I seems that those articles I found at the end of the day yesterday aren’t directly relevant, and that the math Ikaasa did for rotating a half wave plate on top of another one doesn’t turn it into a quarter wave plate. We also discussed modeling the birefringence versus wavelength, and she was able to plot this for one layer of tape using her 10-layer data.
Wednesday 6 August 2014
In the morning I helped individual students with their questions about the research update presentations and the symposium posters. I also worked with Ikaasa - she’s trying to figure out if the theory actually works as far as turning two half wave plates (one rotated with respect to the other) into a quarter wave plate. Using an angle between them that she had calculated with Jones calculus, she got some interesting but unexplainable experimental results, so we’ll need to look more into the physics of what’s happening…
Our pizza lunch meeting this week featured Rachel Sampson, a Stony Brook University rising junior. I worked with her last summer in the LTC, so it was great seeing her again! She spent her summer doing an RE at the University of Rochester in the Boyd group - her project was titled: “Sorting Laguerre-Gaussian Radial Modes Via Projective Measurement,” which was related to her work here in the LTC. After her talk and discussion, we had our students give their research update presentations (with a little extra background than last so that Rachel could be caught up to speed on their projects). Rachel’s abstract and student research update talk titles can be found here.
We ordered more cylindrical lenses from Thorlabs for Jonathan’s project after he found out it was possible to have the shop do a gold reflective coating over them to make cylindrical mirrors - we got one LK1487L1 - uncoated plano-concave with a -400 mm focal length, and one LJ1363L1 - uncoated plank-convex with a 400 mm focal length.
Throughout the afternoon, I worked more with Ikaasa and Marty too to try to figure out the physics behind her project. Marty’s not quite sure why her the “half-wave plate” maxima are flattening out when she rotates one stack of tape on top of the other. At the end of the day, I found a few articles that I didn’t get a change to really go through yet but they seem relevant - the first is Achromatic combinations of birefringent plates (Pancharatnam 1955). This article (part 1 of 2) talks about using two half-wave plates and a quarter-wave plate of the same birefringent material to make an achromatic circular polarizer. But it does mention a previous investigation that used two birefringent plates to "transform incident circularly polarized light to plane polarized light.. or vice-versa." There's also an interesting note about why this can't be called an achromatic quarter-wave plate, but rather an "achromatic circular polarizer." This was done in the article: Réalisation d'un quart d'onde quasi achromatique par juxtaposition de deux lames cristallines de même nature" (Destriau and Prouteau: J. Phys. Radium 10, 2 (1949) 53-55). I unfortunately haven't been able to find a translation yet from the original French version..
The “part 2" of Pancharatnam’s article this discusses "superposing birefringent plates in such a manner that the combination as a whole behaves as an achromatic quarter-wave plate." But it may just be producing elliptically polarized light… We should also do some research into other articles of this type. John pointed out that Pancharatnam is well-known for his discovery of a geometric phase (now named after him) for polarized light passing through crystals.
Tuesday 5 August 2014
Today I sent out a couple of poster templates from last summer that the students can use to start making their posters and had another brief discussion with them about these. These are posters that are meant to be presented, so they really shouldn’t include too much text, but just enough so that someone looking at the poster alone can get a good gist of the project. It takes time to put together an informative and aesthetically pleasing poster that has a good balance of words and graphics. Also this morning Ikaasa very generously bought Starbucks for the lab with the extra money on her meal card :)
I spent some time with John trying to figure out an invite list for tomorrow’s pizza lunch. It was decided that he’d cc: many of the LTC alums about the event, since it’s the last Wednesday meeting for this year’s summer program. Though the talk is featuring Rachel’s research experience at the University of Rochester this summer, our current students will give brief research updates as well.
Since particle rotation wasn’t working out the way Alex had hoped in his tweezers setup, he decided to try using a different liquid than water. We went on a small hunt around the lab and stumbled upon some mineral, baby, and vegetable oils that he’ll try. Note - the “chemicals” cabinet (in the back room with the wooden optics table) actually contains more than just traditional chemicals; it’s also got various oils, syrups, sugar, and baking ingredients.
Ikaasa is still working on creating a quarter-wave plate at the wavelengths for which the tape acts as a half-wave plate. It’s possible that the intersection points between the transmission curves for crossed and parallel polarizers signify the wavelengths for which the tape acts as a quarter-wave plate already. Using this idea, we saw that (between crossed polarizers) when she rotated her second 6-layered filter at about a 170 degree angle, the old maxima (which signified where the filter acted as a half-wave plate) dipped down a little bit past where the intersection points were - which agrees with what we were thinking and possibly illustrates a whole group of wavelengths where the two filters together act as quarter-wave plates. Now it’s a matter of playing around with the angle until those dips plateau and checking that this theory makes sense in a model.
It seems as though Jonathan created an Airy-like beam from two reflective polarizers curved by attaching them to pieces of an empty paper towel roll. Alex was able to get a good video on my iPhone of a copper oxide particle spinning and then stopping after he removed the spiral phase plate from his set up (possibly proving that it was spinning due to the transfer of angular momentum from the optical vortex).
Monday 4 August 2014
This morning Ikaasa started us off with a derivation of the Law of Malus with Jones calculus. It was fairly straightforward - she started with a diagram of linearly polarized light going through a second polarizer with its axis oriented at some angle relative to the first. Using Jones calculus, a linear polarizer is sandwiched between a basic rotation matrix and its negative version, and this is multiplied by the incident light’s electric field. The result squared and put into a ratio of output intensity over incident intensity boils down to cos^2 of the angle between the incident polarized light and the axis of the second polarizer.
I then had a conversation with the students about posters. (The poster symposium is a week from tomorrow, yikes!) It’s important that they start collecting photos of their setups, making detailed diagrams and graphs, and brainstorming text. John will send them a template from a previous year to work from. We’ll probably need to have these done by Friday at the latest so that we’ll have enough time to get them printed before Tuesday morning.
John, Libby, Andrea, and I had lunch with Doreen, the Academic Advisor of Stony Brook University’s WISE program - Women in Science and Engineering. It’s a 20-year old program set up to encourage and support undergraduate girls majoring in the science, math, and engineering fields. Throughout the academic year they have special events and lectures as well as a upperclassman to underclassman mentoring program. Something like this would have been great to be a part of as an undergraduate - in my graduating class, I was actually the only female physics major! Though since Dickinson was a small school, I received a lot of support from the department and my fellow majors. I think WISE is especially beneficial at a large university, since it gives students the opportunity to bond in a smaller community setting.
A couple of other random tid-bits from the day - (1) We got our replacement filter today! - the dielectric short pass 600 nm cut off one from ThorLabs. And then sent even more lab snacks… (2) The power meter probe is unfortunately missing - Alex needed to use it. We found the actual meter, but the probe wasn’t attached, nor was it in the surrounding area or in any other visible place in the lab. (3) Alex captured some videos of trapped particles behaving strangely using my iPhone camera - at some points large particles are repelled from the trap and at other times a bubble-like thing formed when the laser was focused on very large particles. (4) Andrea is working on understanding resonance in an LRC circuit and is currently trying to model her data using Excel. (5) Ikaasa is cleverly using Jones calculus to see how she can use her half-wave plate setup to create a quarter-wave plate. (6) Jonathan is now trying to make cylindrical mirror-like devices to repeat his experiment with a new twist.
Also, John went over to Paul (who does poster printing) in the library to ask about printing deadlines, and he got into a conversation about one-way mirror cubes. What a really neat piece of optics art!
Friday 1 August 2014
Again we put off our morning discussion so that the students could work on their writing (hopefully we’ll have time to start these up again next week!). We’ll still need to have Ikaasa do her Law of Malus derivation with Jones calculus, and I have a couple of other small things I wanted to do with the students as well.
John and I did one-on-one editing with the students - going through their abstracts line-by-line. A good abstract for the webpage and Simons symposium will have an opening with some background about the physics involved and the motivation (starting broadly, and then zeroing in on the focus of the project), a middle paragraph with the experimental methods and results, and (if necessary) a final paragraph with future prospects. It should cite any key papers that the student used and include acknowledgments and the source of financial support (in this case the Simons Foundation).
The CMOS camera arrived today (with more lab snacks)! However, like all ThorLabs equipment, the software is only compatible with Windows computers… I suggested that Alex try downloading the free image/video capture software from Bodelin technologies, which is meant to be used with the company’s specific ProScope camera (that I had used during my honors thesis research), but it can capture stills and video from any generic USB camera. However, it turned out that the problem was with the camera itself not even being recognized on a Mac.
So I did another live chat with a ThorLabs rep and explained how we recently purchased this USB2.0 CMOS camera from Thorlabs (DCC1545M), however the computers that we would like to use it with run Mac OSX. I mentioned how we’re a bit disappointed that it apparently cannot be used without installing the included Windows7 software, and asked if they have any suggestions for how we can utilize the camera? (i.e. any additional drivers we can download or other camera capture software that’s compatible with a Mac). They apologized for the inconvenience, but said that the camera does not support MacOS directly right now and the only option is installing Windows Virtual machine. How unfortunate!
I also uploaded some pictures from various LTC events/moments and created a lab photos page. I shrunk a lot of the pictures using linux’s resize command, but I think I’ll need to also decrease the quality so that the file sizes aren’t as big as they still are.
Thursday 31 July 2014
Today we didn’t do a formal morning discussion again so that the students could work on their abstracts and update their web journals. Though it’s great to get wrapped up in a good project, it’s important to continue to document what’s being accomplished and learned. Being able to communicate well is an important skill for a researcher. Keeping up with the web journals also allows the mentors to be able to gain insight into students’ understanding - sort of like a “window into their head” as John has called it.
So I spent that time updating my own webpage - catching up on journal entries and updating the calendar page. I then repackaged the Thorlabs part (filter with a cutoff that’s too high for a red HeNe) that we’re returning. It’s great that the company always takes care of things very promptly - I emailed them yesterday evening about wanting to exchange the part, and they replied within the hour to give us return instructions and let us know that they’re already in the process of shipping us out the replacement.
There was an AMO physics seminar this afternoon by Michael Keller of the University of Vienna whose talk was titled: Towards experiments with momentum entangled He* atom pairs. He described the process of creating a metastable Helium source and then the slowing and cooling of this beam to create a BEC. He then talked about how to create momentum entangled atom pairs and his lab’s single-atom detector (which costs something on the order of €50k) for reconstructing 3D momentum space. As usual, the physics at these specialized talks is sometimes too advanced for me to get everything, but I always enjoy the experience and find discussions about quantum entanglement very fascinating. After his talk, Michael came into the LTC for a brief tour.
We also started looking over student abstracts today. As always, these types of things take a lot of editing and re-editing to make sure the wording is just right for what we’re trying to convey. It can even take several hours sometimes just to formulate a suitable title! Tomorrow we’ll do some one-on-one (or rather, two-on-one) revising with the students.
Wednesday 30 July 2014
This morning we skipped our daily talks so that the students could focus on preparing for the pizza lunch. John and I spent some time discussing with Ikaasa the best way to plot the inverse wavelengths of the minima (in her parallel polarizers 10-layer filter setup) as a function of “m” (odd integer multiples of pi) to signify how the filter acts as a half-wave plate for these wavelengths of light.
Our pizza lunch this week featured student research updates in the form of short powerpoint presentations. We invited a much smaller group than the previous few weeks so that the meeting could focus more on discussions about our individual student projects. When I get a chance, I’m going to make a link from the calendar page with descriptions of each student’s progress.
This afternoon I worked mostly with Ikaasa and Jonathan to help them figure out some issues with graphs they were trying to make - (for Ikaasa it was normalizing transmission data of light through a 10-layer filter and crossed polarizers, for Jonathan it was fitting the Airy beam deflection theory to his data). By the end of the day, both were resolved! (Marty and Ikaasa realized that something was fishy about her oscillating input light and fixed the graph after retaking the data, and Jonathan and I realized that being off in his beam FWHM measurement by two pixels was causing the theoretical curve to look radically different than his data, since there’s a 1/w^3 dependence).
We received part of the Thorlabs order (the CMOS is backordered at the moment), however it turns out that the filter we ordered doesn’t actually block a 632 nm beam. We ordered the short pass 650 nm cutoff - after doing some research into the product specifications, we decided to exchange this for a short pass 600 nm cutoff (FES0600). Since Thorlabs’ online RMA form generator wasn’t working, I did a “Live Chat” with a sales representative and they suggested that I email the RMA department directly. Hopefully we can take care of this as quickly as possible!
Tuesday 29 July 2014
For our morning discussion, Andrea talked about the derivation for the intensity of sound in decibels as a way to quantify loudness. This equation takes into account the sensitivity of the ear, since we have a certain threshold of hearing. The second thing that she did was go through a calculation she did earlier with John - which compares the theoretical wavelength of the sound wave in the spherical flask of her sonoluminescence project with the radius of the flask. However, we still need to better understand what the standing waves look like in a spherical cavity.
This paper that looked at basketballs as spherical acoustic cavities,
Russell
2009, modeled some of the pressure nodal surfaces for the lowest
modes. But John pointed out that acoustic waves in a fluid will be
different than those in air. These
In the conference room, we had a group brainstorm about abstracts in
which each student listed some key words and phrases that should be
included and thought about possible titles to capture the overall concept
of their projects.
Ikaasa:
birefringence, polarization, polymer (i.e. cellophane, not all
cellophane works), Jones calculus (and possibly Law of Malus derivation),
retardance - (half and quarter) wave plates, these methods can be used to
create a tunable bandpass filter, spectrometer (with specific model
number, results with it), excel spreadsheet, mathematica, evaluated simple
Jones matrices by hand.
Understanding/Examining birefringent properties of cellophane; other
good verbs: Applying, Measuring, Modeling, Simulating, Studying
Jonathan:
Airy beam (generating and properties of, history), propagation
invariant, compared to straight line propagation, accelerating motion,
diffraction, cylinder lenses (utilized those found on hand in lab),
Fourier optics, cubic phase profile, coma aberration, compare to other
methods - e.g. SLM, equipment, description of setup, light source, camera
Generating/Creating 1D Airy beams with cylindrical lenses (i.e. simple
optical elements)
Alex:
optical vortex, optical tweezers, orbital angular momentum, gradient -
scattering forces, torque, spiral phase plate, inverted microscope,
particles that were trapped (yeast, latex spheres, copper oxide),
topological charge, video camera (model number)
Demonstrating the transfer of optical angular momentum to particles
trapped in optical tweezers; other verbs: Quantifying, Analyzing, Studying
Andrea:
modes, acoustics, frequencies, description of single bubble
sonoluminescence, spherical flask, resonance Right after lunch before most of the students returned a tour group
came through with incoming freshman for the CSTEP
program - Collegiate Science and Technology Entry Program - hoping to
speak with Hal. We couldn’t find him but I gave them a brief tour of the
LTC anyway - and since Alex was the only student back from lunch, he gave
them an explanation of his tweezers setup. I think they’ll be returning
with more students another day!
We made another Thorlabs purchase today. First we decided to buy a dielectric
filter - FES0650 which is short pass with a 650nm wavelength cutoff -
to attenuate the beam incident on the camera. We then spent some time
comparing CCD
cameras to the
CMOS we bought last time, and after considering prices and the uses in
our lab, we decided to buy another compact CMOS. We’ll also buy an
external C-Mount to internal SM1 (SM1A9) to put the filter on the camera -
after doing a little bit of research about the difference between camera
C-mounts and CS-mounts, this source
proved to be useful. The difference is in the flange focal
distance - which is the distance from the mounting flange (the metal
ring on the camera and the rear of the lens) to the film plane - shorter
for CS-mounts (12.5 mm, vs. 17.526mm for C-mounts).
Also this afternoon I helped Alex get together a photodetector for beam
profiling and tried to help Ikaasa normalize and graph her data. Overall,
today turned out to be another great productive day!
This morning Jonathan started us off with a short lesson on Fourier
series and the Fourier transform. The math is a little advanced, but the
important difference to understand between these two is that a Fourier
series is used when a periodic wave can be decomposed into discreet
frequencies, whereas a Fourier transform is used when a non-periodic wave
(T => infinity) is decomposed into a spread of possible frequencies (so
there is a certain level of uncertainty). He then talked about Fourier
optics and how one can find the Fourier transform of an object or
aperture.
I worked a little bit on my webpage today - uploaded and resized a
bunch of photos (using the convert command: convert oldfilename.jpg
-resize widthxheight newfilename.jpg) and then used these to update
the pizza lunch page for Wednesday
23 July and the 2014
calendar page.
Finally today I took care of the property control form for the
spectrometer - sent it through campus mail from the physics office. Later
in the day I took a walk down to the Stony Brook Foundation office to
submit student support forms.
I spent some time with Ikaasa talking about how she can normalize her
data if different sets were collected using different integration times.
(She had to use a shorter integration time to attenuate the signal
produced by the incident light, since it was otherwise flooding the
spectrometer and flatlining in the data). We came to the understanding
that if the integration time was (for example) 8 times longer than the
previous sampling, we could divide that data by 8 to account for this.
(This is a good informational
source about spectrometers that Ikaasa found.
We then had a discussion about normalizing the data and taking into
account the incident light, transmission through each polarizer, and the
differing integration times. John is under the impression, which makes
sense, that once the data is normalized (dividing output by the input),
the filter’s transmission peaks should all be about the same height.
Simons abstracts are due a week from today, and the posters not long
after that! The summer is really flying by.
Alex started us off with a continuation of the double slit intensity
derivation. He did a good job of going through the simplifications and
trig identities needed to reduce the intensity equation down to its
4cos^2[ ] form. Then we actually derived the path length difference in
two different ways - the first in which we assumed the lines connecting a
point from each slit to the same point on the screen were approximately
parallel near the slits, and the second used pythagorean theorem and the
binomial approximation. Both arrived at the same answer in the end - so
it really came down to a matter of where you make your approximations.
I continued to have individual discussions with students about their
projects. It’s challenging trying to keep track of everyone’s research -
to be able to have an in-depth conversation with a student about their
work and to check their understanding, the mentor first has to have a good
understanding of what’s involved. So I’ve been spending a lot of time
reading up on the theory behind each person’s work. It was one thing
being a student researcher and diving into my own project, but now as a
mentor, I have to dive into four different ones!
A couple of odds and ends from the day - (1) We received the package
with the adaptor threads already. They arrived this morning even though we
only paid for “next-day PM” shipping. Thorlabs is pretty fast - and they
sent lab snacks this time! (2) Since we’ll be supporting a couple of
Eden’s students, I helped take care of the necessary paperwork, and we’ll
also setup webpages for them soon. (3) I finally worked on (and
completed) the Responsible Conduct of Research RCR through the CITI program (Collaborative
Institutional Training Initative). There were short modules and quizzes
about research misconduct, data management, authorship, peer review,
mentoring, conflicts of interest, and collaborative research.
At the end of the day, I tried to help Ikaasa figure out a Jones
calculus problem in the textbook that she had been stumped by. The tricky
part was figuring out the Jones matrix for a half wave plate with it’s
slow axis oriented at 45 degrees. I didn’t have time to work out the
derivation yet, but this source talks
about the general matrix form for a wave plate with it’s slow axis
oriented at a certain angle and the specific form for a HWP with a 45
degree slow axis.
Today our morning discussion featured a short lesson about Jones
calculus from Ikaasa. Jones calculus is used to mathematically describe
the polarization of light as it emerges from an optical element (such as
polarizers, wave plates, birefringent materials, etc.). Optical elements
are represented as matrices, and the incident light’s polarization is
represented as a vector. The product of these will tell you the
polarization of light that gets transmitted. Ikaasa gave a nice
introduction to the representation of a wave’s electric field in matrix
form and then walked us through a derivation for the Jones vector of
circularly polarized light.
We had a group meeting in the conference room to discuss student
research updates. Libby has built her basic Michelson interferometer
setup with collinear paths, however she needs to make the path lengths
equal. Eventually she’ll replace the laser with an LED and one of the
mirrors with a touch surface. Jon has been able to create an Airy-Like
beam, however he’ll need to account for the room light flooding the camera
and to possibly write to the author with other questions about the
experiment. Alex has been able to get the tweezers setup up and running
and actually trap a particle; he’ll need to deal with some issues with
light scattering off the particles and look into the use of the phase
plate.
Hal took the annual LTC and AMO group photo outside on the steps of the
earth and space sciences building. We took an LTC group photo as
well.
At our pizza lunch today, Eden
Figueroa and his students gave a talk about the concepts of quantum
information processing and quantum information technology. Quantum
information is a very interesting new field that makes use of quantum
entanglement and superposition
states. Their lab
is working to interface single-photons and rubidium atoms through the use
of coherent laser control. After an introduction by Eden, Mehdi Namazi
talked about building a quantum memory for quits, Bertus Jordaan gave a
talk about the production of single-photons tuned to atomic transitions,
Zakary talked about making single-photons interact, and finally undergrads
Chris Ianzano and Eric Fackelman discussed their work in Characterizing
high-finesse optical cavities. We then had a short tour of their
(relatively new) lab.
As far as paperwork, today I prepared more documentation for
reimbursement under the supplies, postage and shipping, and printing
categories. I also looked into buying adaptor threads for the Laser Diode
and SLM that we bought from the UK (which have metric threads). There’s
the AP25E6M
(external M6 to external 1/4”-20) and the AS25E6M
(external M6 to internal 1/4”-20). We chose next-day FedEx shipping, so
hopefully they’ll be here by tomorrow afternoon!
Our morning discussion featured a derivation of the single slit minima
equation, led by Libby. She did a good job of explaining all of the
details, starting from the diagram, creating an equation for the incident
wave amplitude, integrating this over the length of the slit, squaring
this to get the equation for intensity, and then solving for the zeros of
the function - i.e. when we have minima in the diffraction pattern. I
wrote this up in my lab notebook. The plan for tomorrow is to have Ikaasa
give an introduction to Jones calculus.
Again I worked with individual students, helping them with little
things here and there with their projects. We also had a long talk with
Andrea about possible projects - first we reviewed the two articles she
had been focusing on - the Amateur
Scientist article about Hele-Shaw cells (which looked at qualitatively
studying the behavior and interactions of bubbles in a fluid) and the
study of liquid-liquid interfaces article
(which quantitatively looked at how the interface between two fluids
changes with the passage of a bubble). We also did a couple of Am. J.
Phys. searches and found a couple of interesting sonoluminescence articles
- one about creating a single sonoluminescent bubble (Seeley 1998) and the other
about using a strobed LED to measure the bubble radius (Seeley 1999). Then we
checked out the sonoluminescence apparatus created by TeachSpin
- they have a great brochure
that has information about the physics behind sonoluminescence and various
experiments that can be conducted to understand resonance, etc. This then
led us to do a little research into hydrophones and how
it’s possible to create
your own. Finally, we talked about the idea of studying electrical
resonance by means of a classical RLC circuit, but we weren’t able to
locate am Am. J. Phys. article we had found another time… After I did some
sleuthing and found it using the original search terms (acoustic AND
modes) - Cafarelli 2012.
For our spectrometer, I filled out the equipment inventory control form
that was included in our package (Stony Brook took care of assigning a
number and labeling our device before we received it), which we’ll have to
return to the Property
Control Office. Then I did a little more organizing with the receipts
that need to be reported to SBF and be reimbursed. I collected and
documented all of the “Entertainment” charges from Summer 2013 (i.e. all
of our pizza lunches and other special meals with LTC students and
guests). All expenses have been written up on a spreadsheet and
photocopies will be made of the receipts tomorrow.
I also finally updated my webpage with the total power output of the
Sun calculation, here.
Today we started out with a brief derivation of the equation for the
radius of the first minimum in the Airy diffraction pattern. Though I’ve
been asking the question since last week, the students were still stumped
by the factor of 1.22. I led them through the derivation part of the way
and then let them finish it off. (The details are on my “Resolving two
point sources of light” page).
We also talked about the possibility of the students doing mini lessons
the next couple of mornings about different optics topics they’ve been
reading about.
It’s great that most of the students have gotten started with some
hands-on work - I spent most of the day running between them to help find
optical components, pick up the spectrometer package, set up equipment,
have discussions, talk with Marty, get the desktop running, clean optics,
etc … Everyone seems to basically be on track! I think it’s been a
productive day.
I finally also typed up our calculation of the Earth’s velocity as it
orbits the Sun - the details are here.
At the end of the day, I spent some time reading through an article
that Andrea was interested in - “Passage
of a Gas Bubble through a Liquid-Liquid Interface” Kemiha 2007. In
order to better understand it, I had to look up some things (such as
surface vs. interfacial tension), and a good resource is this MIT page for
the Non-Newtonian
Fluid Dynamics research group).
This morning during our daily discussion, we first reviewed derivatives
and then talked about indefinite and definite integrals. For indefinite
integrals, we discussed the mathematical definition and how we “undo” what
happens when we take the derivative - called the “antiderivative.” We
then talked about definite integrals, and how these represent the
difference between the antiderivative evaluated at two limits - also known
as “the area under the curve” between these two points. We used an
example with a mass on a spring and tried to calculate the work done from
pulling the spring a certain distance x. This is a fairly simple
calculation, since the graph of the force is just a straight line, but
it’s a good example for deriving the definite integral by means of a
Riemann sum with an infinite number of rectangles.
I worked on my webpage a little and wrote up the Golden Ratio
derivation (and its connection to the Fibonacci sequence) that we went
over together last week, with some extra links for more information. The
page for this can be found here.
I read through more of the Papazoglou (2010) article about tunable AIry
beams that Jon is using for his research and realized that the lens setup
isn’t as complicated as I had originally thought - well it will take some
careful calculations, but the apparatus to create a 1D cubic phase
modulation is simply two lenses rotated and displaced respectively along
the longitudinal and transverse axes. By imparting a cubic phase on a
Gaussian beam, the Fourier transform of this leads to an Airy beam. While
Jon was tinkering with a couple of cylindrical lenses, John pointed out an
interesting phenomenon in which the net effect of a converging and
diverging lens placed in the right configuration is a converging lens.
This is similar to alternating-gradient
focusing used in accelerator physics.
John then directed the students part-way through the intensity of light
from two slits derivation. It’s a great derivation that includes
pythagorean theorem, complex numbers, and the binomial expansion. The
goal is to derive the equation for the intensity on the screen at an
arbitrary point P by adding the amplitudes of waves coming from each slit
and then (squaring this for the intensity). At the board we also talked
briefly about De Moivre’s
theorem and all the roots that the fourth root of 1 has (4: 1, -1, i,
-i), etc.
After meeting and talking briefly with Richard Lefferts from the
We’ve now finished our third week - time is really flying. But most of
the student are now underway with some hands-on work, which is great!
Piano, piano as they would say in Italy.
We started off the morning with a review activity. I had each student
make a its of 8-10 things that they understand well - equations and/or
concepts that we’ve talked about together or other optics topics that
they’ve been researching on their own. Then they passed their lists to
the student on the right and I had them circle the things on the list they
received that they didn’t understand. The original lists were passed back
to the original students and we made a master list on the board of the
topics that were circled. Then, each student gave a mini lesson on the
topics that were circled on his/her list. Jon talked about the binomial
approximation and lens aberrations, Ikaasa talked about birefringence,
Andrea talked about AOMs and TAG lenses, Libby talked about Poisson’s
spot, CCD/CMOS, oximetry and integrating spheres, and Alex talked about
Euler’s formula and lenses used for burning (like what we did outside on
the first day).
Then I set the students to work on a mini project exploring diffraction
through circular, triangular, and square apertures. With the circular
one, they had to use the diffraction pattern to calculate the wavelength
of the laser (they got 615 nm - pretty good!). They used two different
apertures (200 microns and 500 microns) and projected the pattern of the
larger first on the door and then to the far wall outside the lab. I also
asked them to figure out and be able to explain where the factor of 1.22
comes from in the Rayleigh criterion equation.
David from the Stony Brook Foundation called - he said that there are
two possible reasons why a requisition number wasn’t generated on the
form, either (1) that when we put the account number, we don’t need a dash
in there (though on past forms, it was listed with the dash and it still
worked), or (2) that there’s some issue with it when used with Safari on a
Mac, and that it would work in Internet Explorer. Either way, we’ve
handed in the forms and the spectrometer purchase should be taken care of
by the SBF today.
Ludwig Krinner, a grad student working with Dominik, gave his oral exam
this afternoon on the topic “A Quantum Zeno’s Paradox.” Though the physics
was complicated, it was an interesting experience to witness. He gave a
talk about past research done on this topic by other research groups and
then talked about what his lab is currently doing. It was good that we
had Dominik’s talk yesterday, because it helped me understand parts of
Ludwig’s presentation. As far as Zeno’s paradox - I think I understand it
better in the quantum sense
rather than the classical
examples he described, or at least I can wrap my mind around it better
in the quantum sense. Here, they’re inhibiting the quantum evolution of a
particle by continually measuring it - since it’s continually observed, it
never decays.
In the morning, we skipped our daily discussion so that the students
could work more on their project proposal presentations. I talked
individually with Jon and Ikaasa about their projects - regarding the idea
of spatial frequencies/Fourier optics and birefringent filter theory
respectively. Then we had our group meeting at 11 am and each student
presented their ideas. Libby is most interested in pursuing white light
interferometry for use in characterizing rough surfaces, Andrea talked
about the Hele-Shaw cell and acousto optic modulators, Ikaasa is
interested in doing a project based on the interference birefringent
filter article, Jon would like either to follow the article that described
creating Airy beams from lens aberrations or to create other exotic beam
modes by means of our SLM, and Alex is interested in quantifying the
transfer of orbital angular momentum from an optical vortex to a particle
or analyzing optical vortices in some other way.
At our pizza lunch meeting, Dominik Schneble gave a
great talk on Ultracold Atoms and how his BEC lab worked. Though Hal had
talked a little bit about this stuff last week, it was interesting hearing
it from a different physicist’s perspective. Dominik talked about Bose
Einstein Condensation, how the wave properties of matter are “hidden” at
room temperature (the relationship between the de Broglie wavelength and
temperature), the physics of laser cooling (by means of the Doppler
effect) and recoil limit (there’s always that final photon that must be
emitted so the atoms never have exactly v=0), magneto optical trapping
(with two coils that create a point of zero B-field), evaporative cooling
(by repeatedly removing hot atoms and waiting for the system to
rethermalize), and finally imaging BECs by means of their shadow (with an
absorption technique).
Afterwards, he gave us a tour of his lab - pretty intense stuff! He
said that they leave the laser and machinery running most of the time and
that it takes sometimes the whole day just to realign the setup -
sometimes students will stay until the wee hours of the morning to
complete an experiment or do data collection, because if they leave the
apparatus and come back the next day, it won’t still be aligned.
Back in our lab, I talked with Jon a little bit more about spatial
frequencies and filtering with a 4-f setup. We then did a mini demo of
light diffracting through a circular aperture to create the Airy pattern.
This was at the end of the day, so there really wasn’t time for collecting
any measurements etc, but it’ll be a good hands-on activity for the
students tomorrow!
Also this afternoon, I filled out a Stony Brook Foundation Requisition
form (couldn’t get a requisition number to generate! even with the
tricks..) for the
Thorlabs
spectrometer we’re going to buy. We’ll submit this form, with
the company’s W-9 (which I had called them about), and a printout of the
online catalogue page. This will be great for Ikaasa’s project and
probably future LTC work as well.
Today the topic of our morning discussion was derivatives. A couple of
the students had taken calculus and had some idea of what they are, but
the others hadn’t. We first talked about what the definition of the
derivative is in words (i.e. the rate of change of the function at a
point; the slope of a tangent line at that point) and then in mathematical
terms (i.e. equation for f’(x) in terms of the function and some small
change in x, with the limit as Δx goes to zero, etc). Then we went
through the derivation, starting with the slope of the line and showing
how we can find the quotient difference of the function between x and a
Δx, which tells how the function is changing on average. With a very,
very, very small Δx, we are able to understand how the function is
instantaneously changing at a point. We talked about some instances of a
zero derivative and an undefined derivative, and the impact (or rather
lack there of!) of adding a constant to the function, and then we
proceeded to use the definition to find the derivative of a simple
quadratic and the sine function.
We then had another group meeting in the conference room to discuss
areas of interest and further hone in on possible projects.
With Libby we now talked about white light interferometry
and Doug’s project. From
her interest in Ronchi Testers, we looked at Allison’s project on
Talbot images, which then led us to a paper by Michael Berry, Quantum
carpets, carpets of light - note, all of his papers can be found here.
Then we looked at Alex is still interested in optical vortices used for tweezing, and how
rotating particles (to study the shape of their orbits) would be easier to
see, rather than spinning the particles. The Padgett
group at the University of Glasgow is a good place to search for
resources.
Jon has taken an interest to the Phys Rev article on creating Airy
beams (Papazoglou 2010), and in general he’s still interested in creating
beam modes with an SLM (which Rachel explored this past
Spring with our low-cost SLM).
Looking around the lab for the sonoluminescence setup, we stumbled upon
some other cool things, including Jacob’s spatially-varying
wave plates, a bunch of QEX quantum electronics lab notebooks, and
finally the sonoluminescence setup! All neatly put together in a (TV) box
with a couple of articles (2002, 2007) about the skepticism surrounding
its means for creating fusion.
I briefly looked into buying a compact
CCD spectrometer from Thor Labs, which would be useful for Ikaasa’s
project. We would want to get the CCS100 (universal/imperial), which has
a wavelength range of 350 to 700 nm, a 0.5 nm spectral resolution, and it
costs $1,950. (Note - it’s on pg. 1604 in the big Thor Labs catalogue)
Tomorrow morning we’ll do project-proposal presentations at 11am with
Marty - in which the students will talk about the research project they’d
like to conduct. The presentations should include some basic information
from the paper(s) where they got the idea from, as well as relevant
diagrams etc. Also, it should have a detailed list of all of the physical
things that need to be done and physics topics that need to be understood.
I read through a paper that Ikaasa seems
interested in doing her project on - creating a birefringent filter using
layers of scotch tape (Velasquez 2004), and then did some research into Jones calculus
using this source.
Hecht’s optics textbook will also be a good source.
In our morning meeting, I discussed the idea of the Rayleigh Criterion
with the students and had them estimate the distance from which you could
resolve the headlights of a truck as two separate light sources (given a
long, straight road with no obstructions, and a person with perfect
vision). Our calculations revealed that it’d be possible at about 16 km
away from the truck. I put together a summary of our discussion here.
After we all moved into the conference room for another group
brainstorm meeting. We discussed how a good project will be a mix of
scholarship and hands-on work. A great place to look for possible project
ideas is in the American Journal of Physics - these articles often
describe tutorials for projects that can be completed in an undergraduate
lab. They can provide a great jumping off point for a more original
project, or they can simply help a student understand, simulate,
demonstrate, etc. optics phenomena.
We used AIP
Scitation to do our AJP searches.
Libby is interested in the application of optics to biology and
medical instruments, as well as describing nature with math.
AJP Search: optics AND
biology, oximeter We found an interesting article about
photoacoustic imaging (Leboulluec 2013).
Alex is interested in optical vortices, specifically the light and
matter interaction (i.e. being able to rotate a particle with the beam).
AJP Search: optical
AND
vortex I also suggested he look over Jonathan
Preston’s webpage and Singular Optics
map. In general that’s a good way to organize your ideas about a field
of research - looking at all of the prominent people, topics, papers
written, etc.
Jon is interested in different beam modes, such as Bessel, Airy and
Ince-Guassian beams.
Andrea is interested in the TAG lens and possibly other acoustics
applications.
AJP Search: acoustic
AND modes, acoustic AND lens We found a couple of interesting papers - one was about measuring the
speed of sound in a fluid by light diffraction (Diego 2002) and the other was about using Mie
scattering to determine particle size (Weiner 2001).
Ikaasa is interested in fiber optics, the fiber Bragg grating, and
possibly creating a noninvasive pressure sensor using acousto-optics.
AJP Search: We also talked about Molly’s work with
Mueller matrices to characterize polarize light and Mike’s project in
photorefractive optics (his abstract can be found here
on page 8). After we did some further searching individually. With Jon we looked
at how past LTC projects sprouted from mistakes or curiosities, (for
example Max’s project
imaging intensity from the double-slit interference pattern and Will’s project in
understanding the Fresnel diffractions patterns of a circular aperture.
With Ikaasa we looked up an AJP article in which
tunable filters were created using scotch tape (Velasquez 2005), and other
possibilities with Optical Coherence Tomography, as Jon Wu had studied.
We started off the morning with a calculation - how fast is the earth
traveling around the sun? This isn’t too trivial to figure out, so I made
the students calculate the final number in both meters per second and
kilometers per hour. What I should have also done, was have them then
convert it to miles per hour! I guess I’ve just gotten too used to using
metric units for everything in Italy :) I’m in the middle of creating
a page with some of the details of the calculation, as well as the other
calculations we’ve done together.
Today there was an AMO seminar given by Dr. Yev Lushtak from SAES Getters USA about “Sorption
Mechanisms and Pumping Characteristics of Non-Evaporable Getter (NEG)
Pumps.” A getter
is a device that removes molecules from an evacuated space by sorbing
active atmospheric gases. Non-evaporative getters are made of porous
reactive alloys and are very effective pumping devices. This company
created a number of different compact NEG models, some that combine the
NEG with a sputter ion
pump (SIP) to take care of non-getterable gases. His presentation was
a little bit of a sales pitch for his company’s NEXTorr, but it was
interesting to learn about the sorption mechanisms of NEG materials. The
company is also based out of Linate, Italy!
In the afternoon we took care of some paperwork and finished the
reimbursement forms for the 2013 Lab Equipment purchases. On our way to
the SBF to drop everything off, we stopped by the closing ceremony for the
Physics
Summer Camp and had a talk with the program director, Dr. Gillian
Winters. This camp is a one week program meant to introduce high school
students to physics by means of hands-on activities. It sounds like a
great opportunity for students who have a strong math and science
background, but haven’t necessarily taken physics.
Today I started by talking briefly with the students about Enrico Fermi and what
“Fermi Problems” are. We then did an estimation problem together about
figuring out the focal length used by a camera to take a certain image. I
got the idea to do a question like this from this article, Optical
Insights into Renaissance Art (which I’ll mention more about soon).
The image that I found here
has the actual lens focal length listed, so that we were able to check our
work at the end. The important thing that I wanted the students to
understand was that this problem had nothing to do with the physical size
of the photo, but rather estimating the distances of things in the
photo. I guided the students through a couple of steps, but they were
eventually able to understand how to handle estimation calculations.
I spent some time afterwards putting together a page
with the details of this estimation.
We then had a very productive group meeting in the conference room, in
which we went through each student’s ideas, looked through past LTC
projects, and gave general feedback or suggestions for further research.
Libby has
been interested in the optical properties of skin. She should check out
Foo’s project on using
an electro-optical sensor to measure pulse rate. Libby’s also interested
in zone plates, and we talked about Pradyoth’s project
with linear zone plates.
Alex is
interested in optical vortices, so John directed him to Azure’s work, Les Allen
and Miles Padgett’s book on
the orbital angular momentum of light, and a (autographed!) book that Hal
has with a collection of Padgett’s papers.
Jon has been
looking into Optical Coherence Tomography (OCT), so he should look at
Andrea has
been reading a lot into supercooling and its possible application to
sonoluminescence (though this would require a very powerful pulsed laser,
which we don’t have in the lab).
Ikaasa, in
addition to her research into laser cooling, is interested in
acousto-optics and its application to medical imaging. John suggested she
talk to Marty, since he’s an expert on AOM etc. Back in the lab, we showed the students Kathy’s laser tweezers
setup as well as the blue Argon laser. We also showed them what happens
when the laser goes through a pair of the diffracting grating glasses (the
2D ones make a pretty cool design!) and when it goes through your hand.
We did a little more paperwork and walked over to the Stony Brook
Foundation office in Admin for help in understanding the proper way to
fill out reimbursement requests. We can continue to use the Cash Voucher,
but the purchases must be divided based on the various categories SBF has
set up. Also, for account balance information, purchases, etc, you can
log in to E-RAS (Electronic
Record of Authorized Signatures) for a snapshot of the monthly reports.
SBU
Reporting can be used to check day-to-day reports. Information for
obtaining access to this system can be found here.
David (24469) in the Stony Brook Foundation office suggested we get in
contact with Michael Danielson if we need further assistance.
I then helped John sort through some old receipts and tried to make an
organized system. I labelled a number of small envelopes with SBF’s
category names and descriptions and made sure to sort the receipts
accordingly. There is of course a miscellaneous “Other” envelope (where I
placed Azure’s “SORT” post-it note on the front), for those receipts which
don’t fall into any of these. All the envelopes and papers related to
this are in a nice neat box for the moment.
Today was chock-full of great talks and discussions! We started in the
morning with a review of yesterday’s overview of some important topics in
preparation for Hal’s discussion about laser cooling. These included
harmonic motion (with a quick look at the differential equation and
solution for motion of a mass on a spring), resonance and the Lorentz
function that describes the oscillation intensity, doppler shift (and how
an atom moving towards the laser light would see a higher frequency), the
k’s (spring constant, Boltzmann constant, and wavenumber), the energy
levels in an atom (describing energy and momentum of a photon in terms of
h-bar), and how the temperature of something is a measure of the random
internal kinetic energy of its atoms (and not! related to the overall
velocity of the object. i.e. a baseball wouldn’t get hot just from being
thrown super fast).
Hal’s master class with Ikaasa was a great learning experience. He
began with a general introduction to some key concepts about temperature
and absolute zero, the relationship between pressure, volume and
temperature in PV=nRT (and how your tires (fixed volume) don’t go flat in
the winter, even though the temperature drops it’s on the scale of a few
degrees Celsius, so there’s only a very slight decrease in pressure),
discrete energy levels, the doppler shift, and the scale of accuracy
that is needed to match the resonant frequency of an atom (one part in a
billion! like the leg of a small bug compared to the distance from Stony
Brook to midtown Manhattan).
In laser cooling, a moving atom that sees its resonant frequency will
absorb the light, also absorbing some momentum. Through spontaneous
emission, it reemits the energy and loses momentum. This process
continues until collectively the atoms have slowed down, and therefore
have been cooled. Six lasers are directed at each other to create a zone
of optical molasses. In this region, there will be a force opposing the
atom’s motion in any direction. Once the atom is stopped, the forces from
the laser cancel, there’s zero kinetic energy, and therefore the
temperature should be absolute zero. However, it’s impossible for an
ensemble to reach absolute zero, because on the collective average of the
velocity of the atoms won’t be zero.
We had our pizza lunch (a big group this time! we went through about
5.5 of 6 pizzas) at the usual time and place. I’ve added the abstracts here.
The first presenter was Leighton Zhao, a Simons fellow working with Phil
Allen. He discussed his work on analyzing the normal modes of a seven
particle system. He was given trajectory data from an experiment
conducted by Peter Koch in which seven steel balls (magnetized and
confined within a circular steel wall) were jostled in one direction.
Leighton described his work in writing programs to fit the data and better
understand the behavior of the system.
Taylor Esformes, a Stony Brook masters student working in an off-campus
lab, described hyperspectral imaging (an image created by a stack of
monochromatic images in which each layer represents spectra from a
different wavenumber) and some of its applications. There are two
different methods of collecting data for these images - (1) “push-broom”
method, in which data is collected for one strip of pixels at a time; in
the air at an altitude of 25,000 m, a pixel would be 1 square meter. (2)
filter wheel, a multispectral device that will map an entire pixel array
for one wavenumber at a time. Some of the agricultural applications were
that by examining the detailed information about spectral emissions of
fields, one could check the health of plants, the fertility of soil, water
content, etc. in a quick and noninvasive manner. Taylor is working to
make an inexpensive commercial device that would make use of the filter
wheel technique.
Marty then gave a brief overview and demonstration of a BEC imaging
project. The goal is to image Rubidium atoms that are contained in a
vacuum cell with glass walls. They’re using a finely tuned laser to do
so, however in the image there are extra interference fringes that show up
from dust on the glass because the laser has high spatial coherence. To
limit this, they need to lower the spatial coherence of the beam. Marty
says that using an engineered diffuser (similar to ground glass) and a
5-meter multimode fiber could solve the problem. Furthermore, to deal
with the speckle in the beam after it goes through the diffuser, he
proposes using an acousto-optic modulator to continually deflect the beam
through it (this would be better than any sort of mechanical movement of
the diffuser, which could cause extra vibrations on their work table).
After the diffuser, the beam will need to be coupled through a multimode
fiber and at the output have its spatial coherence measured. He finished
by showing us how sending a laser pointer through the diffuser creates a
large square pattern.
In the afternoon, we did a little bit of organizing in the LTC office -
sorting and filing papers etc. I also updated the calendar
2014 page with pictures from the welcome lunch and first day
festivities.
We started off the morning with brief group meeting to discuss the
upcoming two pizza lunches and the possibility of doing mini lessons. I
asked the students to start thinking about some optics topic(s) that
they’ve either stumbled upon in their literature research or have just
found to be interesting. I think these mini lessons would be best
presented in the form of a whiteboard discussion, rather than a
powerpoint, because this encourages more involvement from the other
students. I also encouraged the students to read each other’s online
journals, to get an idea about what everyone else is reading about. They
might also find something new that interests them or help out if there was
something another student didn’t understand.
The idea for doing a Journal Club is still up for discussion whether,
but I’ve been thinking that it might work best once the students start
focusing on their actual projects. Each student will choose a journal
article and (possibly) create a mini presentation about it - reviewing the
main idea, key points and findings (important equations, graphs, etc), and
explain how this aids in his/her own research. The other students should
read the abstract and (at least) skim the rest of the article to have a
general idea of what it’s about. We can set a few dates and have 2-3
students present per day.
We sat down for a while with Phil Allen’s student, Leighton Zhao, to
review his presentation for tomorrow’s pizza lunch and check on how we can
connect his laptop with the projector. The pizza lunch tomorrow will
feature two presentations (from Leighton Zhao and Taylor Esformes), a
short talk by Marty about a project in the BEC lab that he’s interested in
possibly pursuing with an LTC student, and general updates from the other
students about what they’ve been researching.
In the afternoon, John and I sat in on what became a preview for Ikaasa
and Hal’s master class. They discussed a little bit about her
understanding of laser cooling and also the logistics of how this “class”
would run - John envisioned a dialogue between Hal and Ikaasa that the
others could listen in on. A couple of miscellaneous interesting things
that Hal mentioned: the importance of understanding the role of entropy in
laser cooling and just in general how sacred the laws of thermodynamics
are, the general uncertainty across the internet of the spelling of the Lorentz
Gauge (which he says they’ve decided should have the “t”!), and in the
spirit of estimation problems, he described how he’s able to understand
how much a million is - say you have a million pennies, all laid down next
to each other, if you’re far enough away to be able to see all of them,
you’re too far to be able to resolve a single one.
Back in the lab, we huddled around a computer and reviewed some topics
that would be important for the students to understand for tomorrow’s
discussion, namely the doppler shift, harmonic motion, resonance,
Q-factor, temperature and kinetic energy, and the energy and momentum of
light. Ikaasa also had found a very helpful video in which a
very enthusiastic researcher at the University of Nottingham describes
how it’s possible to use laser light to cool atoms.
This morning I helped the students through a simple derivation of the
golden ratio and showed its geometric connection to the Fibonacci
sequence. I’ll include a write up on some sort of derivation page soon to
keep track of these things… I then updated the lab’s calendar (note to
future LTC-ers, keep this calendar current, erase and rewrite often - my
notes from last summer were still up and it was near impossible to erase
the marker!) with the remaining events for the summer. We’ve got a little
more than 5 weeks, and a lot to get done! In the morning John and I also
made a trip to the administration building and submitted all of the
stipend paperwork to the Stony Brook Foundation.
Jonathan had a couple of questions about the journals he’s been
reading,
so
I’ve been trying to catch up a little on laser vibrometetry and the
articles he’s been looking at. Laser vibrometers detect surface
vibrations without having to be in contact with the surface. Jon linked
to an article in his webpage (
Wang
2009) about using a photo-EMF pulsed laser vibrometer with high
sensitivity and more accuracy than a conventional laser vibrometer based
on optical interferometers. (He also included a link to Prislan
2008, which describes laser vibrometry in general). Speckle
in
light beams makes readings of surface vibration measurements from optical
interferometers inaccurate (i.e. there will be sudden drop-offs from the
speckle, unrelated to vibrations). This is discussed in Numerical
simulation of speckle noise in laser vibrometry, Rothberg 2006.
This seems to be an early article that talks about the photo-EMF
detection technique (cited by Wang 2009), Measuring
vibration amplitudes in the picometer range using moving light gratings in
photoconductive GaAs:Cr, (Stepanov 1990). It might also be useful
to look up what laser Doppler anemometry (LDA) is, which is where laser
vibrometry developed, (as mentioned by Rotheberg 2006). There’s also this
article, Frequency
detector using photo-EMF effect (Lara 2006) which discusses a
novel method for measuring an unknown frequency using a photo-EMF
detector, also giving a short explanation about what this effect is.
They use two phase-modulated interference patterns incident on a device
that will generate a photo-EMF signal - one pattern is phase modulated by
a known frequency and amplitude while the other is modulated by a
vibrating object of unknown frequency and amplitude.
In trying to understand this photo-EMF sensor, I looked up photoelectric
devices. I’ll need to look into these things a bit further, but here
are some brief notes - There are two types: a) photoelectric tube (aka
phototube): vacuum-tube, photoemission, generates electric current, and b)
photoelectric cell (aka photocell): solid-state, internal photoelectric
effect, generates photo-emf. Photoelectric devices have 4 main
distinguishing characteristics:
luminous sensitivity: ratio of
photoelectric current to the luminous flux producing the current spectral response: optical wavelength
range of sensitivity voltage-current characteristic:
relationship between photoelectric current and voltage across the
device conversion efficiency: ratio of electric
power generated to the incident luminous power There was also this interesting 1934
article by Sharp about clarifying the names of photoelectric devices.
We had a group meeting in the afternoon and talked about a few
different things. First was the upcoming pizza lunch meeting - we’ll hear
talks from Taylor Esformes and Leighton Zhao (a Simons student working
with Phil Allen), and Marty will talk briefly about a possible project in
the BEC Lab. The LTC students are also expected to give summaries of what
they’ve been reading and learning about, and discuss any project ideas
they may have. At the pizza lunch next week, the students will put
together a powerpoint and discuss 3 possible projects they’ve been
thinking about (Marty’s idea to do something like this!). We also talked
about the possibility of doing a Journal Club and/or having the students
create mini lessons - more to come about these ideas, but I think
something along these lines will be good for the students. You don’t
really understand something until you can teach someone else about it!
Today I worked on updating my webpage for the new summer program (e.g.
creating a Summer 2014
page, creating a new calendar
page, adding the abstracts
from yesterday’s pizza lunch) and helping with some more of the paper
work. For future mentor reference, here is some information about Minors in Research
Labs, the required Laboratory
Supervisor Safety course, and the Parent/Guardian
consent form.
I attended a Responsible Conduct of Research and Scholarship
lecture/tutorial with the Simons students given by Professor
J. Peter Gergen from the Department of Biochemistry and Cell Biology.
First he walked the students through a registration process for RCRS
training. And actually, accordingto the Stony Brook policy on Responsible
Conduct of Research and Scholarship, as a “non-degree visitor
[conducting] research for less than one year at SBU,” I’ll need to
complete the on-line training component through CITI. The Responsible Conduct of
Research in the Physical Sciences course consists of 9 modules with
quizzes (your quiz average must be at least 80% at the end). Other
training resources can be found here.
For the remainder of his presentation, Gergen talked about how a
scientists reputation is based both on credibility (publishing the truth
and not falsifying
results just to make headlines) and ‘glamour’ as he called it
(publishing results first), the responsibility that comes with authorship
of a paper, the necessity of citations and understanding your field as a
whole, and the importance of acknowledging others and respecting ownership
of intellectual property.
We did a run-through of each student’s presentation in the conference
room this morning and I gave some final feedback before their actual
presentations at the pizza lunch. Overall everyone did a good job! The
abstracts can be found here.
In the afternoon we did student headshots (cropping and resizing them
to 300x300) and got each of them started on their personal webpages –
Libby was a great help in guiding the students through the login process
and showing them the essential Linux commands. I also found a concise "cheat
sheet" that could be useful. Note the login and file upload/download
processes are a little different for Mac users:
Open Terminal
Select New Remote Connection from the File menu
Add laser.physics.sunysb.edu to the
Server list
To log in for normal functions (i.e. viewing directories,
editing files), To upload (“put”) or download (“get”) files, select Secure File
Transfer (sftp) Fill in username in the User box and click Connect. I also helped John with some of the paperwork necessary for the summer
program. For future mentor reference, each of the students who are being
paid a stipend directly from the LTC need: a Participant
Stipend Form, a W-9,
and either a Stony Brook Foundation Cash Payment Voucher or Requisition
Form. (Note the trick to have a requisition number generated on print:
SBF must
be checked, and “Office Phone” “Office Fax” must be filled in.)
We spent the entire day reviewing the students’ presentations and
abstracts for our pizza lunch tomorrow. The LTC started a tradition (last
summer) in which the new students give an informal talk about a project
they’ve completed (or optics topic they’ve researched) as a way to
“introduce” themselves.
I also put together a brief personal introduction
presentation about myself (my experiences in the LTC the past two summers
and other research and teaching I’ve done in between) that I’ll share at
the lunch meeting.
Today marks the beginning of my third summer in the LTC! It’s great to
be back :)
I met the high school students this morning at the Simons welcome
breakfast – Ikaasa,
Jonathan, and Alex, our Simons fellows,
and Andrea, our
independent high school student. After this we headed to the lab and I
met Libby, a rising
sophomore who worked in the LTC this past spring and will continue in the
lab this summer. We spent some time first talking about past LTC projects
(looking over the hallway displays) and then had various discussions in
front of the whiteboard (such as talking about the small angle
approximation, orders of magnitude, and how to keep a proper lab notebook
and mini notebook).
After pausing for a delicious welcome lunch with Marty at the Simons
Center Café, we went outside with magnifying glasses and black paper in
hand to test out what it takes to use the sun to burn a hole in the paper.
The students explored how it was fairly easy with the magnifying glasses
(especially when they were doubled, one over the other, making the focal
length half as long), but impossible using a pair of glasses (sorry Piggy!).
We later had the students calculate the sun’s irradiance that was being
focused by the magnifying glasses by comparing the area of the lens to the
area of the resulting light spot - turned out to be about 1800 kw/m^2.
For the remainder of the afternoon we looked at various demos (the pig
toy, the interferometer, the polarizers) and did a few calculations on the
board (such as, the total power output of the sun, which is about 4x10^26
watts, or “400 yottawatts, that’s a lotta watts!” as John pointed out).
An interesting derivation that I had never done was changing around the
thin lens equation such that it gave you the distance to the image based
on the total distance from the object to a screen and the focal length of
the lens being used. This was a great mathematical representation of the
demo in which the students had to find the correct place(s) to put a
magnifying glass in front of a light source such that it created a clear
image on the whiteboard.
Today is my last day as a summer mentor in the LTC. It’s crazy to
think how fast the summer has gone. I feel like I just got here! Rachel,
Dr. Noé, and I had a nice “Farewell Lunch” at
Muse’s family’s Thai
restaurant, Phayathai.
I spent the rest of the day looking a little more into the customs
issues with our Cambridge Correlators order and also touching up my
webpage. Among a few other things, I made sure to update Week 10 on my calendar
page, with information about this past Wednesday’s pizza lunch talks.
I also tried to organize all of the printouts and forms from the Cambridge
Correlators order and just from my research into SLMs in general.
We bought a small package of CD-R’s – I had this idea of using a CD to
store data pictures from each student, since there won’t be enough space
to hold all of these pictures on the lab camera’s memory card forever! I
only had time to start with Samantha’s caustic pictures. Since there
turned out to be a lot of extra space, I also put photos of her giving
presentations and from the poster symposium on the CD and included a
little “table of contents” type sheet in the case. Since the CD-R allows
a one-time-write, it would be best to buy CD-RW, so that more photos and
other important things (maybe such as Mathematica simulations or
spreadsheets with data, etc) could be continually added. I wanted to get
one sample disc done before I left, so hopefully a future LTC student or
mentor can continue this job.
Overall, I'm glad I had the opportunity to come back to the LTC this
summer - it's been an invaluable experience for me.
The Stony Brook University purchasing agent taking care of our
Cambridge Correlators order contacted us this morning to let us know that
the SLM Kit seems to be cleared for delivery, however the LM635
Laser Module will need to be inspected by the FDA. She forwarded a
form from the FedEx Import Coordinator that we needed to fill out:
“Declaration for imported electronic products subject to radiation control
standards.” I first contacted the purchasing agent who got in touch with
the import coordinator from FedEx with a few questions regarding the form.
I then tried to contact Cambridge Correlators, to ask about whether
they’ve filed a radiation product report with the FDA/CDRH for their Laser
Module or had American customers with similar issues in the past.
As what usually seems to be the case with legal documents, the jargon
was a little hard to navigate. But after studying the declaration form
all morning, I started to understand it better. It looks like unless
Cambridge Correlators has filled out a radiation product report, we may
need to fill out a FDA 766, which puts a limit on the length of time and
dates the product will be in use in the country... (which seems silly
because this is the least dangerous out of any of the lasers we've got in
the LTC!). I don't see an appropriate reason that this device would not
be subject to the radiation performance standards (situations listed under
Declaration A), but I guess we'll have to look further into #2 (under
Declaration A), and see if the device can be excluded based on the
"applicability clause or definition in the standard or by FDA written
guidance."
At the bottom of Form FDA 2877, it says that we can consult the
following
3 FDA web pages for additional guidance:
http://www.fda.gov/cdrh/
- error: directory listing denied, http://www.fda.gov/ora/hier/ora_field_names.txt
- page not found, http://www.fda.gov/ora/compliance_ref/rpm_new2/contens.html
- a very long manual on regulatory procedures. While this manual "provides FDA personnel with information on internal
procedures to be used in processing domestic and import regulatory and
enforcement matters,” I did find the following:
“Questions regarding importation of specific products
should be referred to the appropriate Center…medical devices and radiation
emitting electronic products or their components should be referred to the
Center
for Devices and Radiological Health, Office of Compliance, Division of
Program Operations (HFZ-305).” “radiation-emitting devices must meet established standards” (pg. 9 –
94) But there doesn't seem to be any information in this manual on figuring
out if a product meets certain standards or not ... where are these
standards listed? Do we have to contact the Center for Devices and
Radiological Health directly? Other things to note on FDA 2877 form that
could be useful to remember:
The one that was emailed to us by the FedEx Import
Coordinator had
actually expired on 11/30/2003. I'm not sure that much has changed on the
form, however I found the
more
recent one online. The bottom does read "Previous version is
obsolete."
Under Declaration A – 7, it says to chose this option if the product is
being reprocessed in
accordance with P.L.
104-134, but after looking into this further, it appears to only
pertain to “For Export Only” products. Googling this Center for Devices and Radiological Health didn’t yield
many helpful results. So, I turned to Sam’s Laser FAQ and found a
valuable page on Laser Safety
Classifications, which led to a link for the performance
standard for light emitting products. (This has info on the
applicability clause that we were wondering about! However, it doesn’t
seem like our laser module is applicable …) Our LM635 is a <2mW laser –
according to Sam it’s a Class III A. These are medium power lasers that
can injure the eye if the beam is focused. The official (type-written?!)
FDA classification of Class III A lasers is found here.
I then tried to find some further information on this website, first
searching radiation-emitting
product codes, but this simply listed acronyms for various products,
then searching the establishment
registration and device listing. There was no “Cambridge Correlators”
explicitly listed, but they could possibly use a different name for
manufacturing.
Then at the end of the day we talked to Hal about this problem and he
said
we should either go through the university’s custom’s broker, or just
reject the whole order and start over.
Today I read some more from Tony Phillips column in American
Mathematical Society on catastrophe
theory and linguistics. The number of arguments of the verb in a
sentence (which is usually three, but at most four) corresponds to the
number of critical points (specifically minima) that can simultaneously
exist in a function. For the simple minimum (not a catastrophe),
represented by a quadratic function, the corresponding sentence type is “I
am;” small perturbations to x2 do not change the location of
the minimum by that much, so it’s considered stable. For the fold,
represented by a cubic function, the corresponding sentence type is “The
day begins;” there is a drastic difference in the number of critical
points between whether the control parameter for a perturbation term is
positive or negative, which is consistent with the fact that the process
represented by this sentence type is different depending on the
“direction” (i.e. “The day begins” or “The day ends”). The verb phrases
(which come from the process/event in the external world) get more
involved with each of the more complex catastrophes.
Our pizza lunch was small since most of the LTC students left last
week; we heard short talks from Seth, James, Casey, Rachel, and Stefan:
Casey talked about his work studying the Zeeman effect on the HeNe gain
curve, Seth and James gave a joint presentation on the trials and
tribulations or working with the ARP (adiabatic rapid passage) experiment,
Seth then gave a short presentation on his bichromatic force computer
simulations. Afterwards, Rachel talked about how she was attempting to
create optimized optical vortices with our spiral phase plate, and Stefan
discussed how he was simulating the interaction between atom clouds and
Laguerre-Gaussian beams.
Hal gave us a short lecture on the optical Bloch equations
(OBE). He
started with a short introduction to quantum mechanics and then derived
the Rabi equations (1937), Feynman, Vernon, and Hellwarth’s version for
working with real numbers (1957), and Bloch’s vector for the optical case
(i.e. parallel to the equations for Rabi oscillations!). It was
interesting that these three equations, with three unknowns, were similar
structurally to the output you get from taking the cross-product of two
vectors (i.e. the equation for du/dt contained only the variables v and w,
while the equation for dv/dt contained only the variables u and w, and
finally the equation for dw/dt only contained the variables u and v).
Note also that these are all real quantities.
Later, Dr. Noé coupled single-mode fiber, sent through 100-micron
pinhole,
trying to show the Fresnel pattern with central dark spot, (in the same
way he tried to show Will an Airy pattern but ended up with this unusual
beam) but this time, all we could see is the Airy pattern! After a little
maneuvering, we did end up seeing the dark central spot when the fiber tip
was very close to the pinhole.
We’re having some slight issues acquiring the Cambridge Correlators SLM
– the device has successfully made its way from the UK to the US, however
it’s stuck in customs! There’s some debate as to whether there are
crystals emitting harmful radio frequencies, when really the tiny
liquid crystal display panel has the same electronics as LCD
projectors, TV screens, etc. Hopefully this can all be straightened out
soon, although it doesn’t look like the SLM will get here in time before I
leave on Friday…
I created a short version of the Laser Teaching Center Summer 2013
slideshow and uploaded it to YouTube. Hopefully it’ll be a good
piece to share with those who are not necessarily directly connected to
the LTC but are interested in what goes on here. It’s about 3 minutes
long and contains our group photo, one picture of each student, one of
each mentor, a couple from the pizza lunches, and a few from other special
events (i.e. tour of Eden's lab, welcome lunch for Laser Sam, Simons
students tour the LTC, Simons poster symposium and farewell lunch). I’ve
also added this to my slideshow
page.
In the afternoon I spent some time talking to Rachel about her setup,
which freezes a Fresnel diffraction pattern from a pinhole (at N=2) and
then sends this through another circular aperture to cut off the outer
part of the pattern (which as a dark center). She then uses this output
to illuminate a section of a spiral phase plate to theoretically create an
optical vortex, however there was then some discussion as to whether the
resulting beam was an actual optical vortex or not.
While reaching out to faculty last week who would potentially be
interested in Samantha’s caustic/catastrophe theory poster at the Simons
symposium, Dr. Noé got in contact with Tony Phillips from the Stony
Brook Math Department. Prof. Phillips pointed out a couple of pieces he
had written for a column in the
American Mathematical Society on the “catastrophe machine” and catastrophe
theory and linguistics. The latter, “Topology and Verb Classes,”
describes a few examples from René Thom’s Topologie
et linguistique (1970) of how the elementary sentence types relate
to the elementary topological structures (“elementary catastrophes”)
underlying events in the world around us. He proposed that when an event
or process happening in spacetime can be characterized by one of the
catastrophes, the mental process that perceives the event will imitate the
catastrophe, and furthermore the syntax of the verb phrase used to
describe the event or process will correspond as well. Prof. Phillips
then walked us through a few examples with the first few elementary
catastrophes. I found it all a little bit abstract and hard to comprehend
because I haven’t studied syntax or sentence structure since middle
school.. I decided to look up some information on the argument structure
of verbs and stumbled upon this Argument
Structure guide for Italians learning English!
The AMS column also led me to another interesting article (that Tony
Phillips had cited): How
We Came To Be Human, by Ian Tattersall in the Dec 2001 issue of
scientific American, which I plan to read when I get a chance. The
article evidently poses the question, how was language invented?
Consciousness depends on language, however, many millennia before there
was evidence of conscious activity, there are fossil records of language
(i.e. of the necessary cerebral and vocal apparatuses). The evolution of
human intelligence is pretty interesting stuff!
I first spent a lot of time catching up on my journal from last week –
it had been so busy with all of the deadlines and events that I only had
time to jot down notes each day of what I accomplished. Today I finally
went through and wrote out the full entries.
I heard a clip from NPR titled Why
aren’t more girls attracted to physics? which gave an interesting view
on one reason that more or less girls will study physics in a particularly
area. While this does sort of play to stereotypical situations, I agree
that generally the community and environment in which a child grows up
play an important role in shaping the child's views on achievable careers.
As a young girl growing up in my small suburban town, the only woman I
knew with a Ph.D was my elementary school principal (but it wasn't even in
science), and basically all of my friends' parents and other women that I
was surrounded by were stay-at-home moms, nurses, teachers, lawyers, or
musicians. I honestly didn't even consider the possibility of a career in
science until college.
I finally finished my CCD vs. CMOS
page. Now that we have one of each type of camera in the lab,
hopefully this guide will provide future LTC students with a good
introduction to their different qualities and uses.
Today I also helped Rachel with her research. We got out the optical
fiber breadboard since she’s interested in modeling part of her project
after Will’s. We
were successfully able to couple the multi-mode fiber, however we didn’t
have time to finish the single-mode since we got distracted trying to
maximize her spiral phase plate setup with Stefan – they were hoping to
attach it to an adjustable mount for more fine-tuned adjustments. Stefan
created a useful diagram
of the various patterns on the phase plate in one of his journal entries
back in February.
This morning was the poster symposium for the Simons Summer Research
Program! Everyone’s posters looked great! ☺ There was a nice ceremony
afterwards in which each student was called forward and presented with a
certificate (signed by Jim Simons!).
We had a farewell lunch at the Simons Center Café (John Noé, Kevin Zheng,
Melia Bonomo, Rachel Sampson, Dave Battin, Samantha and her father, Kathy,
William and his parents and two siblings) and took a group picture:
After lunch, William brought his family into the lab to see his
project, Rachel’s laser light show, Kevin’s 1.4-meter long laser, and
Kathy’s tweezers setup. Kathy stuck around for the rest of the day, since
her flight wasn’t until Saturday, however we said our goodbyes to everyone
else.
The lab was sadly a lot quieter in the late afternoon… I spent some
time uploading pictures from the symposium and organizing these on their
own page.
I created a Closing
Lunch Meeting page, to list each student presentation, provide links
to their abstracts, and organize photos from the event. Finally, I
updated the calendar
page with all of our “Week 9” activities - it’s been a very busy week!
This morning we went over the final estimation problem that we had kind
of been putting off for a few days because of all of the deadlines (i.e.
abstracts were due Monday, posters were due Tuesday, and presentations
were yesterday): If you paved a pathway to the moon, how long would it
take to walk, jog, and sprint it? Even though this was a fairly
straightforward problem compared to past weeks, the important part was
trying to come up with a way to estimate the distance to the moon. For
someone who doesn’t know it off of the top of their head, it’s at first
hard to fathom coming up with a number for this distance. Obviously it’s
impossible to just guess, so you have to think more creatively! For
instance, I estimated the radius of the Earth and then used this to come
up with a distance – the moon was definitely farther than 10 times the
radius of the earth and 1000 times seemed too far, so I used 100 times:
400,000 km.
The ranges for our answers were then as follows: it would take 7-9
years to walk to the moon, about 4-5 years to jog, and about 2 years to
sprint. Afterwards I asked the students about whether they thought these
types of exercises were useful / fun, or if they felt too much like
homework problems. They all seemed to agree that the estimation problems
were interesting and should be continued for future LTC students.
In the afternoon
Dexter
Bailey, Vice President for University Advancement and Executive
Director of the Simons Foundation, came to visit our lab. After
introducing ourselves, each student gave him a brief overview of his/her
project. The students are really getting the hang of presenting their
research in a variety of forms (i.e. 1-minute verbal progress reports,
powerpoint research updates, more formal powerpoint presentations, and
demonstrations in the lab) to a range of audiences (i.e. mentors,
professors, other LTC students, their peers in other labs, and non-science
professionals). I think Dexter Bailey enjoyed his visit and mentioned
before he left that he thinks a good meeting is one in which you come away
having learned something new – and after an hour in the LTC, there were
plenty of things that he learned!
Helping Sam shrink the file size of her poster reminded me that I had
to do that for my Dickinson
poster (which I have a link for on my presentation
page). So I went through and shrunk the pdf files for my poster, 2012
REU presentation, and 2012
FiO/LS presentation. There’s a pretty simple way of doing so on a Mac
(I’m not sure if there are similar options on a computer using Windows).
Save the PowerPoint file as a PDF
Open the PDF (the default application for Mac is Preview)
Save As…
Under “Quartz Filter” select “Reduce File Size” In other news, I found the birthday problem article that had come up in
a recent conversation – I had remembered there was some show host who made
the mistake of assuming that the magic number of 23 people for there to be
over a 50% chance that two people shared the same birthday meant you could
pick a specific birthday for two people to share, but I forgot
where I read the article... The article
turned out to be part of that same Me,
Myself, and Math series from the NY Times Opinionator!
Today was our Closing
Pizza Lunch Meeting, which also marks the end (for most of the
students) of the Laser Teaching Center’s 15th summer! In honor of this,
we shared some updates and remarks from some LTC alumni that Dr. Noé wrote
to. (I shared the powerpoint I had been working on and read the quotes
from the alum that had wrote to Dr. Noé. After each of the students gave
their ~10 min presentations, I shared the video slideshow that I’ve been
working on. I had first explained how this summer, as a mentor and
assistant, I’ve had a variety of duties: helping students hands-on with
their research and writing, doing literature research on students’ topics
of interests to keep up with their work, doing research for the spatial
light modulator purchase, and keeping organized records of guests and
other special events we’ve had in the LTC this summer.
For the rest of the afternoon, I spent some time adding to my website –
I created a page for pictures from the Simons
students’ tour of the LTC and an Alumni remarks
page with the information/pictures I had put in the PowerPoint.
Later, I uploaded the slideshow to YouTube.
I also finished going through each students’ poster one more time
before Dr. Noé ran them off to the printer for the 6:30 PM deadline. We
just made it in time!
In the morning I stumbled upon a NY
Times article on catastrophe theory – part of the same Opinionator
series that produced the singularity
article I had used for my senior research: Me,
Myself, and Math, by Steven Strogatz. The article discussed the
theory’s applications to the economy and sleep patterns, among other
things. Just a note about some of the terminology used - Contrary to
connotations of the name of this theory, a “catastrophe” isn’t necessarily
something positive or negative, it’s simply a catastrophic event. The
word “caustic” actually means “able to burn;” in physics it’s highly
concentrated envelopes of light formed by the intersection of reflected or
refracted parallel rays from a curved surface.
The NY Times article cited two important sources; one was an article
in Nature by Berry about caustics through lollipops. Berry’s
poster explained how caustics are catastrophic events in a more
straightforward way than I’ve read about it so far: in a swimming pool,
you see a bright web of light when your eye, the sun, and the water are
all at an ideal distance, in which the light rays (critical points)
intersect.
After lunch, I gathered optics demonstrations for the Simons program’s
tour of the LTC this afternoon. I also planned out how the station
rotations would play out. The tour began at around 4pm with some remarks
by Dr. Noé in the conference room. He went around the room and had each
student say what they’re researching and then think about how that relates
to optics. Afterwards, I divided the students into three groups that I
helped rotate on a 20-minute/station schedule – one group stayed with Dr.
Noé for demonstrations, one group listened to William and Kathy discuss
their projects, and the third group listened to Sam, Kevin, and Rachel
explain their projects and also see a laser light show (run by Rachel).
Throughout the event, I made sure to keep things organized and moving
smoothly. In the beginning I had to be a little creative and rework the
original plan on the spot to fit the lengths of the student explanations.
But overall, I’d say it went really well! And it was great to see how our
LTC students got really excited about sharing their work with their peers.
(I also took lots of pictures!)
Throughout the day and after the tour especially, I looked over the
students’ posters and gave them comments/suggestions. Today I also
finished the iMovie slideshow, the LTC alumni quote presentation, and a
program with the list of student talks/titles for tomorrow’s pizza lunch.
Today I did more abstract editing! I sat down with William for the
entire morning for editing, rearranging, etc his abstract.
Again, it was important that I fully understood each piece of his project
in order to help make constructive changes, so we also spent some time
discussing his procedures and the reasons behind them. I then worked with
Sam after lunch on the theory section of her
abstract to try to define
catastrophe theory
(Dr. Noé later suggested to use proverb “the
straw that broke the camel’s back,” which I had brought up after
hearing it used in Robert
Gilmore’s article on catastrophe theory). For now we ended up with:
the study of how changing control parameters leads to qualitative change
in the solutions of a differential equation.
I did some more literature research on Samantha’s project and looked
over Berry’s
1976 paper that connected caustics with René Thom’s catastrophe theory
and his article
in Physics Bulletin, which sort of summarized it. (It’s really great
that Berry has all of his papers available
online.) Structurally stable caustics are those that are unaffected
by generic perturbation; these are the “elementary catastrophes,” such as
the fold or cusp. The higher-dimensional catastrophes are structurally
unstable and go through an unfolding process (e.g. the parabolic umbilic
that Sam observed in her evaporating droplet went through a series of
stages in which you could see the individual elementary catastrophes).
This higher-dimensional catastrophe appears because of surface tension and
gravity (from the vertical microscope slide she’s using).
We spent most of the afternoon editing student abstracts – it’s a very
time-consuming process! I found out very quickly that in order to
properly help someone revise a piece of writing, you really need a firm
grasp of the content that’s being written about. Editing is more than
just checking spelling and grammar – it’s fixing sentence structure and
reorganizing ideas to make sure the student is communicating his/her
message clearly and concisely. In Sam’s case, I had been keeping up with
her journal and experimental progress but was still not quite sure how the
math behind her research into caustics worked. Therefore, it was
difficult to check over her theory section.
I started with Nye’s
1979 paper that she’s modeling her work after and the Gilmore
catastrophe theory article that I found couple of weeks ago. After
several discussions with her throughout the rest of the day, I think I’ve
come away with a better understanding of the theory for her project!
In short: The germ is a polynomial (with state variables x, y) that is
unique for each type of elementary caustic (these are very complicated to
derive), while the unfolding terms may be common among a few different
caustics and contain the control variables (i.e. a, b, c, d). For a
particular catastrophe (i.e. caustic shape), you produce the generating
function by adding the germ and unfolding terms together. The first
partial derivative set equal to zero (the “formation of the ray”) reveals
the function’s critical points, and the second partial derivative set
equal to zero (the “formation of the caustic”) reveals the degeneracy of
these points. What she’s interested in is finding the caustic curve
equation, which comes from solving the formation of the caustic equation
for the state variables. These plotted against the control variables
produces a graph that looks like the caustic shape she observed.
Today I worked on the LTC Summer 2013 slideshow a little bit more. I
also created a page with general tasks that can be done during a Friday clean
up session to keep people on task and make the afternoon as productive
as possible. As seen from yesterday’s clean up, when there’s a plan laid
out ahead of time, it’s remarkable how much can be accomplished! With the
addition of this new page, I decided to organize my Summer 2013
page, since it was starting to become somewhat of a jumbled list.
Today I spent a lot of time putting together a slide show of pictures
from the LTC’s summer program using iMovie. I first introduced each
student/mentor, then I added photos from special events, and finally I had
a few general photos of happenings in the lab. I’ll add in a few more
photos at the beginning of the week from the Simons LTC tour and then burn
the whole thing onto CDs to hand out (since it’s already too large of a
file to be emailed).
In the afternoon, we all got together and did some very productive
cleaning in the lab – First everyone worked on cleaning up around his/her
individual table space, i.e. putting away extra pieces that may have
accumulated (e.g. posts, post holders, screws, etc) and making sure that
delicate optics that aren't immediately being used (e.g. lenses, wave
plates, polarizers, etc) are either put away / covered / placed somewhere
safe. We started putting together the "laser light show" on the wooden
table for the LTC tour next week, and setting aside some of the other
demos that will be used as well. Other things that were done included
general neatening up of loose papers / books / magazines, sweeping up
loose screws and washers from the floor, and putting up a few more things
on the wall.
I think the lab is looking great!
I helped Rachel with a number of Mathematica-related issues, since
she’s trying to fit a Bessel function to her Airy diffraction pattern
data, similar to what I had done last summer. I had to look back at some
my old Mathematica files, but there were a few things that I couldn’t
remember how I did them and unfortunately I don’t have my actual notes
from last summer with me right now... One important command that I
figured out was what you can use to import lists of data from an Excel
spreadsheet. The data appears as an array of points that can then be
plotted using the ListPlot command:
I was able to help her with a couple of other things that I remembered
having difficulty with – extra parenthesis around the data set and extra
space between the words of certain commands that the program doesn’t like.
(The error message that Mathematica spits back out is never much help with
this type of thing!) There were still some questions about what certain
values were in my equation and why her fit still wasn’t working correctly…
Later in the day I looked over my old Mathematica files some more, and
I'm pretty sure now that the values in my equation were in micrometers,
not millimeters - which would make sense that the "150" was in there
(since my pinhole was a=150um) and that the wavelength was "0.632." I'm
still not sure about my L distance of "11310," because I definitely had
the photodiode farther than 11mm away from my pinhole! There may have
been an issue with my "x" distances not being in microns. I was having
trouble locating the raw data on my computer to check this, but it's
possible that I made an error in their order of magnitude and then somehow
fixed it by adjusting L ... It’s possible that double-checking all of her
units again might help her fit work a little better.
It was also exciting today that William came full circle in his
interests – he actually used a pair of 3D glasses in his setup to
demonstrate what effect a left-handed or right-handed circular polarizer
had on his output beam.
I created a pizza
lunch meeting summary and typed up a brief description of each
presenter’s talk from yesterday. I also updated I updated the calendar
page with information from Jenny Magnes’ visit. When I was uploading
a couple of pictures from yesterday’s events, I found that one of the
pictures was set to private (if you tried to view it online, the page is
listed as “Forbidden”). This isn’t the first time this has happened to me
(I’m not sure what even causes it), but there’s an easy code to make
pictures/files public:
Also, Rabbit, rabbit,
rabbit!
Today Jenny Magnes from Vassar College visited with three of her
students to speak at the pizza lunch and spend the afternoon in the LTC.
As per usual for our lunch meetings, I helped set up the projector and her
presentation in the morning. (Hopefully we’ll be able to get a new
projector for the AMO conference room soon!)
She and her students (Brian, Ramy, and Tewa) spoke about their work in
biological applications of diffraction, which ranges from observing
changes in the intensity of diffraction patterns due to a changing
magnetic field of a regenerating planaria or the
quantification of thrashing movements of the C.
elegans based on its diffraction pattern. A video of her work in
Quantitative
Locomotion Study of Freely Swimming Micro-organisms using Laser
Diffraction can be found in the Journal of Visualized Experiments
(JoVE).
After the Vassar group finished presenting, Rachel and Kathy each gave
a short presentation on their work – Rachel spoke about her initial
interest in identifying bacteria by their diffraction patterns and how she
came to start researching reconstructing an object from its diffraction
pattern and aperture functions. Kathy explained her optical tweezers
setup and the biological applications this type of apparatus has.
I also spent some time during the day working with William to try to
retrieve his images off of the “CCD computer.” We tried hooking up the
computer tower from Sam’s desk to a monitor - the computer started up fine
and went to the log-in screen, but then we had no way of actually
communicating with it because the keyboard and mouse were both
unresponsive (we even tried multiple different mice).
I suggested we purchase a portable
USB floppy drive for the lab, to make transferring images from the
“CCD computer” a lot easier. These are fairly inexpensive, however
usually not in-stock in stores, so we’ll have to buy one online from Staples,
BestBuy,
or even Amazon.
Today I worked with William to try to optimize his setup with the 4-f
component. In order to minimize extra scatter, I had him clean most of
the optics and tried to find a less-scratched polarizer. We then took
some time to set up the CCD camera and computer near his table, and found
that the striations in the stress optic were causing extra stripes in the
output. Even so, William was able to adjust the optics such that you
could see the bulls-eye beam output with either a dark or bright center
depending on the orientation of his linear polarizer. The next issue to
deal with is finding empty floppy discs and a way of transferring them to
a computer with both a floppy disc reader and USB port or network
connection.
I started brainstorming what to put into my presentation for next week,
since I’ve done research into a variety of topics (most in-depth with the
SLM, but also little things here and there to keep up with the students’
interests), and I’ve also helped out with different
tasks around the lab (whether it be assisting students with projects or
recording accounts of the events and visitors we’ve had). I’m thinking
that I might put together some sort of “Experiences as a mentor in the
LTC” presentation…
I started creating a “CCD vs. CMOS
cameras” page with the information that I had been reading about.
I’ll have to finish it up in the next few days. (The html code that I
used to create the table came from Temple University.)
I updated the estimations
page with the answers from last week and a new problem for this week –
since all of the students are busily engaged in their projects now, I
chose something fairly straight forward, but still interesting to think
about:
If you paved a pathway to the moon, how
long would it take (in years) to: I did some research into the differences between CCD
(charge-coupled device) and CMOS (complementary
metal-oxide semiconductor) cameras. There was some useful information on
the Thor
Labs product page, and I also found this Photonics
Spectra article. Both provide a means of converting an optical image
to an electronic signal, but the main difference is the way they’re wired:
in a CCD camera, each pixel’s charge is sequentially transferred to a
common output structure where the charge is converted to a voltage; in a
CMOS camera, the charge-to-voltage conversion takes place at each pixel.
CCD cameras provide superior image quality, but at the expense of a larger
system; they are more suitable for top-notch imaging applications such as:
digital photography, broadcast television, and scientific/medical
applications. CMOS cameras are immune to blooming and the system is
often more compact, but at the expense of image quality (especially in low
light); these cameras are more suitable for high-volume and
space-constrained applications such as: security cameras,
videoconferencing devices, fax machines, and consumer scanners.
I met Jon
Sokolov from the Garcia
Center who discussed their Summer Scholar
program as well as his research in DNA cutting with soft lithography.
(This method allows for greater efficiency with DNA sequencing,
because the DNA strands are cut into pieces in such a way that you’re able
to determine each one’s overall location in the strand based on the length
of the piece.) The scholar program hosts about 60 high school students,
10 undergraduates (REU), and a handful of high school teachers (RET).
Rachel forwarded me a very interesting article: Reading Art through
Science. It described the work done by physicists and chemists in the Metropolitan Museum of Art’s science
department to study and protect great works of art. Their labs use
lasers, electron microscopes, and x-ray machines to perform
ultra-sensitive and minimally invasive experiments. One chemist, Marco
Leona, describes the importance of science to better understanding the
history of a work of art: “Through the ‘materiality’ of a piece we can
learn something about the artist as a person who existed at a specific
point in time, in a specific place and society, with access to certain
knowledge and technologies.” One of my favorite lines from the article is
“Hints of [these scientists’] broad interests line their desks: books on
laser physics sit next to texts on ancient metallurgy practices, Cambodian
history, or Italian Renaissance painters.” The museum offers Conservation
and Scientific Research fellowships – for those who have recently
completed graduate level training, or even professionals in the field.
Today was a very productive day! In the morning I reviewed the
estimation problem I had given the students for this week:
If we had a red HeNe laser with a Fabry-Pérot cavity the length of Long
Island:
What is the frequency spacing between two adjacent longitudinal
modes
in the cavity? (Our range of answers were 600-800 Hz)
How many lasing modes would be present at a given time? (We all got
about 2 million modes) After we discussed our answers, Casey jumped in and asked if the
students
knew where the formula for frequency spacing comes from. They could
somewhat explain it, but he encouraged them to write it out. Kevin
started, and at one point Kathy and William joined him - so all three were
writing on the board at once! They made quick work of it together, and
afterwards Casey explained how he arrived at the equation slightly
differently. It was great that our discussion evolved into this mini
derivation exercise - basically driven by the students.
I spent most of the day jumping around between various student projects
-
I helped Rachel take pictures of her pinhole diffraction pattern with
the CCD camera using the old computer on the cart. We ran into some
issues when wanting to transfer images, since there’s no longer any other
(hooked up) computer in the lab with a floppy disk reader! One
possibility is hooking up the computer to the network and signing into
laser using SSH … In the mean time, we also tried Kevin’s suggestion of
using the Nikon camera with the lens removed. I then showed her how to do
an intensity profile of the beam using Image J, however the Nikon
images were somewhat saturated from the central disk of the Airy pattern.
She instead decided to setup a photodiode to manually profile the beam,
however we ran into some issues trying to find the correct banana clips to
connect a resistor in parallel with the voltmeter (since I had actually
just helped Kevin setup the photodiode to an oscilloscope for his cavity
dump laser setup).
With William we discussed the possibility of using a 4-f setup to clean
up the output from his stress optic, which has a number of striations
effecting the diffraction. Thankfully, I was able to find the lenses from
my setup last summer - 333mm focal length, 40mm diameter achromats. (I
ended up labeling the drawer on the desk in the back electronics room,
since it contains other useful spatial filtering supplies).
Samantha’s project deals with the caustics of water droplets and
catastrophe theory. After reading up on catastrophe theory in general, I
realized it has ties to my senior research project on singularities in
freezing water droplets. The solution to the differential equation I had
used to describe the changing shape of the droplet as it freezes undergoes
a pitchfork bifurcation at a critical density ratio (of the solid to the
liquid). Before the bifurcation, droplets will freeze with a flat top,
but after this critical point, frozen droplets will have a cusp formation
at their tip. It turns out that the appearance of new equilibria and the
disappearance of old equilibria is essential to the study of catastrophes.
I plan to explore this connection further and have started going through a
very detailed and useful source on
catastrophe
theory – it even has a glossary of terms at the end.
The new CMOS camera we ordered from Thor Labs yesterday arrived this
morning! Kathy tried using it in her tweezers setup, however there wasn’t
great contrast on the video fee… Hopefully she can fix this by playing
around with some of the settings, but something I’d also like to do is
read up on the differences between CCD and CMOS cameras.
Today I compiled a calendar
of LTC events, to keep track of all the of the special meals and
visitors we’ve had this summer. I also did a little bit of research into
the USB
CMOS camera, which we just purchased, and found the manual.
I updated my SDE1024
page with information on suppressing ghost spots and fixed the
paragraph I had at the beginning about twisted nematic liquid crystal
cells – this is a reflective SLM so the incident light’s polarization axis
is rotated 90 degrees upon entering the cell, but then rotated back after
reflecting back out of it, therefore it’s a phase-only device. I also
updated my introduction
to SLM page with information on how liquid crystals rotating
polarization of incident light.
Speaking of Rosalind Franklin (Friday 19 July journal entry on the play
that was written about her life), today is her birthday!
Today at the pizza lunch, Giovanni
Milione (who is currently a PhD candidate at CUNY and used to be a student in the LTC)
gave a talk on “Classical Entanglement with a Vector Light Beam.” He
explained how a vector vortex beam has a combination of spin
angular momentum (SAM - circular polarization, specifically radial or
azimuthal) and orbital
angular momentum (OAM – shape of wavefront, specifically (Laguerre-Gaussian
mode). While the polarization and spatial phase of the beam are two
separate qualities, they are “classically entangled” such that affecting
the SAM affects the OAM. This is mathematically equivalent to quantum
entanglement; therefore it opens up the door to the possibility of using
vector vortex beams for advanced communication (i.e. being able increase
the amount of energy transferred through an optical fiber).
During the discussion after his talk, there was some controversy on how
the OAM and SAM could be determined from a single photon, since you can’t
necessarily measure both the polarization and mode of it simultaneously.
Something else that was interesting that came up was the no-cloning
theorem, which states that one can’t make an exact copy of an unknown
quantum state, which is one reason why quantum encoding of information is
so appealing – one would be able to tell right away if someone tried to
“eavesdrop” on an entangled photon.
The students then gave a brief summary of what they’re working on now
and how they got to this point. This was good practice for figuring out
how to concisely describe what you’re researching about to someone who has
not watched your progress over the past month but still has a substantial
knowledge of optics. In such a short amount of time, there is a delicate
balance between providing some context and details, but not getting bogged
down with too much background or small intricacies of the project.
I also started putting together a calendar of special events to keep
track of all the special visitors and pizza lunches we’ve had this summer.
Today I did a lot of research into answering the question- Why do the
liquid crystal molecules in a twisted nematic alignment rotate the
polarization of light? Most of the papers I had read about SLMs simply
stated that light’s polarization axis follow the helical rotation of the
liquid crystals, yet none of them ever really explained why that is.
I started by looking at a Polymers
and Liquid Crystals page from Case Western Reserve University, which
broke down polarization in general and then talked more specifically about
birefringence in liquid crystals, with some useful simulations (that I
couldn’t run properly on my Mac!). This page on Anisotropy
in Liquid Crystals from Kent State University is useful in describing
how the extraordinary ray of incident light sees an “effective” index of
refraction, based on its angle.
After looking over many sources, compiling this information, and a
couple of times confusing myself further, I think I better understand
what’s going on (i.e. how a liquid crystal molecule’s “tilt” changes the
phase of an incident beam and it’s “helical alignment” rotates the
polarization of an incident beam):
If light enters a liquid crystal molecule with its polarization axis
parallel to the slow axis of the molecule this extraordinary ray will be
slowed down; the rays will travel faster when the polarization axis is
perpendicular to the slow axis. Therefore, phase modulation occurs as the
liquid crystal molecule is tilted from having the polarization axis of
incoming light parallel to the slow axis to perpendicular to the slow
axis.
This can be seen in the parallel-aligned nematic liquid crystal, where
the molecules begin in an upright position and then tilt towards the
direction of the electric field at an angle θ in the longitudinal (y-z)
plane. The stronger the electric field, the more the tilting angle
increases in the direction of the axis of propagation, and the more the
phase is modulated.
On a much smaller scale, Rayleigh
scattering occurs between the electric field of the incident light
beam and the electrons of the liquid crystal rod-like molecule. This is a
type of elastic
light scattering, in which negligible energy is transferred and
therefore the wavelength of the incident photon is conserved – only the
direction changes. Since these electrons are bound to the crystal,
scattering occurs along the axis of the rod.
In a twisted nematic liquid crystal, where the molecules are aligned in
a helical fashion, the scattering causes light’s polarization axis to
follow the helix. Since each molecule is tilted away from the
longitudinal axis (in the transverse x-y plane) by a certain angle α, the
polarization of incident light will be rotated by an angle α as it exits
the molecule.
I found a paper that appears to describe this phenomenon: Quasielastic Rayleigh
Scattering in Nematic Liquid Crystals, which I’ll read more into
tomorrow. Upon first glance, it seemed to keep citing previous work and
not explaining the basics. I tried to work backwards and look at the
earliest paper that they cited multiple times, by Chatelain in 1948, who
was the first to study the intensity of light scattered by liquid crystal
molecules, but his
paper is only in French!
In other news, looking at the information page from Case Western
Reserve University reminded me of the Free GRE Flashcards a
professor in the physics department put together. I ordered them last
summer and have only just recently had the time to start going through
them. These have great short-answer style questions that cover all of the
basic physics concepts you need to know for the exam (according the types
of questions asked on previous exams), and everything is neatly organized
by topic. Unfortunately, the flashcards are currently out of stock, but
it seems that they’re working on an iPhone / iPad app!
Today I reviewed the Stony Brook Solar Array (as William termed it)
estimation problem with the students. Our results, on the estimation
page, ranged from 104 to 106 kWh
(1010 to 1014 J). It was great to see that each of
us compared the resulting value to a different thing (i.e. household
energy usage, skyscrapers, light bulbs, and lightning bolts). The new
problem for this week is:
If we had a red HeNe laser with a Fabry-Pérot
cavity
the length of Long Island:
What is the frequency spacing between two adjacent longitudinal
modes in the cavity? [Hz]
How many lasing modes would be present at a given time? I read through the second part of Padgett et al’s paper,
Optimisation of a low-cost SLM for diffraction efficiency and ghost order
suppression, which discussed suppressing ghost traps. When trying to
create an array of multiple spots in the Fourier plane (for example, two
spots in the first diffraction order), they used the complex addition of
multiple individual holograms. This, however, creates a complex field
often with extra, unwanted light spots known as ghost traps. The problem
is that, in addition to the continuous vertical difference in phase, their
“desired field” (for creating these two spots) contained a square-wave
profile on the horizontal axis that can’t be reproduced with a phase-only
SLM. Therefore, the SLM output looked as follows:
The high contrast between columns resulted in more high spatial
frequencies being present in the first diffraction order. To correct for
this, they created a phase profile on the SLM in which the phase contrast
was decreased near horizontal phase jumps. Therefore, when they
subtracted their “desired field” from the SLM output, the “left over”
field contained very little phase modulation, as seen below:
The unwanted light is now concentrated in the zeroth diffraction order
(i.e. not diffracted because low contrast means low spatial frequencies,
which remain in the center of the Fourier transform). The overall
intensity of the resulting first-order diffraction pattern is decreased,
but it also no longer contains the unwanted ghost spots.
Laser Sam and Dr. Noé showed us an example of laser-induced
fluorescence with the green Lightwave NPRO laser (~50mW) in the side room
and a glass cell with Iodine gas. When we shined the laser through the
cell, it excited the gas’s molecules, causing a sharp green/yellow streak
to appear in the laser’s path (at certain times because of the
fluctuating laser). We also tried shining the green laser
pointer through, and it was able to create the same reaction at certain
locations. Dr. Noé said that a green HeNe could also be used, and that
there would even be a weak reaction for a red HeNe. This paper
discusses a more in-depth study of the phenomenon.
Image Source: Bayram
and Freamat (2012) Sam was able to get the temperature-stabilized laser somewhat running -
with this laser, you can see the oscillation between its two orthogonal
modes by sticking a polarizer in the path of the beam and watching the
beam alternate between getting dimmer and brighter. There’s also a
feedback circuit, which has LED lights that show you how the laser
switches between modes. (The feedback circuit switch: angled away from
the board is ON, straight up is OFF, and angled towards the laser is
LOCK). After the laser heats up (~20 minutes), one can then flip the
switch to LOCK. However it turned out there was an issue with the circuit
board’s feedback mechanism, so he’s going to bring that back home with him
to work on.
Dr. Noé pointed out an article in APS News, Physicists
in Outreach Face Tricky Career Choices, which describes the delicate
balance between the need for outreach in the physics community and the
need for an individual to establish his/her career. According to the
article, older physicists often frown upon physicists earlier in their
career for partaking in outreach for not being as serious about their
scientific work. Those interviewed for the article suggest outreach
should be a more of a hobby until a physicist actual establishes
him/herself in the field; however for some, it may suit them better to
pick up outreach as an actual career. It all depends on the individual
person’s interests and goals, and there will inevitably be tradeoffs.
One of the physicists from the article particularly intrigued me - Sidney Perkowitz, a physics
professor at Emory University. He was noted as publishing over 100
scientific articles and many works geared towards non-scientific audiences
(e.g. five books, 2 plays, one performance dance piece). I looked him up
on Google and found a biography on his personal website; the first
sentence read: “Sidney Perkowitz is that rare blend of scientist and
artist—a whole-brain thinker.” Wow! If only I had gone to Emory… The type
of work he’s done is what I eventually would like to do – communicate
interesting/important scientific phenomena and discoveries to the
non-scientific community in various artistic forms.
One of the plays
he’s written is titled Glory Enough, which follows the life and
accomplishments of Rosalind
Franklin. Franklin performed an integral role in Watson and
Crick’s discovery of DNA’s double helix structure, however she
received none of the glory. The play captures this injustice and delves
into male views of women in science. His performance-dance piece, titled
Albert and Isadora, portrays a series of interactions between Einstein and
Isadora Duncan
(who I learned about in a Dance and Culture course I had taken at
Dickinson). Duncan was an American dancer who had an integral role in the
development of Modern
Dance at the turn of the 20th century, but the play’s dialogue reveals
the similarities in her dances and views of the universe to Einstein’s
theory of relativity.
I also updated the Laser Sam visit
page.
Today I added a lot to my Summer 2013
page. Dr. Noé wanted to make sure we keep a record of Laser Sam’s
visit, so I created a page to
document the various events from the week. This includes a separate place
for information on the Pizza
lunch meeting.
I also typed up a page for Marty’s guide
to cleaning lenses and mirrors, which I hope will be useful for
current and future LTC students.
In the afternoon, Sam gave a very informative talk on laser safety. He
described the dangers that lasers can pose, different classes of lasers,
and good habits to get into when creating setups. All of the details can
be found on the safety
page of his Laser
FAQ.
Dr. Noé showed us how one of the IR Cards (infrared
sensitive card) works by first exposing it to visible light and then
holding it in front of the IR beam. Then, you have to keep moving the
card around to reactivate the spot that had come in contact with the beam.
In the morning I worked on putting together a short presentation to
give an update on the Cambridge Correlators SLM and Padgett article that
goes along with it. (In the afternoon I typed this information up and
made a separate
page on my website, which I hope will be a good introductory resource
to future students who will be using the SLM).
At our pizza lunch meeting, Laser Sam gave a very comprehensive
presentation on the different types of lasers, longitudinal modes in HeNe
lasers, and using a scanning Fabry-Pérot interferometer to analyze these
modes. Afterwards, each student presented a short update on his/her
progress in experimental setups and/or literature research. I’ll
summarize the information on a separate page tomorrow -
Since Kevin needed some space on the table in the main room, we took
apart and packaged some of Bolun’s setup
where he studied evanescent waves. For future reference – the box
(labeled of course) is in the back electronics room on a shelf.
Today I read through part of: Independent
phase and amplitude control of a laser beam by use of a single-phase-only
spatial light modulator. The main idea is that Bagnoud et al
(2004) use a phase-only SLM for amplitude modulation by placing a low-pass
spatial filter in the Fourier plane of a 4-f setup (in which the
SLM output was the “object”). It appears that they’re using the SLM to
modulate the phase of the input laser beam at high spatial frequencies,
and then cutting them off with the spatial filter in order to achieve the
amplitude modulation.
I tried to help Kathy find some gold mirrors for her setup, but it
turns out most he ones (pieces) we have are heavily scratched. There were
also a lot of somewhat dirty optics, which prompted Marty to give us a
short demo on how to properly clean them – he showed us with a plane
mirror and with the dichroic lens. I plan to write this up on a separate
webpage later in the week.
After the students left for lunch at the SAC with Laser Sam, Marty and
I discussed progress current student projects. It’s crazy how fast the
summer is going – the undergrads have been here about 6 weeks, the Simons
students 4 weeks, and this will be the end of Samantha’s second week.
There’s a lot still to be done, but just from the students’ journals alone
it’s clear that we’ve got a very serious and dedicated group this summer.
I organized the spatial light modulator binder and added a few more
articles that I thought were relevant. I also included information on the
Cambridge Correlator devices that we purchased. It turns out that Azure (?) had already
started a “Liquid Crystals & SLMs” binder – it was up on top of Dr. Noé’s
bookshelf! At some point I plan to go through and consolidate these into
one resource.
Marty found an article from Padgett’s group on the Cambridge
Correlators SLM - Optimisation
of a low-cost SLM for diffraction efficiency and ghost order
suppression. It describes how increasing the contrast in a blazed
diffraction grating code for the SLM output optimizes the device even with
its shallow phase depth (~0.8 Pi). I haven’t read through the entire
article yet, but I’ll explain some of this at the lunch meeting tomorrow
during my update.
In the morning I did a notebook check where I briefly looked over each
of the Simons’ students' lab books and gave them some comments. Overall,
they looked really good! Everyone seems to be off to a great start and
following most of the criteria listed on my advice
page.
Laser Sam came
today! We had a great LTC lunch at the Simons Center Café, and then he
immediately started getting involved in the long list of laser projects we
had for him this week.
We’ve decided to purchase two SLMs and one laser module from Cambridge
Correlators, who offered us a nice volume discount. They said that
they would be able to ship before the end of the month, so hopefully we’ll
be getting these devices in time for students to use before the summer
program finishes.
I also updated my resources
page today by adding a section on popular SLM and optics companies.
(Eden
suggested we keep ValueTronics
in mind for inexpensive new and used testing equipment).
In the morning I reviewed the “maximum angular resolution of the human
eye” estimation
problem - it was great to hear that all of the students approached
the problem in a slightly different way (William described his creative
method in his July 12th journal
entry), but our answers were all basically within one order of
magnitude of each other (7 x 10-3 radians to 8 x
10-5). The new problem that I gave them to think about over
the weekend is:
If we covered all of the roofs of
buildings on Stony Brook campus with solar cells, how much energy could we
produce in 12 hours? [J] and [kWhr] I finished up my
colloquia
page with the list of relevant talks, abstracts, videos, and
links to information about each speaker, so that’s up and running!
Samantha gave us a very informative tutorial on Python. It seems to be a great tool for
analyzing large amounts of data, especially when having to pull from
multiple files. We also spent a good amount of time in the conference
room exploring different topics with the AJP and Optics Infobase databases. I
decided to include links to these on my resources
page.
I spent some time shrinking the file sizes of some of the images on my
laser account (I had a lot of large photos from the
REU
symposium
from last summer) using the convert and resize command:
There are still a few particularly large files in my home
directory (e.g. pdf files of presentations and my senior seminar research
poster) that I’ll have to shrink down as well at some point.
Dr. Noé briefly mentioned a parable story that he couldn’t quite
remember the details of, but thankfully there’s Google! It’s called the
Blind
Men and An Elephant, and there are numerous versions of it. Most
revolve around the idea that there are a group of blind men in a room with
an elephant; each man touches a different part of the elephant and
therefore when all of the men converse, they are in disagreement about
what they are touching. There’s a great line on Wikipedia that describes
the message of the parable: “While one's subjective experience is true,
it may not be the totality of truth. Denying something you cannot
perceive ends up becoming an argument for your limitations.”
Today I contacted Cambridge Correlators
regarding their SDE1024
Low Cost Spatial Light Modulator. The representative that responded
said that we could get a volume discount, and that the device can be
shipped before the end of the month. He also suggested we buy their laser
module to be used in conjunction with the SLM. We’ll have to do a
little more research into these options, but hopefully in the next few
weeks we can acquire this inexpensive SLM.
Dr. Noé asked me to go through Stony Brook University’s physics colloquia
pages and pick out all of the ones that are relevant to the LTC. It
did take quite a while to browse through the lists, there were separate
pages for each academic year over the past six years or so (which is part
of the reason why I’m doing this, so it’ll be easier to find the ones that
LTC students are most likely to be interested in). I’ve also started
organizing this list on a separate
page, which is still clearly under construction!
Today was Samantha’s first
day! I presented her with her LTC lab notebook, mini “on-the-go”
notebook, and gave her a brief tour around the lab. She then gave a great
talk at our pizza lunch about her research and experiences as an Intel
finalist. Afterwards the LTC students each gave a short update on what
they’re working on.
The third part of the lunch meeting consisted of looking through some
old collectible books that Dr. Noé picked up during his trip to Ithaca.
I really enjoyed flipping through all of them. A treatise by William Hershel
reminded me of my visit to a museum
dedicated to him and his sister Caroline as
part of my History of
Science course that I took in England. (The museum was in Bath in a
tiny three-story home just in the middle of a residential area.) I also
found Lord
Kelvin’s particularly interesting because he mentioned a lot about “ether;” reading
books like this are a great way of seeing into the minds of scientists at
the time. The illustrations are also incredibly intricate and the writing
in general is very detailed.
At the end of the day, I helped Stefan set up the CCD
camera for taking pictures of his optical vortex. Dr. Noé ended up having
to get a new monitor from another computer, but once we finally got it to
work, I gave him a short tutorial on using the Electrim EDC 1000N software
for image capture.
In the morning, I reviewed the Umbilic Torus estimation problem with
the Simon’s students. For the first part, regarding the two lenses that
would be needed to expand the beam enough to fill the aperture, we were
all around the same order of magnitude for the ratio of the first lens’s
focal length to that of the second (103), and our actual
distances to the far-field ranged from high 103 to low
105. Examples of how this problem can be done are in Kathy’s
July 8th journal
entry and Kevin’s write-up
of the problem. The next problem is to estimate the maximum angular
resolution of the human eye (i.e. what is the smallest item we can see at
a certain distance, based on the limitations of the eye). I updated the
estimations
page.
I also cleared up a small mistake I had made regarding the resistor we
used in the photodiode connection for the Simon’s students’ mini project –
I had mistakenly explained the resistor’s function as if it were in
series. But seeing as it is connected in parallel, it acts like a
current-to-voltage converter. Without this, the AVO meter wouldn’t be
sensitive enough to pick up the current created from the laser beam’s
interaction with the photodiode. The larger the resistor, the more the
signal will be amplified.
For most of the afternoon, I helped Kathy start on her optical tweezers
setup. We began by measuring the reflectivity of the dichroic mirror
(reflects red light, transmits all other) that she’ll be using and
noticed some interesting spots on the mirror (which Marty helped explain
later as a product of scattering when light was directed at the "wrong"
side of the dichroic mirror). Afterwards did some brainstorming with Dr.
Noé about possible ways to
raise the laser up to the height that she’ll need the beam to be at.
At the end of the day, I was able to finish up my page
for the square aperture diffraction mini project that Rachel and I worked
on last week.
The hunt for an SLM continues!
Marty heard back from Prof. Pearson at
Dickinson about the spatial light modulators that he’s worked with.
Evidently the Holoeye
LC-R 2500 (discontinued now) and Holoeye Pluto NIR-II (trial model)
both had significant phase-to-amplitude leakage. If I understand
correctly, it seems that the issues he describes were due to the coupling
of phase and amplitude modulations.
Dr. Noé had a long discussion with Kiko
Galvez about the spatial light modulators that they use in their
optics labs at Colgate University. He suggested we go with the Hamamatsu,
however he also pointed out a very low cost SLM kit (the SDE1024)
from Cambridge
Correlators. (I had actually used information on optical
correlators from this company’s website when I was doing research into
the various uses for SLMs). The device is a TN LCOS and doesn’t have a
very substantial phase depth (only 0.8pi at 633nm). However if we were
just using it for amplitude modulation purposes (e.g. to explore
diffraction through various apertures or masks), I think that this
inexpensive spatial light modulator would be a great addition to the LTC.
Kathy has been doing a lot of literature research in optical tweezers,
and it seems that she has a lot of good ideas for potential projects.
The first step will be to rebuild the inverted
optical tweezers setup that Hamsa used (later we
could also try making the tweezers from optical
vortices). We’ll need to track down all of the parts, clear off the
table with the microscope, and get the laser set up. Even before any of
this, a good introductory activity that I helped get her and the other
Simons student started on was to (1) practice creating a beam expander
(which should help with the estimation
problem for this week!) and then (2) profile the resulting beam with a
photodiode. I then had them plot their data and fit a Gaussian equation
to the curve.
Marty came in and explained that the beam could be cleaned up by
putting an iris diaphragm at the focal point between the two lenses of the
beam expander and also cleaning the lenses themselves. (The profile that
the students graphed had a strange double peak; even by eye, you could
tell when looking at the beam that it was a little messy). Marty also
said that he would give us all a little lesson on how to properly clean
lenses at some point later this week.
This morning I reviewed the “homework” estimation problem with the
Simons
students - Kevin and Kathy had both estimated 1 x 106
m3, William was also on the 106 order of magnitude,
and I estimated a high 105 volume. It’s great to see that we
were all relatively close! (Kevin wrote up
a very nice description of how he did the problem in his July 2nd journal
entry). The problem for next week is as follows:
If we use a red HeNe laser and Stony Brook’s Umbilic Torus as our
aperture:
What are the focal lengths of the lenses you would need to
expand the
beam enough to fill this aperture?
How far would we have to go to see the far-field diffraction
pattern? Now that Kevin had his camera with him in the lab today, we redid the
diffraction setup and again sent the laser beam through a square and
triangular aperture (separately) to observe the pattern across the lab on
the door. These photos came out slightly better than the ones on Rachel’s
phone, however it was still hard since the camera doesn’t have as large of
a dynamic
range as the human eye. The extra-bright center of the diffraction
patterns made it hard for the camera to register the lesser-intense side
lobes.
Rachel caught a minor mistake in the calculation we did with Marty
yesterday – we had used the equation to find the distance to the first
minimum in the square aperture’s intensity pattern on the door, but had
incorrectly multiplied our answer by 2 instead of 3/2 to find the location
of the first maximum intensity peak after the central one. Our
calculation is now about 9mm.
We also re-measured this distance experimentally and found that to be
about 9mm! (Note, this measurement was just from marking the distance by
eye, so there is some uncertainty there that we should account for if we
were doing a further study on this; but since this is just a
mini-exploration of diffraction, our measurements aren’t that precise).
I decided to make a separate page to show the calculations and setup,
which I’ll finish up over the weekend.
Today we got to start some hands-on work – recently, Rachel has been
reading about elastic
light scattering and how various bacteria colonies can be identified
based on their diffraction patterns; she therefore wanted to start by
observing the diffraction patterns that are caused from different shaped
apertures. We used the red HeNe in the back room with three different
apertures: circular with diam=200 μm, square with side=1.4mm, and
triangular with side=1.7mm (the square and triangular ones were originally
from David’s
project).
At first we set it up somewhat crudely, trying to bend the laser light
around a little bit in order to avoid disturbing Stefan’s setup. We were
able to observe the Airy pattern, but the others didn’t look that great.
I gave a brief explanation to the students about pinhole diffraction,
Fourier optics, spatial frequencies, and near versus far-field
diffraction, and I also mentioned the mini
project I did last summer.
After lunch Marty stopped by and helped us set up a beam expander for
our setup; we then turned off all of the lights and projected each
aperture’s diffraction pattern across the lab to the far door. It was
pretty neat to see the square and triangular aperture patterns – the square
aperture diffraction pattern had two-fold symmetry with a very bright
square in the center and smaller less-intense squares coming off in a
cross shape; the triangle aperture had a bright triangular shape in the
center and two layers of three-fold symmetric arms coming off of it. We
were unable to take pictures of these, but below are examples from outside
sources that look similar to what we saw. Hopefully on Friday we can use
Kevin’s camera.
Marty also suggested calculating the distance to the first minima and
comparing that to what we experimentally observed. While the diffraction
pattern for the square pattern was projected across the room, we marked
where the central maximum and first order maximum were on a sheet of
paper. We then decided to first calculate the distance we’d have to be in
order to see Fraunhofer diffraction, since these apertures were relatively
large, and afterwards we calculated where the first bright spot should be
and it was pretty close to our measurement!
[Note: these calculations are in the next journal entry, after we fixed
a couple of minor corrections]
I started off the morning by giving a brief introduction to estimation
problems (aka Fermi estimates) for the high school students and walking them through a simple
example: “How tall is a stack of a trillion one-dollar bills?” I
explained the basics about how to approach these types of problems, and
together we estimated that it would be about 2 x 105 km high.
The final important thing to do with estimation problems is to make the
answer relatable. For instance, 105 km is somewhat abstract –
it’s such a large number that we can’t even really comprehend what it
means. We decided to compare it to the circumference of the earth and
found that our stack of bills would wrap around the earth about 5 times!
The “homework” problem I gave them for this week was to figure out
“What is the volume of rubber warn off of all the tires in the U.S. in one
year?” in cubic meters. This is a problem I had to work on for my senior
seminar class last semester. I think that it’s a good starting estimation
for them to make, since it has multiple parts to account for, but it’s not
overly complex. In the upcoming weeks, I’m going to try to develop some
questions that incorporate optics topics. I also created a new
page to keep a
running blog with the problems and results we do together.
I also finished my Introduction
to Spatial Light Modulators page. Hopefully this will be a valuable
resource for LTC students to use once we purchase an SLM.
An interesting article that I started to read, Spatial
amplitude and phase modulation using commercial twisted nematic LCDs,
used a spatial filtering technique to combine four neighboring pixels into
one “super pixel.” This method uncoupled the phase and polarization (for
amplitude) modulations (which normally is an issue with LC SLMs), and the
researchers were able to very precisely modulate the phase and amplitude
for each of these super pixels.
Dr. Noé and I spoke about the various events, talks, and visits for the
coming weeks – there’s a lot we’ll need to squeeze in before the summer is
up! I’m going to start working on an online schedule to keep it all
organized. A previous LTC student, Sage, had created a calendar on her
webpage, so I’ll probably borrow the format from her.
I spent some time in the morning reading over the Simons/LTC Fellows’
journals and providing comments/suggestions. It’s great that each of them
avidly records their daily activities, and it’s interesting to hear what
they’re learning about. I even learned a few things too (e.g.
optical
tweezing, anamorphic
formatting,
sonoluminescence,
etc).
I also created an introduction
to SLMs page on my website using the information from my presentation
with a little bit more detail. I’m almost finished - should be done with
in the next couple of days. I then reorganized my website and made a Summer
2013 page.
This morning we had a white-board talk about double-slit interference.
Dr. Noè asked the students to derive a function to describe the intensity
I(y) of the interference pattern of a wave with wavelength λ on a
screen that was a distance L away from two slits (which were a
distance 2a apart), introducing only the binomial approximation and
the complex notation for waves. The students made very quick work of the
derivation! (Maybe even quicker than Marissa, Jonathan, Ariana, and I did
last summer).
We then talked a little bit about LaTex – Rachel presented a useful equation editor
that lets you create images of equations using LaTex codes, but there’s an
option to choose the symbol by sight instead of having to remember how to
code each symbol. This reminded me of another website I had used, Detexify, where you
can actually draw the symbol that you’re thinking of to find out its code.
Afterwards I gave a brief introduction to the actual text-editing program,
TexShop, and showed how to use some of the important features with my
honors thesis as an example. (I remembered later that TexShop is only a Mac
program, so editing may be slightly different for the Windows version of
the program, MiKTeX. However, the
symbols and codes will be the same for any version.)
I started a resources
page where I plan to put links to outside sources that I’ve found
useful. So far I posted a few things about LaTex (e.g. a tutorial from
Dickinson, where to download different Tex editors, and where to find
codes for mathematical symbols). I’ll continue to update this as the
summer goes on.
Dr. Noé picked up on a small typo in my journal entry from Wednesday,
where I misspelled Casey’s name with a “K.” I think the mistake stemmed
from the fact that this summer I’m working with Casey and Kathy, however back
home I know a Kasey and Cathy - so one can see why I might occasionally
slip up with the spelling :)
The search for an SLM for the LTC continues! I heard back from a
Boulder
Nonlinear Systems representative, who gave us a quote (for an SLM designed
to provide 2Pi phase shift at 633nm) and a helpful description about how
BNS SLMs compare to other companies.’ For the
XY Nematic
Series
(reflective) SLM, BNS pays special attention to:
Refresh rate: other companies design their SLMs to function as
microdisplays, therefore there are often “phase ripples” because the
refresh rate is too slow to sustain a constant phase value across each
pixel
Reflectivity: other companies will often directly coat the silicon
chip with a dielectric mirror, not paying attention to the fact that this
results in a series of grooves to appear where the pixel gaps are located,
therefore often causing higher order diffraction
I also contacted the Dickinson student who made and SLM from an LCD
projector for part of his senior research project. He used the
AJP
article we were
looking at and said that it was fairly straightforward to convert the
LP1000 projector. However, the pixilation of the LCD panel created a
diffraction pattern that interfered too much with the diffraction pattern
they were trying to program for the SLM. In the end they decided to put
it aside because they couldn’t create any useful output from the device.
This will be something we should probably consider – maybe there’s a way
to make an SLM with the instructions from this article using an LCD panel
with a larger fill factor.
An article by Bowman, Wright, and Padgett - "An
SLM-based Shack-Hartmann wavefront sensor for aberration correction in
optical tweezers" - describes how an SLM could be used as a
closed-loop adaptive optics system (functioning as both the wavefront
sensor and the corrective element) for estimating and correcting
aberrations in holographic optical tweezers (HOT). This is based off of
the idea of a Shack-Hartmann
wavefront sensor: an array of lenslets that focus a collimated beam
into an array of spots; the displacement of each spot is proportional to
the tilt of the wavefront at that point (which is integrated to obtain
phase information).
Bowman et al segmented the active area of an SLM into an array
of
circular apertures (each with a different
blazed diffraction
grating).
They then used a lens to focus each aperture to a spot into an array on
the sample plane. By looking at the distortion of the array (which can be
seen by eye!) they were able to estimate the tilt of each region on the
SLM. From here they were able to estimate a phase map of the aberration
and subtract this from the hologram to correct the wavefront.
Dr. Noé pointed out a recent AJP article (submitted Jan 2013): "Reconstructing
the Poynting vector skew angle and wavefront of optical vortex beams via
two-channel moiré deflectometery." The article talks about splitting
an optical vortex beam and sending each arm of the beam through a pair of
moiré deflectometers. (Moiré
deflectometry is an interferometry technique that uses a pair of
transmission gratings to create a fringe pattern that corresponds to the
optical properties of the object being tested). The research group then
described how the moiré deflectogram revealed a relation between the skew
angle of the beam’s Poynting vector
(directional energy flux density) and l value (topological charge).
Last summer when Jonathon did his project on optical vortices and Ariana
was looking into moiré patterns, we had thrown around the idea of trying
to combine the two projects; if only we had followed through!
Today we had our pizza lunch
presentations, and there was a pretty good turn out. I gave my talk
on “An introduction to spatial light modulators,” which I’d like to turn
into an informational page on my website. Stefan and Casey discussed
previous research projects on optical vortices and HeNe laser modes,
respectively, Rachel explained how light scattering patterns can be used
to identify various colonies of bacteria, Kathy and William gave very
informative talks about optical tweezers and 3D effects in film,
respectively, and Kevin described some of the research he had done at the
University of Minnesota.
Afterwards, we talked with Dave Battin in the LTC.
He showed us his Pico
Projector - a pretty neat pocket projector that he was able to hook up
to iPhone. We also talked about spatial light modulators and the
possibility of making our own, since Dave knew someone who had done the
electrical wiring for a similar project.
There’s an AJP
article (from Huang et al) that gives detailed instructions on
how to turn a low cost LCD projector into a spatial light modulator. The
article gives a brief introduction to transmissive TN LCD SLMs, which
describes amplitude modulation from a different polarizer configuration
than
Boruah's AJP article - Boruah explains that due to the orientation of
the polarizers at the entrance and exit face of the LCD, light is blocked
when there is no electric field, whereas Huang et al explain that
the polarizer orientations they’re using block output light when there
is an electric field. The underlying principles are still
consistent with the fact that the TN liquid crystals will rotate the
polarization of incident light when there is no electric field.
Huang et al mention that they start with an Infocus LP 1000 LCD
projector that uses SONY LCX017AL LCD panels. I looked up the datasheet
for these LCD panels and found no information on the pixel fill factor.
This is an important parameter that will affect the overall effectiveness
of the device. At Dickinson, one of the other physics majors actually
turned an LCD projector into a spatial light modulator for his senior
research project. I vaguely remember that he was having issues with extra
diffraction patterns because of gaps between the light-sensitive areas of
the pixel, so much so that he was wasn’t able to get a clear output,
(which he mentions in our class
blog). However, I heard about this before I had a good understanding
of how SLMs work, so I’ll have to contact him to find out more.
I also spent some time cleaning up my Linux directories by making
sub-directories to organize images and files from my Bessel beam project,
Airy beam mini project, research journal, and SLM research.
Today I worked on my spatial light modulator presentation. Since these
talks are meant to be informal and encourage conversation, I’m just
putting together a few slides to help organize what I’d like to say. I
figured the best way to communicate what I had read about would be to
first introduce some applications, describe the basics of what an SLM is,
go into more detail about electrooptical liquid crystal SLMs, and then
explain how a couple of example models work.
The two examples I’m going to talk about are an optically-addressed PAN
SLM and an electrically-addressed TN SLM. I’ve already read a lot about
the latter, but I decided to look more into how the reflective,
optically-addressed PAN works. There was one particularly useful article
in Optical Review,
Phase
Modulation Characteristics Analysis of Optically-Addressed
Parallel-Aligned Nematic Liquid Crystal Phase-Only Spatial Light Modulator
Combined with a Liquid Crystal Display.
Rachel told us about a great website for making
diagrams/charts/schematic
called Creately, so I’m using that for most of
the
figures
in my presentation. For example, I was able to create this one to
describe how a parallel aligned nematic liquid crystal cell worked:
This morning there was a breakfast for the Simons program, where we had
the chance to meet the three Simons/LTC Fellows who will be working in our
lab – Kathy,
William, and
Kevin. Afterwards
we
invited
the students and their families to the LTC for a few demonstrations (which
included activities with the pig toy, the optical fiber bundle,
polarizers, the oscilloscope, the large interferometer setup, 3D glasses,
and finished with using magnifying glasses to burn black paper in the
sun). We then had a welcome lunch in the Simons Center Café with Marty.
The afternoon was spent talking about (1) titles for our lunch meeting
talks
this Wednesday, (2) how to keep a good lab notebook (all of the details
can be
found on my Advice
on notebooks page) and (3) how to edit the students’ web pages (Rachel
made a
very useful Linux
guide
for beginners).
On an unrelated note, Marty mentioned an exhibit
currently at the Guggenheim by James Turrell, which
explores perception, light, color, and space. Among other works of his on
display, Aten
Reign is particularly interesting; it’s an installment in the main
rotunda of the museum that transforms both the natural and artificial
light in the space. Using hundreds of LEDs and a few large concentric
fabric
circles suspended from the ceiling, Turrell created a mesmerizing display
of light that plays with the viewer’s experience of both space and time by
means of the Ganzfeld effect –
a phenomenon in which a person exposed to a uniform field of color
experiences a loss of visual perception and/or hallucinations. The
exhibit runs through September, so I may try to visit on a free weekend or
at the end of the summer!
As far as the hunt for an SLM: the Holoeye representative I’ve been emailing
with said that we would be able to achieve about a 1.5Pi phase shift with
a 632-nm laser, and that unfortunately they do not sell the discontinued
devices. I also contacted Boulder
Nonlinear Systems about their two
dimensional spatial light modulators, just to see if that’s another
option for us.
I looked over the LC 2012 user manual – most of the information was
already online,
but there were some important passages about the connection scheme and
sequence for powering up the device (i.e. HDMI cable, then power cable,
then USB). An AJP article from 2009 actually went into detail about using
the LC 2000 (basically the same as the LC 2012, just with a lower
resolution) with a 632-nm laser: Dynamic
manipulation of a laser beam using a liquid crystal spatial light
modulator, by B. R. Boruah. The article described the theory
behind TN LC (twisted nematic, liquid crystal) cells and how polarizers on
either end can achieve amplitude and phase modulations; they use a
computer generated holography technique to achieve the desired optical
wavefronts. Boruah also mentions one key issue stemming from the LC
2000’s poor fill factor (around 50%) - there are optically inactive gaps
between adjacent pixels, therefore even when a uniformly bright or dark
image is sent to the cells, there will be extra diffraction orders present
besides the 0th order.
Something else that might be useful to consult is Experiments
with the HoloEye LCD spatial light modulator from an MIT research
group, and I want to look more into the birefringence
of liquid crystals as well.
I contacted Holoeye to ask about possibly purchasing discontinued devices
and to double check that the LC 2012 would be able to appropriately phase
modulate a 632 nm HeNe beam for our desired applications (optical
vortices, higher order Bessel beams, etc). Dr. Noé also suggested that we
contact Boulder Nonlinear Systems, to see what the cost and estimated
delivery times are for their SLMs.
After discussing my
Advice on
Notebooks page with Dr. Noé, I added a couple more things
and
made it a little more specific to researching in the LTC. Hopefully
future students will find it useful :)
I emailed back and forth today with Holoeye about their SLMs. The
representative I spoke with suggested we look at either the PLUTO, LETO,
or LC 2012 models for the applications I had described (vortices, Bessel
beams, etc). The PLUTO and LETO SLMs were both expensive, reflective PAN
LCOS (liquid crystal molecules aligned in parallel nematic on silicon)
whereas the LC 2012 was a more reasonably priced, transmissive TN (liquid
crystal molecules in a twisted nematic alignment). In addition to the
individual SLMs, there’s also an OptiXplorer educational
kit, which includes an LC 2002 SLM, laser, polarizers, and various
softwares for completing 6 experiment modules:
Using the SLM as amplitude modulator for image projection
experiments
Figuring out the parameters of the SLMs TN-LC cells by measuring
their Jones matrix (see below) components
Creating beam-splitter gratings with the SLM
Using Ronchi gratings for measurement of the phase modulation of
the SLM Computer generated holograms (with lens and prism phase
functions)
Interferometric fringe-shift measurement of the phase modulation of
the SLM
I think our best bet might be to purchase the individual LC 2012, which
seems to be a good fit and price range for the kinds of experiments we’d
be doing in the LTC. I looked up some of its specifications and found:
it can perform a maximum 2π phase shift for 532-nm light it has a resolution of 1024x768
with pixel pitch (size) of 36-μm and 58% fill factor (the ratio of the
light sensitive area of the pixel versus the total area of the pixel).
[A useful resource about pixel size and sensitivity can be found here.]
it can be addressed simply like an external monitor using a
standard DVI/HDMI interface or more complexly with the USB interface and
SLM software input The Holoeye
SLM software seems very impressive. Among various other abilities, it
can program the LCD to act as an aperture (e.g. rectangular, circular,
single slit, double slit), a lens (e.g. Fresnel zone,
Axicon), or create an image representation of a vortex phase! I found a
useful source from MIT about experiments
that can be done with the transmissive SLM from Holoeye.
As I mentioned above, one of the experiments from the OptiXplorer kit
dealt with the “Jones matrix” of the TN-LC cells. I wasn’t really
familiar with what that meant, so I quickly looked up Jones calculus.
Basically it’s used to figure out the resulting polarization of light
(which was already fully polarized) emerging from an optical element.
Jones vectors describe polarized light (e.g. linear x, linear at an angle,
right circular, etc), whereas Jones matrices represent various optical
elements (e.g. lenses, beam splitters, mirrors, polarizers, etc).
Therefore, to find the resulting polarization of light, you simply operate
on the Jones vector of the incident light with the Jones matrix of the
optical element it passed through.
I continued reading about SLMs today from two different sources: Hamamatsu
LCOS-SLM information sheet and Liquid Crystal
Spatial Light Modulators in Optical Metrology. [Also, for future
reference, I found a useful technical
glossary from Applied Materials, which helped with some of the
acronyms I came in contact
with.]
During our pizza lunch meeting, Marty brought up an article he recently
read about how researchers were trying to switch up how arithmetic is
taught in elementary school so that students aren’t simply memorizing
answers, but rather learning how to figure them out. It immediately
reminded me of a discussion I had had in my Introduction to
Discipline-Based Education Research course (Fall 2012 at Dickinson) about
how math is traditionally taught, but I couldn’t quite recall the details…
After looking over the blog
our class had kept, I quickly figured out that I was thinking about an
article by Richard Skemp, Relational
Understanding and Instrumental Understanding.
Instrumental understanding involves the memorization of rules and
mathematical situations to come to an answer; equations and theorems are
simply means to an end (for example: memorizing a table of the sine and
cosine of special angles). On the other hand, relational understanding is
achieved through conceptually appreciating the math behind a certain
result, through careful selection of a method to figure out the answer
(for example: using a unit circle and special triangles to figure out the
sine and cosine values). It’s hard to say which method of learning is
better: relational understanding clearly appears to be the more useful
type of comprehension, however instrumental understanding can make
complicated problems easier to work through in a less-discouraging amount
of time. If I become a teacher, I will probably try to incorporate both.
I started brainstorming some points about the lab notebook and research
journal that I definitely want to share with the high school students.
These are organized on a new page
that I created today. I also put a link for it on my main
webpage called “Advice for Notebooks” for now, but I’m not sure if I
want to keep that label or call it something different.
This morning we had a mini LTC meeting to plan out the upcoming
week because the Simons/LTC Fellows arrive on Monday! There’s a welcome
breakfast at 9am
for the Simons program, and then we’ll have an LTC welcome lunch at noon.
Also on Monday we’ll be distributing supplies (lab notebook, mini
notebook?, optics book?), teaching how to keep a good lab notebook,
and showing how to access and update their laser webpages. On
Wednesday during the pizza lunch meeting, each student will give a
10-minute talk on something they’ve been working on or some other relevant
optics topic. (I agree with Dr. Noé, this should be a good ice
breaker/get-to-know-you event!) At some point during the week, we’ll need
to also show the students around the LTC equipment and explain the lab
rules.
We got the printer on my desk to work! Well really all I did was plug it
into my Mac and press “print,” but for some reason it doesn’t work
that easily with
Windows computers. Until we buy a new printer, I’ll just be the
intermediate step for students who want to print from the lab. For future
reference, it’s an HP Photosmart C4480, and
here
is the fact sheet with cartridge information.
Since the Holoeye website doesn’t list prices for its devices, I crafted
an email asking for these, an expected delivery date, and the possibility
of getting an education discount for the LTC. Hopefully we’ll hear back
ASAP so that we can order an SLM and have it delivered in time to be used
this summer for research.
Dr. Noé showed Rachel and me an online optics textbook written by
Prof. Peatross (from Brigham Young University): Physics of
Light and Optics. For
future
reference, the textbook can be found
here.
I started making an
information
page
about spatial light modulators. There’s still a lot to
add/format, but it’s certainly a start! I spent a lot of time trying to
reorganize the information I got from the tutorial article I’ve been
reading (since the way they divided their topics wasn’t exactly the
clearest way of presenting the information), and soon I’ll also be adding
in info from
Azure’s
paper and other sources. Next week I’ll be giving a presentation on
SLMs
to the high school students at our pizza lunch meeting.
Today I spent most of my time reading more of
Two-dimensional
spatial light modulator: A tutorial. Some of the things I’ve taken
notes on are: (1) SLM applications-
optical
correlators
(very fascinating!),
optical
crossbar switches (used in broadcasting, also very interesting),
digital optical
architectures (for parallel computing), and displays (improving cathode
ray tube (CRT) systems). (2) modulation mechanisms- mechanical, magnetic,
electrical, and thermal. (3) modulation variables- intensity (amplitude),
phase, and polarization. (4) addressing modes- optical (with a special
detection mechanism) or electrical (which is functionally identical to CRT
displays). I’ve been writing everything up in my lab notebook, and
tomorrow I plan to start organizing the information on a webpage.
Using the
Holoeye website,
I’ve learned some more about the differences between each of their spatial
light modulator models. First of all, there are two types of liquid
crystal displays: LCD (liquid crystal display) models transmit the
incident light, while LCOS (liquid crystal on silicon) reflect it. There
are then three types of orientations for these microdisplay cells: VAN
(vertical aligned nematic), PAN (parallel aligned nematic), and TN
(twisted nematic), where nematic refers to liquid crystal molecules
oriented in parallel but not necessarily in well-defined planes. (Twisted
nematic orientation of the molecules means that there is typically a
45/90-degree difference between the top and bottom of the LC cell, where
the inbetween molecules are arranged in a helix-like structure). VAN and
PAN cells can only modulate the phase of an incident beam, while TN can
modulate phase and amplitude. There are several other distinguishing
characteristics of each model (as I mentioned in my journal entry from 13
June: resolution, input image frame rate, phase shift ability based on the
incident light wavelength limits, pixel pitch, and size of active area),
which I still need to do more research into.
Two-dimensional
spatial light modulator: A tutorial has proved to also be
a very useful and detailed source for learning more about SLMs. Some of
the things that I’ve read about so far- (1) the two overarching types of
modulators: electrically-addressed (which uses an electrical signal to
change a variable associated with the incident beam) or
optically-addressed (which uses one light beam to change something about
another light beam), (2) main functions: analog multiplication (when an
optical wavefront amplitude is modified by the reflectivity/transmissivity
of the propagation medium), analog addition (when the optical input
signals are summed), signal conversion (to various frequencies, incoherent
to coherent, etc), and thresholding (create a binary image from the analog
input). After I finish this article (which is pretty long and highly
technical), and also look over Azure’s paper and journal, I’m going to
organize all of my notes on SLMs into a separate webpage.
Random Find: From a convoluted chain of internet searches and page
surfing, I somehow stumbled upon a very intriguing
research
center
led by
an anesthesiologist Dr. Hameroff, which applies quantum mechanics to
theories of consciousness. As of right now, consciousness is something
that scientists still don’t know much about; even in medicine, it’s
unclear how general anesthesia actually works to bring patients into and
out of consciousness. Some
research
suggests that conscious thoughts and responses are products of signals to
stimuli that are sent backwards in time; using fMRI to monitor brain
activity while test subjects were shown a series of neutral or violent
images, Bierman and Scholte found that the subjects exhibited a
precognitive emotional response up to 4 seconds before the violent
stimuli were displayed. While there is still much research to be done to
come to more concrete conclusions about consciousness, I still think it’s
a very fascinating interdisciplinary field of study.
In the morning, we watched J. Eberly’s lecture “When Malus tangles with
Euclid, who wins?” on how the Bell inequalities do not hold up for quantum
mechanics. He began with a classical example with coin tossing, in which
there were three coins (penny, nickel, and dime) that could land on heads
(P, N, D) or tails (p, n, d). He set up an inequality that was always
true:
This is because both components of the total outcome for (N,d) are already
in the other parts of the LHS of the inequality. Therefore, the RHS will
always be equal to or less than the LHS. Eberly then transposed
the same idea into an example with 3 pairs of birefringent calcite
crystals (which have a different index of refraction for beams of light
with different polarizations), that have x/y, θ/Θ, and ϕ/Φ polarization
channels. He creates a (seemingly) similar situation to the three coin
toss equations by setting up three experiments with these loops (the
details of which can be read in his
article).
However, the Bell inequalities only work in a classical world when we know
the coin has to land on heads or tails, even if we’re not “looking”
at the outcome of that particular coin. In each calcite crystal
experiment there was always one loop that we didn’t “watch,” but in our
equation we assume the photon must have been polarized either one way or
the other. This is incorrect! Since we didn’t make a measurement, the
photon existed in a superposition of both states.
Dr. Noé asked me to do some research into
Holoeye spatial light
modulators since he’d like to buy one for the lab. An SLM in general
is a
device that can modulate (in space and time) the phase, amplitude, or
polarization of incident light waves. They have a liquid crystal
microdisplay that’s either translucent (LCD) or reflective (LCOS, liquid
crystal on silicon).
Holoeye currently has 5 different models: PLUTO (LCOS, phase only), LETO
(LCOS, phase only), LC-R 1080 (LCOS, phase and amplitude), LC-R 720 (LCOS,
phase and amplitude), and LC 2012 (LCD, phase only). Tomorrow I’m going
to read up on each feature of these models (type of LC microdisplay,
resolution of pixels, input image frame rate, wavelength limits, size of
active area, etc) to figure out which would be the best fit for our
research needs.
I found the AMO lecture this morning very interesting: A roadmap for the
production of ultracold polyatomic molecules, by
Dr.
Sotir Chervenkov. There are two methods that can be used to produce
ultra cold molecules: indirectly by combining ultracold atoms (which is
only applicable to a few dimers), or directly by decelerating a sample and
filtering out the slow molecules. While the latter has not yet been
achieved, this research group aims to combine three successful cooling
processes: opto-electrical cooling, cryogenic buffer-gas source, and
mechanical deceleration, in order to come up with a large sample of slow,
cold atoms.
Just an interesting note: the opto-electrical cooling portion is done by
means of a Sisyphus process, in which a finite well-like potential is
created to trap slow molecules; radiofrequency is then applied to trap
molecules in a more shallow potential. If we wanted to visualize this,
it’s as if the molecules are forced to continually “travel uphill,”
therefore slowing down. I then found out that
Sisyphus was a figure in
Greek
mythology who was forced to roll a stone up a hill for eternity in the
underworld; every time he reached the top, the stone would roll back down
to the bottom.
We were fortunate enough to have
Prof.
Eden Figueroa give us a tour of
his
lab, which is working on creating quantum systems that can be used to
transfer information. The “work horses” (as Prof. Figueroa called them)
that will carry this information are photons. Their aim is to create a
system without cooling atoms, which is a method used by other research
groups; this is because the eventual goal is to shrink down everything to
put into a computer.
He used a good analogy to explain the unique capabilities of quantum
computing and information exchange: If a regular car hits a fork in the
road, it needs to separately travel down each path to gain information
about them; however, a quantum car could simultaneously travel down both
paths and obtain information about them at once. As far as computing, our
systems currently use bits, which can be either 0 or 1; on the other hand,
quantum computing would make use of cubits, which can contain a
superposition of much more information at once.
Their research group is also working on creating a quantum memory, in
which the photon containing information can be stored and released later.
The lab is overall very clean and organized (it’s also very new, as of
February, so they’re still waiting on some more equipment). There are
large covered chambers for each piece of the experiment,
computer-controlled lasers, and wires and optical fibers running neatly
overhead in special enclosures.
At the Pizza Lunch we discussed important dates and the possibility of
having a reunion event in which previous LTC students would come back and
give talks. While it might be difficult to schedule one date that works
for everyone through email, maybe we can create a
doodle poll with a couple of weeks of
dates
and ask all of the nearby LTC veterans to let us know their availability.
Hal decided that this summer he would talk to us about entanglement, an
important phenomenon that distinguishes classical and quantum systems, but
is rarely covered in undergraduate quantum mechanic classes. He opened up
by explaining that quantum mechanics
violates our common sense because we live in a classical world, which is
completely true. The “sense” that we’ve acquired has come from a
collection of interactions and experiences from living in a classical
world; therefore we really don’t have any physical intuition about the
quantum world. So as strange as it may seem, we have to just accept the
fact that, before a measurement is made, the particle exists in a
superposition of all possible states.
Tomorrow Hal will show us Eberly’s lecture on the Bell inequalities, in
which he proves how the equations do not hold up for a quantum system.
I’ve seen the video once before, when Hal showed it to us last summer,
however since I’ve now taken a quantum mechanics course and learned a
little bit more about this topic, I feel like I’ll appreciate the lecture
more. That’s the thing about physics- sometimes you need to read/see/be
taught a topic many times over before you actually come to a complete
understanding of it. It’s usually difficult to grasp something
(especially as complex and strange as quantum mechanics) from just a
single exposure to it.
Dr. Noé brought out the 34th book in Encyclopedia Britannica’s series:
“Great Books of the Western World,” which contained the works by Newton
and Huygens. I flipped through it a little bit and found a few
interesting discussions about visible light in Newton’s
Optics section.
In Proposition 6, he discussed a detailed scheme for figuring out the
color and degree of its intensity for a certain mixture using a complex
color wheel.
It was a little difficult to follow at first, but interesting once I
understood it better. He simply used the geometry of the circle and
devised a method of taking into account the different quantities of
reflected light in each mixture to characterize the overall hue. In
general, the book was filled with very intricate propositions and
diagrams.
Today I focused on reacquainting myself with the Linux environment and
updating my webpage. The last time I had really altered anything was back
at the end of last summer, and as a result I had forgotten some essential
commands. For instance, I had thankfully written down my password in a
safe place, but then once I logged in, I realized I had no idea what the
next step was! But after rereading some of my old journal entries and
googling a few Linux/html help sites, everything starting coming back to
me. I successfully figured out how to change directories, list all of my
files, edit them, upload pictures, etc.
I then restructured my
main page
such that I could separate out the research I did
last
summer
from
the pages that I’ll continue to update this summer in a way that should be
easier to navigate. I also created a
new bio that
briefly
talks
about my research last summer, how I recently graduated, what I’ll be
doing here this summer, and my plans for next year. (I then put the
old one on the
Summer
2012 page). Finally, I updated my
presentations
page to include those that I made for my senior research project at
Dickinson, and also to add some pictures of the other students who were
involved.
Today was my first day back at Stony Brook. After quickly moving into my
summer housing, the LTC group had a wonderful lunch in the Simons Center
Café with Marty, Hal, and a couple other undergraduates as well.
We then spent some time cleaning up and organizing the lab before heading
over to the AMO Seminar by Dr. Stephan Ritter: “An Elementary Quantum
Network of Single Atoms in Optical Cavities.” A quantum network was
created between two spatially separated labs (connected by a 60-meter
optical fiber) using two single atoms as nodes. Each was trapped by means
of a Magneto Optical Trap (MOT), transferred into a cavity, and controlled
by means of a 3D optical lattice. A single photon was then produced using
a vacuum-stimulated Raman adiabatic passage (vSTIRAP). From what I
understood, information could then be exchanged, stored, and reemitted
between the two labs using the entanglement created locally between the
state of the atom and photon. This research has applications in quantum
communication, cryptography, and computing.
Following the talk, we went back into the lab to do a little more
organizing. I found an interesting article in Photonics Spectra while
sorting through piles of old magazines: “Photonics for Art’s Sake,” by
Hank Hogan (June 2007). The article talked about how photonics was used
in a variety of ways to preserve and restore works of art. For instance,
using what we know about the absorption of different wavelengths of light
by certain pigments and materials, we can alter how a painting is
illuminated such that it won’t shorten its lifetime. Another example
discussed how infrared reflectography could be used to examine the
underdrawing of a painting and possibly reveal hidden features; this is
because IR penetrates surface pigments, but is reflected by the prepared
canvas/wood underneath. While I had already heard about a few of the
methods discussed, I still enjoyed reading the article. I’m always
intrigued by the connections between physics and art, and conservation
science is one of the flourishing fields at this crossroads.
Today was the big day: our final presentations for the REU program. I
decided at the last minute before leaving my room in the morning that I
would bring my camera, and good thing I did! It turned out no one else
had brought theirs, so I became the official photographer for the event.
I put up photos from the symposium
here. Overall
I enjoyed the event. It was interesting to see the outcomes of everyone’s
projects, considering the past few weeks we only heard little snippets of
what each person was currently working on at our Wednesday REU meetings.
I felt like Marissa and I delivered our presentation successfully, and
I’ve put up the newest version on my
presentation page. Afterwards, Dr. Noé took the LTC group out to lunch at the Simons
Center Café, which was a delicious treat, as always. We then went back to
the lab to do some cleaning and neaten up the area around our setups. I
also picked out a few more tomatoes to bring home.
It was sad saying bye to some of the other REU students, some of whom I
may never get a chance to see again.. But I’m sure we’ll stay in touch!
Though I didn’t have to worry about saying a real goodbye to the LTC
group, since I’ll be seeing them again at the Rochester undergraduate
research symposium in October. Despite the fact that the Stony Brook REU
program has ended, there are still a few more loose ends to tie up with my
Bessel beam project. So as I continue to work on it, I will continue to
update my journal.
Today we all busily worked on putting the finishing touches on our
presentations and collecting last minute data.
Using the same technique I explained yesterday with the double-lobed ring
or light, I compiled an intensity profile of the Bessel beam at a distance
z=340 mm behind the final lens. (As expected, the central spot size
varies slightly in size and intensity over the axis of propagation). I
averaged the intensity of 10 different radial lines that stretched the
full diameter of the beam (which consisted of about 6 concentric rings).
The central spot size at this distance was 44.4 microns.
In total, I took 130 more images of the Bessel beam. First I took a
series of images behind the final lens, from 50 mm to 750 mm. By taking
out the variable polarizer and using a very long exposure time, it turns
out the camera can capture what’s going on right behind the lens! (Also-
by taking out the variable polarizer it turns out you can see the whole
evolution with your eye too—not the Bessel beam’s concentric rings, but
you can see the ring of light, the two lobes converging and then diverging
on either side, and then the bright center of the Bessel beam). I didn’t
worry about making sure there were no overexposed parts of the images in
this round, since I took these to qualitatively analyze the evolution of
the beam, instead of trying to quantitatively analyze the intensity
profiles and such.
Next, I took a series of images (from 70 mm to 470 mm behind the second
lens) of the beam created from a setup with a collimated laser beam going
into the OBJ aperture. This was done by using a telescope configuration—I
had a lens with a short focal length placed right near the HeNe and then I
used another one of the 333mm focal length achromats after this to
collimate the magnified Airy pattern. At the 1 mm aperture, the center
Airy disk was about 1 cm in diameter.
In front of the focal plane (which was at 293 mm… even with a collimated
beam), I did not observe the mirrored Bessel beam formation, as I had when
using an uncollimated beam. The center area was clearly brighter, but
there was no clear central circle; also, there were concentric ring-like
features. But the way this looked was incomparable to the very clear,
bright central circle and crisper concentric rings that appeared in the
Bessel beam after the focal plane. Interesting.. When I have time, I will
also string these photos into an animation and upload it to my webpage.
Today I worked on creating an intensity profile of the double-lobed ring
of light. I used ImageJ to determine a radial average by figuring out the
intensity across 20 different lines from the center of the ring to the
outside, subtracting background, and then graphing these all together. It
took me a while since I had to line up the peaks in each individual line
of data, but once finished, I figured out that the peak-to-peak spacing of
the double-lobed ring was 14.8 microns.
In regards to the brainstorming I had done yesterday, Marty said that the
part he’s unsure about is whether the delayed rays of light coming through
near the edge of the OBJ aperture become part of the outer lobe in the
intensity profile of the ring of light IMG. He suggested the best thing I
could do was to email the author of the 4-f paper and see what their
opinion on the matter is. It would also be interesting to learn if they
saw the symmetric Bessel beam evolution on either side of the ring of
light.
During the final LTC Pizza Lunch, Ariana, Jonathan, Marissa, and I
presented our research. It was a good way of hearing feedback and
practicing for the presentations we’ll be giving at the REU program’s
symposium on Friday. I received a lot of helpful suggestions and spent
the rest of the day improving my PowerPoint.
After a long day of working, Dr. Noé took us out to dinner at the tavern
restaurant of the
Three Village Inn, which served really good oysters! Afterwards we
went
to Pentimento and had dessert while enjoying another great jazz night with
Ray Anderson.
Today I figured out how to make an animated gif using ImageJ by stringing
together a series of images. So I created one of the Bessel beam evolving
from the ring source. On each image of the animation I included both a
1000 micron scale and the distance that it was taken from the final lens
in my setup. At some point when I have free time, I’ll put some of the
images and this animated gif up on my webpage.
I went back and carefully readjusted my setup so that all the distances
were the exact f distance apart. It was basically only the final
lens that needed adjusting, since it turned out to have been a full
centimeter too close to the spatial filter. But even after doing this,
the ring of light still came to a focus at 293 mm behind the final lens
(instead of at the expected 333mm). So this means that the too-close
focal plane was not caused by the misalignment of the setup. Maybe it has
to do with the fact that the input light beam at the object plane was not
collimated? I’ll have to see what happens when I rearrange my setup to
incorporate a collimated beam.
I've been doing a little more thinking about illuminating the OBJ aperture
with the image of the 150 micron pinhole instead of a collimated beam. As
I had figured out with Dr. Noé, illuminating the OBJ with a diverging
wavefront means that the light waves propagating through near the edge of
the aperture have a longer distance to travel than those in the center as
determined by the Pythagorean theorem (even though it is only a 1/16 of a
wavelength difference in phase). I think that if you carry this
information through the 4-f setup, it ends up helping in the end..
These delayed rays of light coming through near the edge of the aperture
become part of the outer lobe in the intensity profile of the ring of
light IMG (see intensity versus radius graph in Fig. 6 of
4-f paper). If you look at the graphs comparing the ring of light's
amplitude and intensity profiles (Fig. 3, (c) and (f) are clearest), you
see that the outer lobe of the intensity profile was the negative lobe of
the amplitude profile. Then if you look to the diagram (Fig. 1) that
shows the propagation delay between the lobes and how the constructive
interference of these creates the Bessel beam on axis, you can see that
the negative lobe is the one that is delayed (again, this can be
determined by the Pythagorean theorem).
Therefore, my thinking is that by adding the original delay of these outer
light rays (from the phase variation of waves illuminating the OBJ
aperture) to the delay caused by the geometry of the diverging thin ring
of light (Fig. 1), this increases the overall propagation delay between
the two lobes. Meaning, a longer Bessel beam should form.
Saying that the original phase variation helps the setup obviously goes
against the need for a "uniformly illuminated annular aperture" to create
a Bessel beam. However, as I discussed in my journal entry from
yesterday, this spatial filtering method is fundamentally different than
the one described by Durnin and Eberly. It depends on the propagation
delay between the two lobes of the thin ring to create the Bessel beam.
Tomorrow I’ll discuss whether this logic is correct with Marty and try to
figure out if it’s actually beneficial to illuminate the OBJ aperture with
a phase varying wavefront.
In the morning, Marty helped explain the Fresnel/Fraunhofer zones in my
setup that I was confused about. As I already understood, the distance
between the OBJ aperture and the first lens is subject to Fresnel
diffraction. Since the lens is placed one focal length away from the
aperture, we now are moved into the Fraunhofer diffraction regime. This
continues through the spatial filter to the second lens. Then after the
second lens, we are back in the Fresnel zone: the light rays converge
towards the focal point in the reversed way that they converged originally
from the OBJ aperture to the first lens. After they come to a focus to
form the thin ring, they start to diverge again, in a mirrored process.
(I feel like this mirrored Fresnel diffraction might explain why I’m
seeing a double Bessel beam form before and after the thin ring of
light..)
After going back through some of the new photos I took over the weekend, I
zoomed in on the Bessel beam ones using ImageJ and counted that the
average central spot size is about 5 pixels in diameter
(times 7.4 microns per pixel), which translates to about 37 microns.
Dr. Noé called me after he left to discuss the illumination of my OBJ
aperture. He says there is a slight phase variation of the light waves
passing through the center of the aperture versus those passing through
near the edge (which will have a slightly longer path, as clear from the
Pythagorean theorem). After doing the calculation, we came out with a
phase variation of 1/16 in the wavefront from the center of the aperture
to the edge. We can correct this by collimating the beam and/or sending a
beam through the OBJ that has a larger diameter. This can be done by
using a lens with a really long focal length or by using two lenses in a
telescope configuration: one to magnify the beam right after the pinhole
and the second to then collimate it. This way we’ll know there’s no
phase/intensity variation of the light illuminating the aperture.
On a different note, I finally think I’ve come to a pretty good
understanding of how spatially filtering this circular aperture creates a
quasi-Bessel beam, and the reason that we have to block some of the high
frequencies (even though we are trying to make an edge-enhanced image).
It starts from the fact that the amplitude of light going through a
circular aperture will resemble a square wave (see Fig. 2c graph from the
4-f paper); with no frequencies blocked, there is a little bit of a Gibbs
overshoot at the edge of the aperture (this in turn means that there is
always going to be a zero in the diffracted field of the ring source when
r = the radius of the OBJ aperture). Now with the spatial filter, it’s
clear that the inner diameter controls how many of the low frequencies are
being blocked. The outer diameter determines the shape of the
edge-enhanced image. The article describes how a ring image with a
well-separated double-lobed amplitude is desirable (as seen in Fig. 3c
graph). And this will of course still have the zero at r = radius of OBJ.
But if the amplitude lobes are well-separated from the zero, this means
there will be a propagation delay between them (as seen in the diagram in
Fig. 1).
It is the propagation delay between these two amplitude lobes that causes
a zone of constructive interference on axis, aka the Bessel beam! (If
there was no propagation delay, this would cause a zone of destructive
interference, and no Bessel beam would form). So, we want a large
separation between these distinct amplitude lobes. We can achieve this if
we diminish the overshoot at the edge of the aperture. (A useful
connection I made to understand this is visualizing the Fourier series
needed to fit a square wave with the summation of sines and cosines. The
more sinusoidal waves you use, the closer the overall curve will be to a
square wave; however, the Gibb’s overshoot becomes more prominent.) To do
so, we limit the number of high frequencies that are allowed through in
the
Fourier plane, aka using a spatial filter with an outer diameter limit.
So as the thin ring of light diverges, the double lobes of the amplitude
continue to be separated by the same propagation delay, but they begin to
spread too as you move along the z-axis, creating a line of constructive
interference on axis. Eventually at a certain distance away from the ring
source, the lobes have diverged to the point where they now destructively
interfere on axis, which corresponds to the end of the Bessel beam. This
also explains why you can’t include an extra lens at the end of the setup
to collimate the thin ring of light, as Durnin and Eberly did.
Collimating the thin ring would prevent these two lobes from diverging at
all, meaning they destructively interfere on axis from the start and you
don’t get a Bessel beam.
Just as a final note, I reworked my abstract with Dr. Noé and Marty for a
long time today. It’s sounding much more concise and almost ready to
submit. I now have a separate
page on my
website
for it.
Over the weekend I took a bunch more photos of my setup. I started by
recording the evolution of the thin ring into the Bessel beam behind the
last lens in the setup. This time, I took care to make sure I had at
least one photo taken with a 1 ms exposure time for every distance; this
way it will be easier to compare one photo to the next just by looking at
them. This was done with the initial pinhole of 150 microns, focused down
to a magnified image of 2.6 mm, sent through 1 mm OBJ aperture, and
spatial filter outer and inner diameters of 20 mm and 6 mm.
Next I tried using the Airy pattern to illuminate the 1 mm OBJ aperture
(in other words, with the lens removed from in front of the 150 micron
pinhole), but it didn’t seem like there was enough power in the beam by
the end of the 4-f setup. I probably will need a smaller inner diameter
for the filter or use a larger aperture, namely the 2.4 mm washer hole.
Either way, it would call for a lot of realigning, so I figured it would
be smarter to finish all the photos with this setup before changing things
around.
I next took a progression of photos along the 4-f setup (a) image the
Fresnel diffraction zone between the object and first lens, (b) image the
Airy pattern between the first lens and spatial filter, and (c) illustrate
the effect of using an annular filter by taking photos behind the Fourier
plane with and (d) without it in place. The one snag that I hit was that
once the computer memory filled up, it didn’t notify me, but instead
continued to “save” my photos. It wasn’t until I had finished that I
realized the second half of the images were “0 bytes” and couldn’t be
opened. So I had to spend some time redoing these…
I decided to take a break and work a little more in Beam2. I have my
setup basically all coded out with the correct measurements in centimeters
and the rays programmed correctly as far as I can tell. (I used the
Lensmaker’s formula to figure out the necessary “curve” value for my
lenses, 0.03, and measured the width and diameter to be 0.6 cm and 4.0 cm
respectively). But it seems like the rays in the diagram cross/come to a
focus before the final image plane in the setup.. I tried making a thinner
lens, smaller focal length, and even throwing off the distance for a few
of the optical elements. But in each case, the rays still crossed
slightly closer than the image plane. This is something I’ll have to look
into more..
Afterwards, I realigned everything so that my setup would work with the
central disk of the Airy pattern (which expanded to about 20 mm) going
through the 2.4 mm diameter aperture. But the ring of light was a lot
messier than it looked with the 1 mm aperture (it now has numerous
extraneous bright features in the center, kind of like in the photo on pg
232 of the 4-f paper). The Bessel beam wasn't as well defined, and it
only formed after the ring of light came into focus and not before.
Overall, it seemed like there was less intensity in the beam as it
propagated through the setup. (The messier ring could have been due to
the fact that the 2.4 mm washer hole didn’t provide as clean of an
aperture as the 1 mm pinhole.)
I then moved the camera behind the aperture, like I had done earlier, and
took a few shots of the Fresnel zone diffraction patterns; similar to
before there were areas where the center was bright and areas where it was
dark. I tried taking pictures of the beam after the filter but I couldn’t
collect enough light to find where the rays were. It’s possible that I
need to decrease the size of the inner diameter of the filter since the
larger OBJ aperture would create a smaller diffraction pattern in the
Fourier plane.
We've all got a very busy week ahead of us!
I spent a lot of time today working with Mathematica and attempting to fit
the intensity data for my Bessel beam at a certain distance with the
actual intensity equation, however it wasn’t fitting correctly. When I
plugged variables that Mathematica defined based on my data back into the
intensity equation, it did not produce a curve that resembled anything
like my data plot. So I’ll have to look into this more over the weekend
and see what’s wrong with the coding I’m trying to use.
After looking through the sequence of images I had taken of the evolution
of the Bessel beam, I marked out the distances where the beam formed and
where the rays were focused into a ring. The first beam started forming
(as in, there was a central core with concentric rings visible) at about
220 mm and dissipated (when there is no longer a clear central core) at a
little fewer than 270 mm. The ring of light came into focus at 293 mm.
Then the second Bessel beam started at about 320 mm and ended at a little
under 370 mm. The processes were mirror images of each other! I guess
that’s to be expected with ray geometry, however it was still interesting
to have calculated with the experimental results. It’s also curious to
note that the ring comes to a focus before the 333 mm mark… This could
have been caused by the distances being a little under 333mm between a
couple of the optical elements in the 4-f setup.
When I finish creating a ray-tracing model, I want to first see what the
ideal ray trace would look like with each element exactly 333 mm away from
each other. I then want to see how much the rays change if one or more of
the elements are slightly off of the f distance. It would helpful
to use the model for seeing the effect of changing the filter size and
even changing the object aperture size. I then want to change the filter
width in my setup and see if this affects the formation of the pre-focal
plane Bessel beam.
So I started putting in the actual values from my setup into Beam 2 and
learned how to include the annular filter. One problem I faced was that
the light rays didn’t seem to be affected when going through the lenses
because the curvature was so shallow (since a focal length of 33.3 cm
yields a radius of curvature of 66.6 cm and the program asks for the
reciprocal of this value, 0.015). So I decided I’m going to need to use
much smaller but proportional values to use this program.
I also worked on my abstract for the REU presentations that will be held
next Friday, Dr. Noé gave me a few initial suggestions for what to
include/not include. It’s difficult writing about my project when I
haven’t even finished it yet, and even more so because I’m just starting
to analyze the results! However, I’m sure by the end of the weekend I’ll
have more concrete conclusions to write about.
I went through my series of 45 images and cropped them all to about the
same size. In this way, I’ve zoomed in but kept them all to the same
scale. So it’s now possible to flip through them quickly and see the
evolution of the beam. Later in the day I actually put them into a
separate PowerPoint presentation and labeled the distance, exposure time,
and scale on each photo.
At our pizza lunch meeting, each of us in the LTC gave a short talk on
what we had been working on and the current goals we have to work towards.
We also had a visit from
Dave Battin; he gave a lot of valuable input during each of our
presentations.
After giving a brief background on Bessel beams and my 4-f setup, I
discussed my creation of one of these beams and showed the series of
images I had taken; I also explained a little bit about the imaging
software I would be using to analyze these images. Marissa then explained
her interest in the TAG lens and how she’s still in the process of trying
to get a hold of one. Jonathan discussed his MPI and how the shop was
finally able to drill one for him (later in the day we actually saw it
work!). Ariana gave a very informative talk on moiré patterns
(superimposing two patterns to create a new one) and aliasing (having to
do with the ability of a camera not being able to resolve the detail of a
pattern with pixels). Two things that I found especially interesting: (1)
that there are two different kinds of aliasing: temporal (for instance the
wagon-wheel illusion of the spokes turning backwards in a forward moving
vehicle) and spatial (for instance, a zebra against a picket fence
appearing to be a white horse or black horse depending on where you look),
and (2) that moiré patterns can be used in navigation, (for instance
underwater to alert ships of oncoming hazards, with a pattern hovering
over it that changes depending on whether the hazard is being approached
or passed over).
I spent a lot of time later in the day analyzing my sequence of images. I
created a surface plot of the intensity of each image, so it was also
interesting to see the progression of the beam in this way. I then
created a graph/list of data of the intensity across each transverse
profile, especially taking note of the maximum value. Finally, I
attempted to measure the central spot size and its average intensity over
the course of the actual Bessel beam.
With 7.4 microns being the smallest distance that the camera was able to
resolve, it was difficult to see the exact boundaries of the central
bright spot and its concentric rings; even the small detail of the
double-lobed structure of the ring source of light was hard to resolve (as
seen below, the intensity profile drastically changed from one radial
slice to the next due to the coarse gradient of pixels). I’ll have to
work on creating average values of the intensity profiles based on
combining data from multiple radial axes.
Interesting to note: It seems that there is a Bessel-like beam that forms
both before and after the light is focused into a clear ring, which is
something I hadn’t expected to see. I found an article that discusses
this phenomenon, so I’ll read over that tomorrow to hopefully gain some
insight in the matter.
I briefly looked at how to do ray tracing in a program called Beam 2. I
started out just trying to make myself familiar with how the program
works, but I’d like to use the software to create my own ray trace diagram
of the 4-f setup (like
Will had
done) and maybe see if I can include the spatial filter in the Fourier
plane. This would then be a nice way to model how the ray diagram would
change with different sized filters.
Dr. Noé took us out to
Pentimento
for dinner and to see a jazz performance by
Ray Anderson. (The name of the restaurant is actually an
art term
that
refers to when part of a painting has been altered, usually with another
layer of paint, due to an artist changing his/her mind. "Pentimento"
actually means
repentance in Italian.) Between the food and the music, it overall was a
fun lab night out!
I started off in the morning by taking more pictures of the resulting beam
in my setup. The images were a little over-exposed, but my main focus was
just to see which object size and initial pinhole would provide the best
results. I started out by changing the initial pinhole to 150-microns
(instead of 75-microns); the beam of light coming through here was then
magnified to 2.6 mm. With the 2.4 mm aperture now being used as my
object, I found that the ring source at the end of the 4-f setup
was not as clean as when I had used a 1 mm aperture. Additionally, there
was no clear evolution of the ring into a Bessel beam. To fix this, I
went back and tried to make sure all of my optical elements were neatly
aligned. Additionally, I included a high pass filter in the image plane
where my ring source was forming to try to clean up the center; in other
words, I used a small circular block that was about the size of the middle
of the ring in order to eliminate the extra bright features inside.
However, there wasn’t much of a difference in the results. A central
bright spot formed in the diffraction pattern, but there were no clear
rings.
So I decided to go back to the 1 mm aperture. Out of the couple of
filters I tried, the central circle size that worked best was 6 mm in
diameter, and the outer radius that provided the cleanest ring source was
28.5 mm (I figured this out just by slowly reducing the size of an iris
aperture and not measuring until after seeing what produced the best
results). The ratio for the radii of these filters turned out to be 4.75,
which is larger than Kowalczyk’s magic ratio of 3.83. This disparity
could have arisen from the different ratios of the sizes/strengths of
optical instruments I used when compared to their setup. However I plan
to look into this more and maybe try some other sized filters..
Dr. Noé showed me some of the special features of the EDC 1000N imaging
program I’ve been using to capture pictures. We first looked at how to
work in sub-array mode, in which only a portion of the camera screen is
used (based on the number of rows and columns of pixels you specify); this
could presumably save some memory space, though it’s a little more time
consuming trying to make sure the light source remains visible in the
cropped portion of the screen.
He then showed me how to check for and correct over-exposure. You can see
if the camera has been saturated by using the “tag pixels” option and then
checking how many pixels are at the maximum intensity (pure white = 254).
This is a good tool to consult while adjusting the polarizer; Dr. Noé even
suggested adding in a neutral density filter too. Additionally, by
capturing a picture when all the light is blocked, you can use the “tag
pixels” option again to see at what value the majority of dark pixels are
labeled; then you know how much to lower the initial bias (which will
retag those dark pixels at a value closer to zero).
It’s also possible to count the number of pixels to figure out the actual
size of features of the transverse pattern. To do so, I looked up the
size of the camera screen. I couldn’t find an official specifications
sheet for the ECD 1000N model, however I found two separate sources that
confirm each pixel is a 7.4 micron square: a
website that lists specifications
for all different CCD camera models and a
journal article which describes
research that made use of the ECD 1000N.
I reconfigured my camera setup so that the track to slide
the camera back and forth on was more stable. To make measuring easier
and more
consistent, I taped a ruler down at the foot of the lens. I then
implemented two neutral density filters (total 0.3) in between the laser
and initial pinhole, and moved the polarizer right up against the camera
to attenuate the beam. But when the captured images were still
over-exposed, I used a second polarizer attached
directly to the front of the camera and then put the variable polarizer
between the laser and initial pinhole.
When I started to take some more pictures, I was promptly notified by a
pop-up that the computer was out of hard drive space… (The computer
actually only holds 4 GB of memory total; it’s funny to think how advanced
technology has become—even my inexpensive flash drive can hold 8 GB!) It
suggested that I empty the recycling bin, which gave me about 4 MB of
memory. Then Dr. Noé went through to find some stuff we could delete and
cleared up about 10 more MB of memory for me for the time being.
I took a lot more pictures in small increments to really show how the
Bessel beam forms from the diffraction of the thin ring source of light.
Afterwards, I transferred all of these image files onto floppy disks and
then used another computer that had both a floppy drive and USB drive to
transfer the image files onto my flash drive and then onto my laptop.
With 4 floppy disks, space for 4 images per disk, and about 50 images to
transfer, it seemed like it might be a tedious job, but I had a nice
rotational system going that got the job done in under 10 minutes.
I downloaded ImageJ onto my mac for analyzing the images. After playing
around with it a little bit, I figured out how to set the 7.4 micron scale
(even including a key on the image) and how to graph an intensity profile
of a portion of the image. So far I determined the intensity across the
transverse profile of the ring source and of the Bessel beam. Pretty
exciting stuff! Tomorrow I’m going to analyze multiple images and compare
the intensity of the beam and calculations of the size of the central spot
and rings. In this way, I’ll be able to see if the central bright spot
retains its size and power over the axis of propagation.
Today I reconfigured my 4-f setup so that I would have more table
space at the end for placing a camera (a rough outline of the layout is
pictured below). In doing so, I realize that there are a couple of
different parameters that I can play around with: the object size (which
is related to how much the initial pinhole is magnified) and the spatial
filter parameters. To start, I’m sending the laser beam through a
75-micron pinhole, magnifying it to 1.3 mm, and sending it through my
object aperture (diameter 1.0 mm). The second possible combination
utilizes a 150-micron pinhole at the beginning, which gets magnified to
2.6 mm, and then sent through the object (diameter of 2.4 mm).
With my spatial filter in place, (currently an inner radius of 8 mm and an
outer radius of 30 mm) the setup produces a very clear thin ring of light
at the end; afterwards it becomes very dim, so it’s hard to see what’s
going on, if anything.. However! Later in the day, I used the CCD camera
(with a polarizer in front of it to attenuate the beam a little)
and took some photographs of the resulting beam. After the thin ring of
light, it appears that the beam evolves into a Bessel beam! (The pattern
has a very bright center, which remains at a basically consistent size
over a certain distance). Tomorrow I’m going to experiment with a larger
object size and different filters.
I spent some time with Mathematica trying to model what the intensity of
my resulting beam will look like at various distances, however I’m having
some difficulty at the moment. I was successfully able to model what the
intensity would look like in a setup such as Durnin and Eberly’s that
contains a lens after the ring of light. However its more difficult
working with the z-dependent diffraction equation… I also was looking
around the internet to see if I could come up with a simulation of what
the ray diagram would look like with two identical lenses and the spatial
filter in between them. It seemed highly involved to create one with
Mathematica, but I might try to code it if I have some extra time.
(Speaking of Durnin and Eberly-- I still, at some point, want to try to
include a lens at the end of my setup, to see what would happen even
though Kowalczyk made it clear that his thin ring source of light is
fundamentally different than that which comes as a result of a uniformly
illuminated circular aperture.)
Also- this afternoon Dr. Noé brought in some tomatoes for us from the farm
stand. They were huge! And also very tasty.
Since I had been fairly busy this week putting together the Bessel beam
presentation, I didn’t have enough time to regularly keep up with my
journal entries, so this morning I spent a lot of time catching up with
them.
Using a Mathetmatica package that Jonathan had showed me I made a couple
of lines of different sized dark circles to use as high-pass filters
(since it was too hard to make a clean edge with whiteout). I then took
it a step further and found the codes to make an array of white annular
shapes on a black background. As far as the dimensions, I wasn’t sure how
the graphic might get resized when trying to print it. Therefore, instead
of figuring out exact sizes for the inner and outer radii, I calculated
what the relative width of the annulus should be based on the ratio
proposed by
Kowalczyk.
Marty then helped me print these shapes onto transparency paper
(Transparency Film for Monochrome Copiers LCT PBS 100) with the special
printer upstairs. The only issue was that the printed black color was
highly translucent. We tried adjusting the exposure to correct for this,
but even using the darkest setting didn’t make much of a difference.. So
what I ended up doing was layering the pages, which turned out to fairly
effective. I then played around with these different sized filters in my
setup, faint ring showed up at end, which is definitely a step in the
right direction!
I uploaded a compressed pdf of the
Bessel beam presentation to my
website
on
a
new
Presentations page. This took a little while because I was unfamiliar
with the process of transferring a file to the website with a mac. But I
was eventually able to figure out the appropriate secure file transfer
protocol commands using this
helpful website.
Today was a very long but fulfilling day. It began with the drive into
the city, during which Marissa and I did a few more practice run-throughs,
as well as take notes on useful last-minute suggestions from Dr. Noé. We
arrived at the City College of NY for the 2012 Optical Vortex Party around
noon.
Giovanni first gave an introductory talk on optical vortices, explaining
the idea behind a light wave having angular momentum. He discussed some
of their applications, including communication—for instance, being able to
encode information in each level l of topological charge and then
sending a larger amount of information all together. Giovanni also
discussed the Berry phase, which is when a vortex acquires a phase from
moving along the Poincaré Sphere; in other words, the vortex starts with
one phase and undergoes a change based on the geometry of the situation.
A useful example is that of a cat that can twist to land on its feet if
falling.
Additionally, there were numerous interesting student talks and poster
projects. One CCNY girl gave a talk on characterizing Q-plates, which
could be used to give light a polarization. Another CCNY student
discussed how an OAM sorter is able to transform the donut shaped vortex
into a line, separating the OAM states, while still maintaining its phase.
One of the posters done by a Colgate REU student was about quantum
computing and being able to encode information in entangled photons by
altering their polarization and phase (this allows for much more
information to be encoded than with the traditional binary bit computing
since really there are numerous characteristics of a photon that can be
altered).
Kiko Galvez gave a very comprehensive talk on the Poincaré Sphere and this
idea of mapping polarization states onto its surface. He discussed the
goal of singular optics was to search for singularities. For instance, an
optical vortex has a dark center because it contains all phases and
therefore they cancel to zero; same goes for the research with the
Poincaré modes and polarization singularities. As a side note, I really
liked the quote that he opened up his presentation with: “Research is to
see what everybody has seen and to think what nobody has thought,” Albert
Szent-Gyorgyi.
Afterwards, Marissa and I presented our Bessel beam PowerPoint and then
Jonathan presented his Multi-Pinhole Interferometer research. Then what
was really cool was that we took a short tour of one of their optics labs
and actually had the opportunity to see a spatial light modulator in
action.
I think that the Optical Vortex Party was a great experience overall! I
very much enjoyed sharing my research and hearing from other REU students
who were doing similar or even completely different projects. It was also
very valuable forging connections with some of the students and making
plans to follow up with the research we each were doing. Before heading
back to Stony Brook, Dr. Noé very kindly took us out to dinner at an
authentic Greek restaurant
Loi on West
70th
Street. Everything was absolutely delicious!
The weekly Wednesday REU meeting was structured a little different than
usual. Today instead of each of us presenting to the group what we had
been working on the past week, Michal Simon gave us a presentation about
his work in astronomy, since it was somewhat related to Jonathan’s
multi-pinhole interferometer. However, the difference was that the
pinhole layout for the astronomical device was purposefully irregular
(which was developed through trial and error), whereas Jonathan’s pinholes
would have to be aligned perfectly in a circle formation. The reason for
this disparity obviously stems from the way in which the device is put to
use.
Michal Simon is an observational astronomer who focuses on studying young
stars. In order to correct for atmospheric blurring and improve
resolution when using a telescope, it’s necessary to use a
non-redundant mask. Since no two pairs of holes have the same
separation
vector, each pair provides a set of fringes at a unique spatial frequency
in the image plane. Jonathan, on the other hand, needs the pattern of
pinholes to be symmetric because he is looking to use the MPI for
uncovering the topological charge of his optical vortex without having to
interfere or split up the light beam.
Besides this meeting, Marissa and I spent the whole day working on our
presentation for the Optical Vortices Party tomorrow. We first added
together our individual slides into one PowerPoint and took some notes on
how we would make the transitions. At the optics pizza lunch we presented
what we had so far to the group. It was very helpful hearing everyone’s
comments and suggestions after doing a run-through. The afternoon was
spent making corrections, rearranging the slide order, and writing out
notes for how we would discuss each slide.
Marty helped me understand a couple of items from the 4-f setup
article a little better. First of all, there was the part about not using
a final lens in the setup, which was something Durnin and Eberly had
included in theirs. It turns out it has to do with the nature of the thin
ring source of light. Whereas Durnin and Eberly simply used an annular
aperture, Kowalczyk created theirs through spatial filtering; therefore
there’s a zero between the two intensity peaks of the ring source which
would not have been present with the use of annular aperture.
Secondly, I was concerned about the very small diffraction pattern that I
presumed I would have to filter with an equally small high-pass filter
(that is, use a very small whiteout dot to block the central bright spot.
This being the case, I figured I would have to magnify the light beam more
to use a larger aperture for the object so that at the Fourier plane the
diffraction pattern would be larger. But Marty helped me realize that the
high-pass filter mentioned in the article was actually somewhat larger
than the central bright spot of the diffraction pattern. Therefore the
problem of my filter being too small was not actually that big of a
problem after all.
I combed through the barcode scanner
2003 patent to really try
and
understand how these devices work. Inside the barrel portion the beam is
created form a laser diode inside of a metal channeling tube. After going
through a first lens to partially collimate the beam, it is directed
through an axicon lens, which transforms the Gaussian into a Bessel beam.
The beam is then reflected out of the tube by a folding mirror towards a
pivoting mirror, which oscillates to generate the scanning movement of the
beam. After exiting the beam comes in contact with the optical code. The
ability of the beam to resolve the symbol is limited by the density of the
bar code, but more importantly the working range of the laser beam, which
is the distance over which the central spot size of the beam is unaffected
by diffraction. The use of an axicon produces beam that has a constant
spot size over a more substantial distance, two or three times the range
of a conventional Gaussian beam.
After backtracking through the sources cited, I found the earlier
1992 patent for the
original
idea of making optical scanners with the axicon element. It’s interesting
to note that the chief inventor from both patents (Vladimir Gurevich 2003
and Joseph Katz 1992) was from Stony Brook.
I decided to read through McLeod’s article, The Axicon: A New Type of
Optical Element, more thoroughly and ended up learning some more important
facts. First of all, he listed various examples of axicon optical
elements, such as a conical lens, narrow annular aperture, and certain
hollow objects such as a cylinder, cone, flared reflector, or sphere. For
the most part, axicon lenses don’t suffer from chromatic aberration, since
each color of light finds its own path through the cone to the image. A
telescope that employs an axicon lens is able to simultaneously view two
or more small sources in focus that are placed along the same line of
sight; because the nearer sources do not block light that is coming from
the farther sources. Another important application is to autocollimation,
in which the axicon element is used to determine if a mirror surface is
perpendicular to the line of sight.
Dr. Noè, Marissa, and I spent some time in the afternoon clearing off the
wooden table in the back room so that I would have more space to expand my
4-f setup. It looks a lot cleaner, and there’s so much space now!
I then spent the rest of the day working on my part of the Bessel beam
presentation.
Prof. Metcalf showed us a very interesting video today; it was a lecture given by
Joseph Eberly (when he received the Frederic Ives Medal in 2010) titled
When Malus tangles with Euclid, who wins? It described in fairly simple terms
why the Bell inequalities violate quantum mechanics. He started out by using a
classical example of how one of the inequalities holds true when counting the
outcomes of a series of penny, nickel, and dime coin tosses. Eberly then applied
the same logic to a photon polarization experiment, in which three types of
calcite (crystals that have an index of refraction determined by the polarization
of incident light) analyzer loops took the place of the three types of coins. He
developed the inequality using Malus’s law (the intensity of polarized light
transmitted by the analyzer is proportional to the squared cosine of the angle
between the transmission axes of the analyzer and polarizer), which turned out to
not be compatible with Euclidian geometric trigonometry (specifically after using
the cosine identity to simplify); additionally this inequality was also
experimentally disproved. The problem arose from the fact that we developed the
inequality after assuming the existence of specific states of photon polarization,
which is incorrect according to quantum mechanics. In actuality, the polarization
state doesn’t exist if we don’t observe it; specifically here, we chose not to
observe one of the three analyzer loops, which means the photons assumed both
states. It is from the extra unknown polarization information that the Bell
inequality fails.
I played around with my 4-f setup a little more, specifically by adding in
the high and low pass components of the spatial filter. Even after making the
necessary annular filter width calculations, the outcome didn’t really appear to
be much of anything because the incident beam of light was too small at the
Fourier plane to properly be affected by the filter. So I still will need to
magnify the incident beam some more, but to do so we’ll have to clear some more
space on the table first.
Prof. Metcalf later came in to the LTC and asked if we knew what Brownian motion
was. After reading a little bit about it, I learned that it refers to the
irregular motion of minute particles of matter (about 0.001 mm in diameter and
smaller) in a fluid; this random movement is caused by the thermal motion of
molecules in that fluid. A useful analogy to think of is the erratic motion of a
very large beach ball in a stadium of people; due to the random directions in
which people exert force on the ball as it comes to them, it gets propelled at
various angles around the stadium. Brownian motion was important to the
development of Avogadro’s number and therefore the size of molecules.
Marissa and I discussed our Bessel beam presentation some more- we divided up who
would present each part and also started making a PowerPoint from our outline.
This lead me to start organizing all of the Bessel beam articles I had read and
rewriting my notes.
Today Dr. Michal Simon took the REU group on a trip to the
(http://www.amnh.org/) American Museum of Natural History. On the train
ride, I read through most of Cheng-Shan Guo’s article:
Characterizing topological
charge
of optical vortices by using an annular aperture. The introduction
had a
very useful summary of what the topological charge of an optical vortex
was (which is that it refers to the orbital angular momentum of the beam)
and previous methods that have been used to determine this value (such as
interfering a wavefront with a mirror image of itself, using a
Mach-Zehnder interferometer with a Dove prism at each arm, or as
Jonathan’s been reading about- using a multi-pinhole interferometer).
Guo, however, sent the vortex beam through an annular slit (of about 1 mm
width) and used the fact that the resulting beam retained its azimuthal
phase variation to measure the vortex’s topological charge. The aperture
was placed in the front focal plane of a lens (f=240 mm) and the screen
was located in the rear focal plane. The number of bright rings in the
spatial frequency spectrum of the observed far-field diffraction intensity
pattern (which was determined by taking the Fourier transform of this
pattern) was equal to the topological charge of the vortex.
Guo specifically notes that the resulting intensity pattern approximated
to the square modulus of a higher-order Bessel beam (the order of which
determined by the topological charge of the incident vortex beam).
However, the article was not focused on the fact that they had stumbled
upon another method to generate a higher order Bessel beam, that is, by
way of sending a beam with an azimuthal phase variation through an annular
slit. This could be an interesting method to try with the intent of
making a Bessel beam since a 1 mm ring aperture is definitely achievable
(that’s about the size of the ring I had used when playing around with
spatial filtering an Airy pattern, 8 July 2012).
At the museum, we had the opportunity to go behind the scenes to the staff
section where we had been invited to sit in on the AMNH
REU program’s weekly
meeting.
Four students presented on various astrophysical topics based on their
personal interest. Jumari had studied the rover Opportunity which
had landed on Mars in 2004 and recently was required move to a sun-facing
slope known as Greely Haven so that it would be able to maintain its
solar-powered batteries. Munazza described the increased frequency of
solar activity spikes; what I found most interesting was when she was
explaining the general make up of the sun and mentioned that the
equatorial region rotates faster than the polar regions. Nicole presented
on Hanny’s Voorwer, a mysterious cloud of green gas emitted from the black
hole jet of another galaxy. Finally, Nettie explained the growing issue
of light pollution (in the form of light trespass, light glare, sky glow,
and light clutter) and its effect on nocturnal and ecological life as well
as human health.
We then had the opportunity to explore the museum on our own. I happened
to find, slightly by accident, a small hallway that described the imaging
tools used by the museum’s
Microscopy and Imaging
Facility. The exhibit described the four imaging
techniques: confocal laser scanning microscope (for fluorescence imaging
and surface detail), scanning electron microscope (for magnified details),
electron microprobe (for determing chemical composition), and CT scanning
(for 3D interior images). This was especially fascinating to me because
it dealt with a research endeavor I want to engage in after graduating
next year, that is, to study the degradation, conservation, and
restoration of cultural heritage objects by employing imaging techniques
that were primarily developed for the medical world. However, I’m more
interested in the use of Nuclear Magnetic Resonance, which is an imaging
technique that has yet to become popular in the research facilities of
American museums.
I also enjoyed the
Creatures of Light: Nature’s Bioluminescence exhibit. As well as the
actual material covered by the exhibit, I was very interested in the
education aspect of how the information was presented. In a very
kid-friendly environment, it discussed the science behind organisms that
either chemically produce their own light (such as fireflies, certain
fungi, glowworms, various deep-sea fish) or re-emit absorbed light (such
as fluorescent coral).
I found a
comment on Durnin and Eberly’s paper, written by DeBeer. He explained that him and
his colleagues saw a connection between Durnin’s experiment and the
Poisson (Argo) spot. (This is a relationship that has now come up a few
times in my readings lately...) If an illuminated opaque sphere is placed
in the focal plane of a following lens, the bright spot retains its
intensity and size over the axis of propagation. It can be thought of as
a line image, since the spot doesn’t disappear if an obstacle is placed in
its path. This is proof that the Poisson spot is a product of conically
interfering rays, since it could not self-reconstruct if it had
formed from traveling on axis.
Marissa and I brainstormed on the white board about how we would structure
our Bessel beam presentation at the Optical Vortex party next week. We
decided to first touch on the basic properties, appearance, amplitude
equation, ideal beam vs. what’s experimentally possible, and the
difference between zero-order and higher-order beams. Next we would
explain the uses and applications of these nondiffracting beams.
Afterwards, we would discuss the various methods of generating Bessel
beams that we’ve come across from various physicists in the field: by use
of an aperture, an axicon, with spherical aberration, a TAG lens, optical
fibers, or an SLM. Finally, Marissa and I would each briefly discuss our
current research projects.
Duocastella and Arnold actually wrote a very straightforward
summary article about
Bessel beams, which would be useful to consult while trying to piece
together a 20-minute presentation on all of this information. In the
publication, they discuss the distinguishing properties of Bessel beams,
each of the methods by which they can be created, and the major
applications. I thought it was also interesting that the article discusss
the fate of the Bessel beam in the far field (since it has been typically
created from Fresnel near-field diffraction); after some time, the beam
actually becomes annular, with a Gaussian intensity pattern in the radial
direction.
The achromat lenses arrived in the mail today! At the end of the day I
spent some time setting up the 4-f spatial filtering system, as
described by Kowalczyk. Earlier, Marty had expressed his confusion as to
why they did not include a final lens in their setup. The article
mentions several times that it would make for a more accurate Bessel beam
if the lens was included (as with Durnin and Eberly’s endeavors), however
the article also mentions how the it was not possible to use it in their
experiment. Marty and I decided we would look at what actually comes from
the 4-f setup, and see if we run into any problems while attempting
to include this final lens.
Though I had some difficulty in working with the limited space I had on
the table, I was able to fit everything for now (as I start to reconfigure
things, I’ll probably add in a couple of mirrors to bend the setup around
and make more space). I sent the laser first through a 150-micron pinhole
and then through a 10-cm focal length lens to magnify the beam size for it
to fill a 2-mm diameter aperture. About one focal length behind the
aperture (33.3-cm) I placed the first achromat. After marking the midway
point between two subsequent focal lengths (for the inclusion of a spatial
filter later) and placing a second achromat lens, I came out with the
image of the 2-mm diameter aperture one more focal length away. I might
need to rearrange things slightly, since the beam size in the Fourier
plane (spatial filter location) is still relatively small and it would be
difficult to filter a ring out of it. But it was nice to be able lay
everything out as a starting point.
In other news, I’ve started using EndNote: a really great application
(courtesy of Stony Brook) to assemble and categorize all of the articles
and resources I’ve been consulting. It organizes the citations, allows
you to attach PDF files or links to the articles, and then search through
them based on author, title, year, keywords, etc. It’s too bad that I
didn’t realize I could download this application at the beginning of the
REU, because it would have been easier to just add in each source as I
printed it out. Though it will take some time to catch up with entering
in all of the articles I’ve read so far, overall this should be a helpful
way to organize my research.
Today I read though Marston’s
comment on Kowalczyk’s “Generation of Bessel beams using 4-f spatial filtering system” which pointed out
that their nondiffracting Bessel beam is the result of a diverging pattern and
has an approximation similar to that for glory scattering of spheres (glory scattering-
scattering of light that causes a bright halo of color around a shadow). Normally for
creating a Bessel beam approximation, Marston thought that a final lens needed to be used, as
in Durnin and Eberly’s setup (which I talk about in the next paragraph). There was then a
reply by Kowalczyk in which he acknowledged the terminology issue, however their resulting pattern did
have a Bessel function radial profile and the specific beam properties. He also explained
how their diverging pattern approximation to the beam was more closely related to the Poisson
spot (bright spot in the shadow of opaque circular disk created from the scattering off hard
edges), rather than glory scattering (a polarization-dependent scattering of light off
spherical objects).
I read through Durnin and Eberly’s paper
Diffraction-free beams, which was one of the first papers written on experimental
recognition
of a beam with nondiffracting properties. They explained how the intensity distribution of
(what we now call) a Bessel beam is part of a special class of non-spreading solutions to the
Helmholtz equation on diffraction phenomena. Durnin and Eberly illuminated an annular slit
and then placed a lens in front. The 1987 publication put simply what I had inferred from
reading several more recent and complex articles on this topic, which is that: Each point on
the slit acts as a point source, which is then each transform into a plane waves (by the
lens) with its k-vectors lying on the surface of a cone. The maximum distance of propagation
of the resulting Bessel beam is dependent on a large lens radius, long focal length, and
small annular slit width. This was figured to be much longer than the Rayleigh range (which
is the distance over which a normal beam remains undiffracted while propagating in free
space).
At our Wednesday REU meeting, each student explained what he or she had accomplished in the
past couple of weeks. I explained my mini-project: profiling the Airy pattern from pinhole
diffraction and then fitting the data with a Gaussian and Bessel curve using Mathetmatica.
Marissa explained her interest in the tunable acoustic gradient index of refraction lens for
making Bessel beams and how an acousto-optic modulator works. Sara and Kate have been
plotting the wavelength spectra from nine stars (M and K) and analyzing the presence of
certain elements at certain wavelengths, such as the sodium doublet. Jonathan explained his
newest interest in the multi-slit interferometer through which one can send a vortex to
figure out its orbital angular momentum. David is having trouble with his simulation at the
moment since the fact that his basis is not orthonormal, therefore the program cannot compute
the necessary algorithms for understanding atomic band structures. June is currently writing
up his report from his mini-project: profiling a Gaussian laser, which turned out to not be
Gaussian after all. Yakov demonstrated with his laptop some of the beam simulations he’s
been programming. Joe, who is another student working with Dr. Michal Simon, explained how
he was looking at the spectral energy distribution for certain stars and trying to detect the
presence of dust in the data.
Next, at our optics lunch meeting, each of us in the LTC lab explained to the rest of the
undergrad students what we were currently working on. I gave a brief overview about what
Bessel beams are and the methods to go about making them. I then explained my current
reading on axicon lenses, bringing up how the apex angle of the cone is important in
determining the range of the Bessel beam, as well as the ring spacing and central spot size.
The shallower the angle, the larger all three of these values will be; however Prof. Metcalf
was interested in what the limit was on this angle, in other words, how shallow is too
shallow that the resulting beam would no longer be a conical superposition of plane waves.
This is something I haven’t come across yet in my reading, so I’ll be sure to do some
brainstorming on the matter.
Dr. Noé and I spent some time searching for less-expensive axicon lenses, in hopes that could
use one to create a higher-order Bessel beam with an optical vortex, but didn’t come across
anything too helpful. Instead, an LTC alum
Giovanni is kindly letting us borrow the one from his lab, which we can pick up at the
Optical Vortex party he’s hosting next week. So while we wait for the axicon lens, Dr. Noé
suggested I do some research on how to make a higher-order Bessel beam using some of the
simpler methods I’ve already come across (in other words, the spatial filtering and annular
aperture setups I had studied first).
Today I read through most of Herman’s
Production and uses of diffractionless beams article, which went into both mathematical
and
conceptual detail about using an axicon or highly spherical lens to create a Bessel beam.
With the axicon lens: the incoming plane waves bend according to the apex angle and index of
refraction of the lens, which results in the superposition of positive and negative conical
waves around the optical axis. To use a lens with high spherical aberration (which means
light rays are focused tighter at different distances from the optical axis), you illuminate
it with a ring of light as far as possible from both the margin and the center of the lens.
In this way, the light will be focused in a conical fashion between the central and marginal
focal points. The very center of the lens is blocked by an obstruction to limit the
complicated interference pattern that would arise from these central rays. Herman spoke only
of creating zero-order Bessel beams with these methods.
I then decided to geometrically brainstorm a little more about Prof. Metcalf’s proposal of
using a glass tube instead of axicon lens. Here, the angle that the resulting Bessel beam
rays make with the optical axis is 90º - θc (the critical angle that the
incoming diverging rays make with the optical axis which would cause total internal
reflection between the glass and air). If the light source diverging from a point is placed
at a distance L away from the tube, this means that the tube would have to be L
long, and it would create a Bessel beam about the optical axis that had a propagation range
of L. The incoming light beam would have to be diverging in such a way that after the
distance L from its origin to the tube entrance, it would have a diameter D,
approximately the same D as the diameter of the tube to ensure it was coming in at the
critical angle. Using a trigonometric analysis of the situation and the index of refraction
for crown glass, the ratio of D/L is 2.29, and for flint glass the ratio is
2.55. The next question would be to figure out the necessary optical power for a lens to
produce a beam of light that diverges to a diameter D from a point L away.
Milne’s article
Tunable generation of Bessel beams with a fluidic axicon described a method that involved
creating a
mold of an axicon and then changing the fluid inside of it to alter the index of refraction.
But I thought it was a particularly useful article because it clearly laid out the importance
of the apex angle (as well as the index of refraction) of the axicon to the maximum beam
range, ring spacing, and central maximum size with their respective equations.
I read through an article by Jaroszewicz from Optics and Photonics News:
Axicon- The Most Important Optical Element. The actual definition of an axicon, as
defined
by
McLeod in 1953, is an optical element with
rotational symmetry that images a point into a line segment along the optical axis.
Jaroszewicz explains that the “first axicon” was the pinhole camera, first mentioned by a
Chinese philosopher in the fifth century B.C., which provides an infinite depth of focus.
The article also provides a brief comparison to the Argo (or Poisson) spot, which is created
by interference in the center of the shadow of an opaque disc/sphere when this opaque sphere
is being used as an image-forming device. Finally, it brought up Bessel beams, and how they
can be used as an application of an axicon to define a reference line, since the resulting
beam is long and narrow.
For future reference, after looking through Pradyoth’s
Intel report, we found the actual name of the company he used for his printing job:
Darkroom Specialties LLC, Eugene, OR.
This morning Dr. Andrew MacRae came in for a tour of the LTC so Jonathan, Marissa,
Ariana, and I explained some of the projects we were working on. Later he gave a
talk about the generation of arbitrary quantum states from atomic ensembles. He
discussed two methods for entangling photons to isolate single states: spontaneous
parametric down-conversion and the use of a vapor cell. I was familiar with the
SPDC process from my sophomore year Intro to Relativistic and Quantum Physics
course, since we had used one of these crystals in our experiments to demonstrate
the existence of single quanta of light. Later in the afternoon, Dan Stack
presented his thesis: Optical Forces from Adiabatic Rapid Passage, which basically
described an alternative method for cooling atoms-- instead of laser cooling, he
had used coherent optical forces.
I started reading some of Herman’s
Production and uses of diffractionless beams article which describes two
methods to
create zero-order Bessel beams: using a conical lens or by means of spherical
aberration. He flat-out explained what I had assumed from reading other papers
about the basic Bessel beam criteria which is that: (A) the central region keeps a
constant size and intensity due to energy being diffracted into this region from
the surrounding ring system, and (B) the transmitted intensity pattern remains
unchanged at a distance past an obstruction of the central intense region due to
energy being diffracted into the region on the other side of the obstruction. I
will finish the article tomorrow.
After reading some of Arlt’s
Generation of high-order Bessel beams by use of an axicon paper, I’m beginning
to understand the
difference between zero-order and higher-order Bessel beams. A J0 beam
has a bright central maximum while a Jn (from this point on, assuming
n≠0) beam has a dark central core. You can use the same optical elements to
create both a J0 and Jn beam, it just depends on the input
light beam that is used. In other words, if an axicon is illuminated with a plane
wavefront, it yields a J0 beam with an annular spectrum; if the axicon
is illuminated with a beam that has an azimuthal phase variation (such as from a
Laguerre-Guassian mode), the resulting Bessel beam has an annular spectrum and
azimuthal phase variation, signifying a Jn beam. Again, I will finish
reading this article tomorrow.
As far as the advances I had made with my pinhole diffraction setup over the
weekend, Marty pointed
out that according to Durnin and Eberly’s
Diffraction-Free Beams article, it
would need a second lens (after the filters) to focus the ring of light into the
Bessel beam. He suggested making the first lens (right behind the pinhole) one
with a longer focal length.
Dr. Noé helped Jonathan set up a camera that takes pictures of the transverse
wavefront of a beam of light. He explained that a circular polarizer was needed to
prevent the camera from being flooded. The polarizer was set up very close to the
camera and configured so that the light was almost completely attenuated. For
future reference- the program that was used to capture images was EDC 1000N.
Marty brought up a fascinating application of Bessel beams that I hadn’t ever
realized—Evidently the light beams used on the scanning devices at supermarket cash
registers that read the UPCs are Bessel beams! The 2003
patent describes how the device makes use
of an axicon optical system to generate nondiffracting beams of light. Since the
central peak in the transverse intensity does not diverge for a range larger than
the typical laser, it allows for an increased maximum working distance of the
scanner to about 520 inches.
Dr. Noé and I brainstormed creating Bessel beams by using a long glass tube, as
Prof. Metcalf had suggested during our Wednesday 27 June meeting. After drawing a
couple of diagrams and thinking things through based on the other known methods of
generating Bessel beams, we decided that sending a Gaussian beam through would
yield a zero-order Bessel beam, while sending a vortex beam (from an LG mode) would
yield a Jn beam. I tried to search for any publications that might
discuss this method but was unsuccessful in finding anything. The search did bring
me to
Tom’s journal entry from 19 June 2009 where he describes the similar
conversation
he had had with Prof. Metcalf about how a glass tube would give a similar ray trace
as an axicon lens. If we can figure out the correct tube dimensions, this would be
an interesting alternative to try. I think once I finish reading the articles that
discuss the use of an axicon, I’ll have a better understanding of the proportions
that would be needed for the glass tube.
It seems like I might have created a Bessel-esque beam from spatially filtering the
diffraction pattern so that only a thin ring of light was allowed to pass through.
When following the beam along its axis of propagation, the ring developed a bright
spot in its center about 50 cm behind the filter system (which consisted of the
hole-punch high-pass filter and iris diaphragm low-pass filter). As the distance
increased, a couple of inner concentric rings began to develop from the outside in.
The pattern basically remained constant from about 80 cm through 100 cm. Then
around 130 cm the rings started to collapse so that there was only a bright center
and one ring around it. Farther down, though the central dot remained bright, the
rings started to become fuzzy (160 cm) and eventually spread so much that they
meshed together (210 cm). Soon after (220 cm), it was possible to see that a very
tight Airy diffraction pattern had faded back in.
I decided to test the self-reconstructive abilities of the beam I was observing and
placed one of the pieces of transparency paper that had a misshaped whiteout circle
at about 80 cm from the filters so that the beam’s bright center was blocked. The
center continued to be clearly obstructed until around 50 cm behind the obstruction
when a new bright spot began to appear again. By around 90 cm, the center had
definitely reappeared, though the outer rings were slightly fuzzier than before.
Despite the fact that what I observed was not a very well-defined Bessel beam, since
it was fairly small (maybe only a little more than 1 cm in diameter) and only
contained the bright center and two outer rings, it still exhibited the Bessel-like
qualities of (A) being the product of a thin-ring light source diffracting, (B)
containing a uniformly-sized bright center over considerable distance, and (C)
having the ability to self-reconstruct. I’m sure with a thinner ring of light, as
would be created with the
4-f spatial filtering system, the Fresnel diffraction pattern would
develop into a more
pronounced Bessel beam.
I was finally able to figure out the correct code in Mathematica to fit a Bessel
function to my Airy pattern intensity data, and it’s clear right away that it’s a
more suitable fit than the Gaussian one. This function takes into account the
aperture diameter, wavelength of the laser, and angular radius from the pattern
maximum. Afterwards, I also plotted all three of these curves on a semi-logarithmic
plot. Again, it was clear instantly that the data did not behave like the Gaussian
curve, which was parabolic.
My
Ideas and Resources page has
now been updated with the Bessel beam brainstorm that Dr. Noé and I came up with.
It contains all of the major ways we’ve come across to generate these nondiffracting
beams as well as links to the articles that describe each method. I’ve started
reading through more of these articles and will continue tomorrow.
Dr. Noé showed me an
article that explained why we were seeing different patterns over a certain
distance
behind the focused image of the pinhole yesterday. Evidently with pinhole aperture
diffraction, the classic Airy pattern is only present at the point of paraxial focus,
in other words the intermediate image plane. The article contained an axial intensity
distribution plot that showed why we were observing the dark-center diffraction
pattern at certain distances; there was also a helpful demo to click through for a
transverse representation of the diffraction pattern at each of those distances. I
thought it was also interesting to note that there were more higher-order diffraction
rings at a distance ±6π from the point of paraxial focus than there are in the classic
Airy pattern at this paraxial focus point.
Prof. Metcalf gave us another quantum lecture, this time focusing on the Bloch sphere
and Rabi frequency, since these would be topics covered in the thesis defense on
Monday. He made an interesting connection to the oscillation lecture he had given to
us on Friday 29 June 2012: moving an atom between quantum states is similar to driving
an oscillator at its resonant frequency. When an oscillator is driven at its resonant
frequency, it is said to be in one of its normal modes and moves in a clean and
repetitive motion. Between normal modes, the oscillator’s motion is a superposition
of all frequencies. The discrete energy levels of atomic states are in essence the
normal modes of the system, and in between these discrete states, the atom exists in a
superposition of all its states. For the atom to change states it has to be driven
with a certain frequency; in other words, it has to receive a certain amount of energy
to make the clean transitions.
Later we located a multi-slit interference simulation for Mathematica on
Steph’s LTC page. It was really useful to be able to play around with the different parameters
(wavelength of light, number of slits, spacing between the slits, and the distance
from the screen) in Young’s experiment model to see what the resulting interference
pattern would look like. Additionally, it was interesting that when there were many
slits it was possible to observe the Talbot effect (when an image of the slits can be
seen at multiples of a discrete length) at various screen distances.
I did a little bit of internet searching with Ariana to see if we could come up with
some possible project ideas that connected a few of the topics she was interested in.
We came across a couple of attention-grabbing articles so far; unfortunately neither
would work for a potential optics exploration, but they were interesting none the
less: one was about how moiré patterns could be used for
visual cryptography, and another one was about the moiré fringes that appear from
interfering two acoustic Airy patterns.
I attempted to set up a high-pass filter in my Airy pattern setup in order to see the
effect on the image. Since the high spatial frequencies contain information regarding
the edges of an object, I assumed I would see the pinhole image with a sharper border
and maybe a darkened center. I tried creating a circle of whiteout on a piece of
transparency, but no matter how uniform the circle looked in my hands, once I placed
it in the setup in front of the beam of light the shadow it created revealed the
whiteout shape’s uneven edges. Nonetheless, Marty helped me to configure my setup so
that the pinhole image would be magnified enough for us to observe the effect of the
filter. The image was similar to what we had expected: there was a bright circular
ring of light with a dim inside, but it also seemed messy inside- with an extra softer
ring of light and some speckle outside. This was probably due to the irregular shape
of the filter and maybe some kind of aberration effect from the transparency sheet.
Later I tried to solve the filter-edges issue by substituting the whiteout with a
hole-punch cutout attached to a microscope slide. Since this was larger than the
whiteout circle, some of the inner rings were being blocked along with the bright
center. So I decided to take it a step further and spatially filter the beam so that
only one ring of the Airy diffraction pattern was allowed to pass. By placing an iris
diaphragm about 7 cm behind the high-pass whiteout filter, I was able to isolate a
single ring. This was, in effect, a rudimentary version of the methods suggested in
Kowalczyk’s
and
Basano’s
articles that call for a thin ring of light to create a Bessel beam. Over the weekend
I plan to play around with this setup a little more.
I spent a lot of time working with Mathematica this morning and was able to
figure out: 1) how to import data from an Excel spreadsheet, 2) graph the list as
points in the x-y plane, 3) fit a Gaussian function to the data to find the
parameters for the equation (height, width, and central position), and then 4)
graph the data points and Gaussian curve on the same axes. In my previous physics
courses that touched on Mathematica, we were always just given the straight codes;
therefore I see figuring out these trivial operations as being a major
accomplishment for me. The next step is to figure out how to fit a Bessel function
to the data; I’ve tried out a few codes so far, but haven’t figure out the correct
one yet. Dr. Noé hinted that I would need to incorporate the aperture diameter as
a parameter to find the spacing of the maxima for fitting the Bessel function, so
I’ll probably look into this in greater detail over the weekend.
Dr. Noé also explained that the calculations I did yesterday with my “diffraction
equation” were incorrect, since I used a relationship reserved for diffraction through
two or more narrow slits: d Sin θ n = n λ. We then had a
group discussion about
diffraction starting out with the difference between two terms that are sometimes
confused: diffraction and interference. Diffraction is what happens to light as
new wavefronts are formed, according to Huygon’s principle. Each point on the
wavefront is a source of a new “wavelet,” and the envelope of wavelets becomes the
new wavefront of this propagating wave. Interference is the process of adding up
the resultant of individual waves that are constructively or destructively altering
each other.
We then discussed the difference in the intensity pattern from different numbers
and sizes of slits, and it turns out that diffraction through two finite-width
slits produces an interference pattern that combines the one finite slit and two
infinitely small slit patterns. As more slits are added, the peaks of the
diffraction pattern become thinner and thinner (until they become spectral lines,
with the use of a diffraction grating), sort of like how the shape of the Fourier
transform graph will change as the amount of uncertainty decreases.
Next we examined the distinction between near and far field diffraction. Fresnel
diffraction occurs in the near field; the shape of the pattern depends on the
location on the longitudinal axis of propagation where you’re observing it.
Will observed this
accidentally
when he noted a dark spot in the center of his Airy pattern, and then subsequent
changes in the pattern as he moved farther away. For Fraunhofer diffraction in the
far field, the pattern’s shape is only dependent on the angle of diffraction and no
longer on the longitudinal distance. Therefore, the farther you move away from the
aperture, the diffraction pattern will get larger but its shape will remain
constant. So Dr. Noé proceeded to help us derive the equation for the intensity
distribution of two infinitely small slits; we saw how the intensity has a
cosine2 shape, like we expected, and also how the Fraunhofer diffraction
only depends on the angle of the waves coming at the screen, and not on the
distance of the screen from the object.
As a group, we looked again at the Airy pattern and the image in focus at the
opposite side of the lab. Dr. Noé showed how you could see the Fresnel diffraction
patterns as you move a piece of paper closer to the lens to observe the transverse
plane of the beam. At a certain distance, there was a dark spot in the middle of a
light ring, then a light spot in the center, etc. This pattern was what the lens
was imaging right in front of the pinhole, and it alternated until you reached the
image of the Fraunhofer diffraction zone. We then saw something unexpected, which
was that when we moved the paper farther than the focused pinhole image, out of the
lab to the wall across the hall, we noticed the same alternating Fresnel patterns
again. These patterns were what the lens was presumably imaging on the other side
of the pinhole? But we weren’t exactly sure and are going to think on it a little
more..
I decided to collect more data points for the profile of the laser beam, in order to
more clearly see what’s going on in the wings of the graph and show that the beam is
not completely Gaussian. This time I collected intensity information from the n=3
diffraction fringe on one side of the center bright spot to the n=5 diffraction fringe
on the other side (the unsymmetrical data collection is due to the positioning
constraints of the photodiode on the moveable stage). I again graphed the results in
Excel and added a Gaussian curve to the graph. This time it was more apparent that
the data values did not follow the ideal Gaussian values on the wings of the graph;
and even more apparent was the un-parabolic shape of the data curve on a logarithmic
scale.
I then decided to use the diffraction equation along with the distance of the
photodiode to the pinhole and the spacing between fringes to work backwards and
determine the wavelength of the laser. With a slit distance d = 0.15 mm, a
longitudinal distance of 1194 mm, and the transverse distance from the central bright
spot to the n = 5 maximum of 25 mm, I calculated the wavelength of the laser as 627
nm. The actual HeNe wavelength is 632 nm.
Afterwards I tried sending the diffraction pattern across the length of the lab and
projected it onto the main door to again make the appropriate measurements and work
backwards with the diffraction equation to check the laser wavelength. The distance
from the pinhole to the door was 1317 cm and the distance from the central maximum to
the n = 3 diffraction fringe was 16.5 cm, meaning the calculated wavelength was 626.5
nm.
For my final measurements of the day, I spent some time using different lenses at
varying distances in the setup to try to focus the image of the pinhole onto the door
across the lab. I achieved this with the BSX085 lens (f = 20 cm) at a distance of
21.6 cm from the object and 1295 cm from the image. Using the lens equation, the sum
of the distance to object and to image reciprocals was 0.047 cm-1,
relatively close to the actual focal length reciprocal of .05 cm-1. The
magnification equation with these distances resulted in a magnification of 60
times, which means the calculated image height was 9 mm. The actual crisp-edged
pinhole image had a diameter of about 11 mm.
The source of discrepancy between calculated and actual values for the above mentioned
mini-projects was probably mostly due to the means of measurement. Especially while
examining the airy pattern projected onto the door across the room, it was difficult
to see the edges of the diffraction fringes, so the measurements are estimates.
Additionally, I was measuring the longitudinal distance on my own with a tape measure,
so it is possible that it may have moved slightly from its actual position while I
stretched it across the length of the lab.
Today I was also able to download Mathematica and Maple from the Stony Brook website
and tried playing around with them a little. I still haven’t be able to successfully
graph my data from profiling the laser beam (with the Gaussian and Bessel curves on
the same graph), but after working more with the programs in the next few days I’m
confident that I can figure it out.
After Dr. Noé explained that I could obtain a much better airy pattern by moving the
pinhole closer to the lens (BPX065, f = 7.5 cm) and using a cleaner pinhole, I
reconfigured my setup. Now with a 150-micron pinhole, and both the lens and pinhole
moved closer to the laser, the airy pattern is much more prominent. I then
experimented with different lenses to see the distances at which I could focus the
airy diffraction pattern back down to create an image of the pinhole. For each
configuration, I used the thin lens equation to relate the reciprocals of the distance
of the object to the lens, the distance of the image to the lens, and the distance of
the focal length. And in each case, the results were fairly accurate. For instance,
with the BSX085 lens (f = 20 cm): the object was 28 cm away, the image 68 cm away, and
the sum of their reciprocals was 0.0504 cm-1, very close to the focal
length reciprocal of 0.05 cm-1. The magnification equation revealed that
the pinhole was magnified 2.43 times, (meaning its image was 364-microns). By
changing the object to lens distance slightly, I observed the following: the object
was 21.5 cm away, the image was 365.76 cm away, so therefore the thin lens equation
yielded a sum of 0.04924 cm-1, which is still close to the 0.05
cm-1 reciprocal focal length.
Jonathan and I spent some time practicing how to profile the laser beam with a
photodiode (connected with a 100 ohm resistor to an AVO meter) placed in the line of
the airy diffraction pattern. We started by sweeping the intensity of the center
bright spot of the pattern on a moveable stage (which took some time to set up, since
the first stage did not allow a wide enough range of motion, and the second one we
found didn’t have standard screw-hole sizes, but then we came across another one that
worked perfect for our needs). At first the results we were getting seemed off—the
sides of the center beam were Gaussain-esque, however the center seemed to just
plateau at a constant value. Dr. Noé explained that the hole of the photodetector was
too wide to make a fine measurement of the intensity across the small light spot. So
we had been in fact measuring a convolution of the wide hole and the Gaussian shaped
intensity of the beam, which (according to Fourier mathematics) appears as a square
pulse with rounded edges. He also suggested that we use a much stronger resistor to
make the AVO meter more sensitive to small changes in the intensity.
So now with a 200-micron pinhole covering the photodiode and a 10 M ohm resistor in
place of the other, we set to work at charting the intensity (in milli-volts) across
the central bright spot of the airy diffraction pattern. When we had finished, we
graphed the results in Excel and tried fitting a Gaussian curve to the data. For the
most part, it appeared to fit, with the exception of the edges of the data points.
However, when using a logarithmic y-axis, the data points did not form a true
parabola like
an actual Gaussian curve would. Though it’s too difficult to do in Excel, it would be
best to try fitting a Bessel function to the data points; Dr. Noé suggested using
Mathematica or Maple.
On another note, Prof. Metcalf pointed out that my explanation of his setup
(from Friday
29 June 2012) was incorrect, since the negative momentum doesn’t necessarily
signify a negative energy transfer. So I’ll have to rethink the problem a little
more..
After looking through a few different sources (including
Lidiya’s journal) over the
past couple of days, I feel like I’ve come to a better understanding of what it actually
means to break up an object into its spatial frequencies. As I had superficially
understood, high spatial frequencies are associated with the object’s edges.
Mathematically, the spatial frequency is the reciprocal of the wavelength: the number
of cycles over a certain distance. In other words, it is a rate of change in space.
Therefore, thinking of an object as a 2D picture, at an edge where
there is a more abrupt change (in the instance of a
grating, it is the transition between the transparent slit and opaque part), there is
a steeper gradient (rate of change with direction). It helped looking over a website
about
edge detection,
which described the technique as finding the steepest gradient between neighboring
pixels. For the other areas of the object where there is no (or very slight)
variation between pixels, the gradient would be zero (or very close).
In a 4-f set-up, for instance, light has to bend at a greater angle at the
edge of an object, therefore the lens will focus these rays at the outer sections of
the diffraction pattern. On the other hand, transparent parts of an object allow
light to be transmitted unbent, which is why these parallel rays (aka the low spatial
frequencies) pass through the lens and become focused down to the focal point in the
center of the pattern. The Fourier transform is what organizes the different
frequencies that make up the overall object into a diffraction pattern; the order
numbers of the pattern refer to how much the rays have bent at the object’s edges,
with the higher orders signifying higher spatial frequencies. It would be
interesting to play around with spatial filtering and see what a diffraction pattern
would look like for a two-dimensional object (such as a transparent slide with a
design or simple picture).
Dr. Noè and I sketched out a quick list of the different methods to create a Bessel
beam based on the articles we’ve come across so far. This week I plan to reorganize
my ideas/resources page to create a map of these different possibilities with links
to the publications that describe their methods.
We first looked up
axicon lenses made by Thor Labs however these were fairly expensive. It’s
possible that they may be cheaper if we could get them without the anti-reflection
coating..
Compound 1000mm FL Planoconvex Lenses
We did some brainstorming for the 4-f spatial filtering method to
create a thin ring light source; we weren’t able to find the exact lenses used in
Lidiya's setup, and the larger ones we did find would be difficult to mount
apex-to-apex
(as suggested in
Kowalczyk’s setup).
Achromat Lenses
We found some achromat lenses from Surplus Shed that would definitely fit into
the equipment we have here. (Achromat lenses limit the effects of chromatic or spherical aberrations; they are
made from two lenses that have different dispersive properties, bringing the rays of
light with slightly different wavelengths to the same focal point.) Tomorrow Dr. Noè
said he would order some of the 400mm focal length lenses.
As for creating the transparent ring photo in the setup described by
Basano,
Dr. Noè showed me on Xfig how it was easy to produce mathematical graphics.
(There isn’t a straightforward way to install Xfig for Macs, but I found a set of
steps
here that I’ll take some time to go through tomorrow.) The project called for a
4mm-diameter transparent ring with a width of 0.016mm; however we figured out that a
normal printer would only be able to resolve 0.025mm, meaning we wouldn’t be able to
print out the required size..
I looked up Pradyoth’s LTC
journal to try to find the name of the printing company he used for his project
and
found that on 3 August 2010 he obtained “contact information of a transparency
printing service through Professor Michael Raymer at the University of Oregon.” In
the next couple of journal entries it seems that he first tried to order the printing
job from a Mr. Walt O’Brien but instead used a Mr. Gene Lewis when the former
notified Pradyoth that he couldn’t work with the desired film size. A quick google
search of the names with some keywords didn’t yield much, however I’ll do a more
thorough search tomorrow or see if Dr. Noè has any ideas. Also- I thought it was
interesting that Pradyoth had Bessel beams down as a potential project on his
ideas page. He commented
on
the possibility of devising a tunable lens that could create a Bessel beam
approximation, instead of using an axicon lens.
Dr. Noé suggested that I play around with a simple pinhole setup to achieve an airy
pattern (diffraction from a pinhole- light center with concentric dark and bright
rings). With
a second lens after the diffraction pattern, it would be possible to refocus the rays
into the shape of the pinhole. I started out using the BPX065 planoconvex lens, 75mm
focal length, to focus light into a 200-micron pinhole, but the airy pattern was
pretty deformed. I plan to work on this more tomorrow.
I started reading through a
diffraction grating handbook that Dr. Noé gave me. The first section described
the specific
properties of two different types of diffraction gratings: reflection and transmission
gratings. The reflection grating is an array of evenly spaced grooves on a reflective
surface, while the transmission grating is a pattern of evenly spaced transparent
slits on an opaque screen. The distance between grooves or slits is supposed to
approximately be the wavelength of the light being studied. The electromagnetic wave
will be diffracted from the grating with a change in amplitude, phase, or both.
Professor Metcalf explained how he planned to give a lecture series on quantum
mechanics and started out today with oscillations. Specifically, in a doorframe he
had set up two masses on separate strings that were connected by a horizontal straw;
the connected pendulums were meant to represent a coupled oscillator. Prof. Metcalf
showed us the normal modes of the apparatus: the special cases when these pendulums
would oscillate at the same amplitude for an infinite amount of time. We watched a
few more demonstrations of normal modes of different oscillating systems in a very
useful video. Finally, Prof. Metcalf left us with something to think about- With the
coupled pendulums, you can start moving one mass and have it eventually transfer its
energy to the second mass, which will start oscillating as the first mass comes to a
stop, and have this continue infinitely. At one point during the cycle, both masses
have the same amplitude and frequency before one mass starts to slow down as the other
continues speeding up. So the question was how is it that the masses “know” whose
turn it is to have the energy transferred to it when they are in this equal state of
motion?
The way I approached the problem was to think conceptually about the momentum and
direction of energy transfer in the system. I drew out a series of simple sketches to
describe the basic motions of how the first pendulum moves, the second one starts to
move
as the first one slows down, they move at the same speed, the second one is moving
faster than the first, and then how eventually the first pendulum is at rest as the
second one moves with its original speed. At the time when the first pendulum has
slowed down enough and the second pendulum has sped up enough to be swinging at the
same speed, the first mass is already in the process of slowing down and is losing
kinetic energy. It has a negative change in velocity, therefore a negative momentum.
The second mass is already in the process of speeding up and is therefore gaining
kinetic energy; it has a positive change in velocity, therefore a positive momentum.
This can be seen on the amplitude versus time graph that a student had made at one
time and posted next to the set-up. At the time when both amplitudes are the same,
one curve has a positive slope while the other curve has a negative slope,
illustrating how the masses “know” to continue their energy transfer in the
appropriate direction.
Later we did some more of our usual Friday afternoon cleaning of the LTC. Today I
focused mainly on organizing the desktop shelving units according to the use of the
material. In this way, all of the optical instruments and pieces are easy to spot on
one side and the mechanical parts for building setups are on the other side.
Dr. Noé left the July/August 2012 issue of OPN Optics and Photonics News on the desk so
I flipped through it a little and came across an article on physics education,
Photonics Explorer: Working within the curriculum to engage young minds.
The article discussed how
there is an increasing number of students not showing an interest in science, which is
something I’ve noticed, and actually it’s one of the main reasons why I want to go into
teaching. Oftentimes teachers are able to spark students’ interests with a fascinating
demonstration, but this does not last long enough to inspire a career in science.
Therefore, the article cites that a possible solution is to promote continuous hands-on
discoveries throughout the curriculum, even on a daily basis. The Photonics Explorer
kit is meant to do just that-- make abstract concepts (for light and optics) easier to
understand based on guided inquiry-based learning. Students have the opportunity to
create their own setups, predict results, test different theories, and then discuss the
applications of what they found out or how it could be useful outside of their simple
experiment. I think it’s definitely more valuable to actually make a real world
connection with the material and come to an inherent understanding instead of simply
memorizing equations and concepts.
Then Prof. Metcalf stopped by with a researcher who was looking for help in designing
new automotive features, such as a camera that could read street signs without being
saturated with light from the taillight of the car in front of it. This sparked my
interest in reading up on another article from OPN,
Vision Sensors in Automobiles. It discussed new exterior cameras/sensors
(for night/fog vision,
360-degrees panoramic views, and 3D imaging) that were being tested in India to improve
safety. Instead of the usual CCDs, they used CMOS (complementary metal oxide
semiconductor) sensors, which are photodiodes that collect light, generate charge, and
immediately convert this into a voltage at the pixel. I found it interesting that as
they described each type of vision implement, they also described how most of their
inspiration was picked up from nature. For instance, they are looking to develop
polarization based vision systems to see through fog, springing from the fact that fish
seem to use polarization to easily move through dense aquatic fog. This reminded me of
a point that was brought up at the graduate school talk yesterday, about how important
multidisciplinary research is.
I was also a little curious about this strange phenomenon about fish so I quickly did a
little extra research and found an article about the
polarization vision in cuttlefish. Evidently most aquatic creatures can sense
polarization because of how the
photoreceptors in their eyes are orthogonally oriented; therefore they have a high
sensitivity to how light waves approaching them are oriented and can improve the
contrast of the image scene in front of them. Using an imaging
polarized light analyzer, researchers actually found that cuttlefish give off a
prominent polarization pattern of light around their eyes and forehead. This pattern
however disappeared when they were camouflaged, attacking prey, or laying eggs. A
study was conducted where researchers noted the behavioral responses of cuttlefish when
the polarization of their reflected image in a mirror was changed. They found that the
cuttlefish stayed in place when the polarization of the reflection was distorted, but
they retreated from their mirror image when the polarization was left unaffected. The
research concluded that cuttlefish use their polarized vision and the polarization
coming off of themselves for recognition of and communication with each other.
Today also I started reading the Diffraction Grating Handbook that Dr. Noé gave
me and updated my Ideas and Resources page (to reorganize the topics a
little and to include some more of my interests).
Today we had our second REU group meeting in which everyone described his or her progress
since our previous get-together (20 June 2012). Kate and Sarah are currently working with
the actual spectral data for their star, specifically trying to apply the
χ2 method of reducing the data for their use; Sarah also mentioned that
their task was to study the sodium doublet in the spectral data, which I already knew about
from Benjamin’s LTC project that I read yesterday. David has started producing actual
graphs charting the band structure of silicon crystals and how the bands change when he
substitutes boron into the structure. Yakov is in the process of switching over to a new
software program to do the calculations for his group’s simulations of the electron and
proton collisions. June has been spending some time figuring out how a new light sensitive
camera will work with the AMO group’s apparatus, as well as practice profiling Gaussian
laser beams. Jonathan explained how he’s working on a
Singular Optics Map for his website as a
resource to trace the research and publications written about optical vortices and related
topics. Marissa explained the step-sweep method of aligning a beam to go through an optical
fiber and briefly discussed the difference between single and multi-mode fibers.
Afterwards there was a seminar on getting into graduate school, specifically to continue
science research. A panel of professors and the dean of the graduate school described the
importance of the six key components: your undergrad GPA (especially from junior and senior
year), your GRE score (mainly the quantitative and verbal combined), your personal statement
(highlighting your passion for a subject), your letters of reference (one of which should
definitely come from your research advisor), your on-campus interview (at which you should
also ask plenty of questions to demonstrate your engagement and interest in the field), and
(most importantly) your previous research experience.
Then we had an optics group meeting in the conference room where each of us discussed out
present work. While I was discussing my interest in the creation of Bessel beams using a
spatial filter, Professor Metcalf asked if I had grasped the concept of “spatial
frequencies” and what it actually means to decompose an image into these. I understood that
mathematically the spatial frequency, as the inverse of the wavelength, is the number of
cycles of a wave per meter, (similar to how the temporal frequency, as the inverse of the
period, is the number of cycles of the wave per second). It’s easy to see this on the graph
of a sine wave; however, I realized that it was difficult to picture how a 2D object in the
spatial domain could be decomposed into a pattern of bright and dark spots in the frequency
domain, as seen in this
example. The Fourier transform is what describes the object in terms of the individual spatial
frequencies that make it up and by filtering these frequencies you can change the appearance
of the image. But it’s confusing to think of an object being described by 2D Fourier
analysis.. Tomorrow I’m going to look into this some more to see if I can better understand
the visual application of this seemingly abstract concept.
Later in the day I also helped out Ariana with some of the basics of Fourier series and then
showed her some examples on the oscilloscope (the same useful examples that Dr. Noé had
shown me, such as comparing the complex sound wave of your voice to the single sine wave of
a tuning fork or a whistle).
Today I read through Benjamin’s LTC project
Diffraction Grating: Can We Detect the Doublet. He had examined the use
of a diffraction grating in spectroscopy. Spectroscopy is the analysis of radiated energy of an
object by looking at its emission spectrum. The “sodium doublet” that Benjamin
looked at is a pair of two of sodium’s spectra lines from two electrons in the same
orbital that have separate energies associated with them based on their magnetic
moment, and therefore they have different but very, very similar wavelengths. He was able
to resolve these two lines with a pair of toy glasses (the kind that give a light
source a rainbow of halos) that had diffraction grating “lenses.” A diffraction
grating basically spreads out the wavelength of light comprising a light source. It
works like the double slit experiment in which the light propagating through multiple
slits interferes to create a pattern of high and low intensities; for the grating,
however, there are an extensive amount of slits, meaning the resulting interference
pattern becomes very narrow peaks of intensity (aka the spectra lines).
I did some research on the concepts behind
Bessel functions
since I was having trouble grasping what the equations actually meant. As I learned
from
Kowalczyk’s
article, the Bessel beam created from diffraction of a ring source of light is
directly proportional to the zero-order Bessel function. The general Bessel function
is a cylindrical function that describes a converging series (which is the first kind
of solution to the Bessel differential equation). The different “orders” are
parameters that refer to various solutions; they govern the shapes of the graphs: an
even ordered Bessel function has an even curve, an odd ordered function has an odd
one, and a real order in general makes the Bessel function curve’s amplitude decay
like a damped oscillation over time.
I also was curious about what a “CCD” camera actually was, since it seems to be used
often with collecting image data, so I did some quick
Wikipedia research (and cross
checked with an information page from the
University of Oregon). The CCD is a
charge-coupled device that contains a number of
image sensing pixels. Each pixel is a photosensitive cell made of a semiconductor
material that gives off electrons when a photon strikes it. The cell collects these
charges and then shifts them within the device to an area where they can be converted
into digital values.
I read through most of the article:
Demonstration experiments on nondiffracting beams generated by thermal
light
by Lorenzo Basano et al.. At one point it started talking about spatial
coherence and temporal coherence, and I realized that I wasn’t too sure about the
distinction between these two types. The section in K. K. Sharma's book:
Optics: Principles and Applications, makes the difference
easy to picture. Temporal coherence is a longitudinal coherence; it occurs when two
points along the direction of propagation (z-axis) possess a phase relationship.
Spatial coherence depends on the physical size of the light source and if the points
are radiating together; it occurs when two points lying in the transverse plane are
still correlated in phase after a certain amount of time. Therefore, the
“nondiffracting” Bessel beam is spatially coherent, since its transverse intensity
profile is independent of the z-axis.
The apparatus can be used with either a HeNe laser or 150W halogen lamp (halogen
lamps can run at higher temperatures because a halogen cycle chemical reaction
prevents the tungsten filament from evaporating). The light source is focused
through a microscopic objective and then through a pinhole aperture. The light is
then sent through a transparent annular ring (made from a photographically produced
black and white drawing), focused in a converging lens, and collected in a CCD camera
as a quasi-Bessel beam. This can be used to study the difference in spatial
intensity and self-reconstruction ability between a laser light and the halogen lamp,
the effect of large and small pinholes, superluminality, and optical coherence
theory.
The two setups described by Kowalczyk and Basano are fundamentally similar: a light
source is sent through a small aperture (the center of a washer in the first and a
pinhole in the second), it is spatially filtered to a certain extent (Kowalczyk uses
a washer with its center filled-in suspended concentrically in an iris diaphragm and
Basano uses a black and white ring image), and the Bessel beam is the product of a
final diffraction of this annular light source (detected a certain distance away from
the second lens of the 4-f system in Kowalczyk’s, and brought together a
certain distance from a converging lens in Basano’s). However it seems like the one
Kowalczyk describes (see description below in 25 June 12) produces a beam more true
to the actual Bessel beam (though an actual Bessel beam is impossible to make,
since
you need an infinite amount of power). The setup described by Basano still seems
very useful for becoming acquainted with the peculiar properties of this type of
beam.
This morning Dr. Noé asked me to join him at the Simons program breakfast to meet
Ariana, a high school student who will be working with us in the Laser Teaching Center
this summer. It seems like she has a very broad spectrum of interests, like myself,
so I’m excited that she’ll be joining us. After the breakfast, we walked over to the
lab (luckily the torrential downpour from this morning had let up!) and had a group
meeting to discuss research notebooks and our interests in optics. Then I spent some
time helping Marissa and Jonathan try to realign the single-mode optical fiber, by
walking the beam with the position and angle mirrors.
I finished the theory section on how to create a ring source (which can then be
diffracted to produce a Bessel beam, see 21 June 12 below) from the
Generation of
Bessel beams using a 4-f spatial filtering system article. The method
employs a
4-f system (similar to Lidiya’s spatial filtering project setup), in which
there are two lenses that facilitate a two-stage operation of successive Fourier
transforms. Kowalczyk et al. designate 3 planes: the object plane, the Fourier
plane (between the two lenses), and the image plane. The object plane is the input
focal plane for the first stage, the Fourier plane is the output focal plane for the
first stage and input focal plane for the second stage, and finally the image plane is
the output focal plane for the second stage. The input plane (in both instances) is
converted into the output field by a spatial Fourier transform, and we can spatially
filter the image by altering the diffraction pattern in between these two fields. The
goal is to only transmit the high-spatial frequencies that compose the sharp edge of
the object’s field.
This can be done with an annular mask that has a specific ratio of its outer radius to
inner radius (3.84 was used in this case). A very large outer radius of the filter
allows more high spatial frequencies to pass, meaning the image will have a very sharp
edge and the graph of amplitude versus image radius will display Gibb’s phenomenon at
the edge of the aperture. A very large inner radius of the filter determines the
overall width of the filtered edge because it suppresses the lower spatial
frequencies.
I also read through the apparatus section and made a diagram for myself based on the
focal measurements and object/filter radii Kowalczyk et al. used. A HeNe laser
is sent through a pinhole to improve the mode quality (by means of two polarizers, two
lenses, and a mirror). The beam is then collimated with a third lens and sent through
the object, which is a steel washer mounted on a glass slide with an iris diaphragm
fitted around the outside to keep excess light from leaking around washer. The next
part is the 4-f spatial filtering system in which the light rays are sent
through a compound-planoconvex lens, a spatial filter, and a second
compound-planoconvex lens, all separated by one focal length. Then about 9 cm past
the image plane, the Bessel beam forms from diffraction of the thin ring source, which
is recorded by a CCD camera.
It's a complicated set up, however if possible, I'd like to try to see if I can build
it to create a Bessel beam. There's also supposedly a simpler way to produce one,
using thermal light, which I'll read about tomorrow.
I read through the abstract from Jonathan Wu’s project,
Fourier
Transform Spectroscopy , which
discussed the Michelson interferometer. He described how Fourier
transform spectroscopy plays an important role in Optical Coherence
Tomography (OCT), which is a non-invasive imaging technique that uses a
Michelson interferometer. It works with light sources that have a very
short coherence length (that is, a short distance over which the
various light waves stay in step). On my first day in the LTC, we did a
project with one of these interferometers (see 12 June 12 below)
where we altered the path length of one of the beams of light and
counted the number of passing fringes in the subsequent interference
pattern to determine the laser’s wavelength by working backwards. But
now after reading through this abstract I’ve come to realize that
there’s so much more to the apparatus: the interference pattern is a
Fourier transform, showing the spectral distribution of the laser light
(intensity versus wavelength).
Which leads into Doug Broege’s Observing the Sodium Doublet and Laser
Diode mode structure with a Czerny-Turner Spectrometer project. The
spectrometer he used, which was donated by Dr. Wagshul,
separated the components of a particular source of light according to
wavelength. He discussed how he rigged a set of mirrors and a
diffraction grating to project a light source onto an array of
photodiodes. By connecting the photodiodes to an oscilloscope, he was
able to view the relative intensities of different wavelengths of light
and how this relationship changed over time as the light source warmed
up. Photos from his apparatus and oscilloscope results can be seen
here. The spectrometer displayed the separate modes running through a multimode laser and
therefore could be used to determine more of its properties. Though the
results are obtained by a different means than Jonathan Wu, Doug’s
project seems very similar to Fourier Transform spectroscopy, since it
deals with analyzing the spectral components of a light source.
Today I read most of the second section of the theory in
Generation of
Bessel beams using a 4-f spatial filtering system . I am going
to
finish up the last bit on Monday morning, so I will wait until then to
post a complete summary. Then in the afternoon, we spent some time
cleaning the lab. First Dr. Noé gave us a tour of where things should
go and showed us what areas needed the most organization. I spent some
time straightening up the electronics area- neatening some of the
drawers, putting away objects that had been left out, and rearranging
the resistor drawers by dividing them up and labeling the different
strengths.
While I was sorting out the resistors, Dr. Noé explained to me that some
of the equipment in the lab had special markings to show which pieces
were donated by Dr. Mark Wagshul, such as the cabinet I was organizing.
Currently,
Dr. Wagshul is at the
Albert Einstein College of Medicine in the Department of Radiology and
the Department of Physiology and Biophysics. His ongoing research
efforts include examining the uses of Magnetic Resonance Imaging (MRI)
to image blood flow and cerebrospinal fluid flow in the brain, the uses
of MR-spectroscopy to quantify concentrations of common metabolites in
the brain, and the manipulation of pulse sequences for MRI to obtain new
types of informative images. (That last part is something that I again
can connect to the medical physics class I took last semester, since we
went over how important the sequences of radiofrequency pulses are. For
instance, if you want to gain information about the relaxation times of
the nuclear spins of a type of atom, you use a pi pulse first to rotate
the spins by 180-degrees. However, if you want to gain information
about the desynchronization times of the spins, you first use a pi/2
pulse to initially excite the spins and then a pi pulse to measure the
spin-echo.)
Dr. Noé then got on the topic of Dr. Bill Hersman, who is a physicist at
UNH who discovered that it is possible to use MRI techniques to image
the lungs with the use of
polarized xenon gas.
It was already commonly known that helium (though more expensive) could
be polarized by mixing it with vaporized rubidium, polarizing the
rubidium with a laser, and then having the rubidium transfer the
polarization to the helium atoms before condensing back into a solid.
But the problem was that rubidium didn’t polarize xenon (a more
accessible gas in the medical field) as efficiently. So he created an
elongated contraption that alternatively pointed the laser in the
direction against gas flow to polarize rubidium better, therefore
polarizing 60-70% of the xenon gas. The part that I found most
interesting about Dr. Hersman’s story was that he came up with this
apparatus with much less funding than the other leading researchers
around the world who were working on the same task. Due to the fact
that he was on a strict budget, he had to come up with a different way
than what was widely anticipated to be the answer, and it turned out
that his creative approach is what succeeded. In general, I think it is
important to try to always look at all angles of a situation before
diving into the obvious solution, because sometimes it’s necessary to
use unconventional reasoning.
I found these medical physics tangents very intriguing, since this is a
branch of physics that I’ve become increasingly interested in. What
I’ve currently been looking into on my own is the connection between
various medical imaging techniques and their application to conservation
science. In other words, the use of nuclear magnetic resonance imaging
or x-ray tomography to non-invasively study the degradation,
restoration, and conservation
of elements of cultural heritage: artifacts, works of art, or important
structures. Conservation science has become an increasingly popular
field in Europe, especially in Italy. A particular example is at the
University of Bologna where there is a
Magnetic Resonance of fluids in Porous Media
(MRPM) research group that uses MRI to test the efficacy of
certain hydrophobic treatments to elements of Italy’s cultural heritage.
As I mentioned in my
biography, I’ve always had a love of art and art history, and it is fascinating when these topics can
be innovatively incorporated into physics (or vice versa).
I was able to get my
Ideas and Resources page up and running
after looking up how to add a webpage to my directory. Right now it
contains links to the sites and papers I’ve found most helpful and/or
interesting. As I begin to fine-tune my project idea, I’ll probably
add/remove some of the links.
We spent some time today in the conference room going over past LTC
projects; Dr. Noé pointed out some of the ones that pertained to the
topics Marissa, Jonathan, and I are interested in. One of the projects
that stood out for me was Simone and Daniel’s Understanding "Walking
the Beam." They analyzed the process of adjusting two mirrors (the
position and angle mirror) in order to send a beam through two consecutive
pinhole apertures. It can be a tricky process to make sure everything is
aligned—Simone and Daniel described how you have to go systematically back
and forth between the two mirrors, optimizing the position mirror, then
the angle mirror, then back to the position mirror, etc. Another
interesting project was Sarah Campbell’s Single Mode Optical Fiber,
where she measured the high-intensity profile of a Gaussian beam by first
measuring the main lobe and then blocking out that part in order to
measure the
much-less intense side lobes. Also, a random but important thing to note
is that when you’re cleaning optical equipment, such as a mirror, you are
only supposed to wipe once in one direction to avoid altering its optical
properties.
I looked over the abstract for Annie’s LTC project, Investigating
optical vortices created with a single cylinder lens, where she
describes how an astigmatic lens causes two orthogonal portions of a laser
beam to diverge and gradually become circular in the far-field. This
process converts the Hermite-Gaussian (HG) laser mode to the
Laguerre-Gaussian (LG) mode, a votex with a dark spot in the center. The
hollow part has zero intensity from the helical phase fronts cancelling
each other out. She also found out that this vortex beam
disappears in the focal region, where the HG mode subsequently reappears.
There’s a problem with the link to her actual Intel report, however I
found it with a simple Google search and will read over it tomorrow.
Today I studied part of Generation of Bessel beams using a 4-f spatial
filtering system by Jeremy M. D. Kowalczyk. The publication discussed
how to make a Bessel beam from the diffraction of a thin ring source of
light. The ring source comes from a 4-f spatial filtering setup
where a uniformly illuminated circular aperture is subjected to a
high-pass filter. (As I already learned from Lidiya’s project, this type
of filter enhances the edges of the image by blocking out the lower
spatial frequencies located in the middle of the diffraction pattern.) It
turns out that the zero order Bessel beam is a uniform superposition of
plane waves (each with a complex amplitude and angle of propagation in
relation to the optical axis); with a two-dimensional spatial Fourier
transform, you can calculate the angular spectrum of plane waves for the
beam.
I read through the first part of the theory that describes creating a
Bessel beam from the ring source. When I first started the article, I
struggled for a little bit with the derivations of equations. I
understood some of the math would be difficult, but this looked downright
impossible! I decided to look back at the article on the computer, and it
turned out that all of the parenthesis, integrals, and summation signs did
not come out on the printed copy I was reading from. Strange.. After
hand-writing those in, the math became easier to follow. It started out
with the Fresnel diffraction equation using cylindrical coordinates; this
accounts for the curvature of the wavefront approaching the diffraction
field, and how the phase of each individual portion of the light varies
depending on the radius (this is assuming the input field is azimuthally
symmetrical). Through simplifying, subbing in the Bessel function cosine
identity, and some integration, you come out with the Hankel transform,
which is the two-dimensional Fourier transform of a circularly symmetric
function; it is the weighted sum of an infinite number of Bessel functions
of the first kind. Using the delta function to represent the thin ring
source of light, the result showed that the diffracted field was directly
proportional to the zero order Bessel function.
Evidently the equation does not produce a perfect Bessel beam, since it
violates two of the requirements: planar wavefronts (our equation was
derived from a spherical wavefront) and a constant spot size throughout
propagation (the central lobe has a radius that increases with distance).
The use of a thin lens to collimate the diffracting waves would convert
the beam into a standard Bessel beam with a uniform phase (plane
wavefront) and constant amplitude (constant spot size). Though Kowalczyk
et al. did not use a collimator in their setup, they assure
that it all still works.
Tomorrow I’ll read the second part of the theory (which discusses how to
use a 4-f spatial filtering system to create the ring source), and
describe the experimental setup. There was also another interesting
article I found about creating Bessel beams with a thermal light, and
Jonathan told me about an article that described how to create complex
beam shapes with an array of individual phases (which sounded like the
optical version of the sonic screwdriver I read about yesterday).
We had our first REU group meeting today in which everyone in the group gave a
brief summary of the project they were working on. I explained my general
progression so far from reading the book on Fourier analysis, to becoming
interested in its role in diffraction patterns and spatial filtering, to
trying to correct optical aberrations with amplitude and phase filters, and
now to the idea of nondiffracting Bessel beams. David is working on a
theoretical solid-state physics project in which he’s currently using computer
simulations to see what would happen when silicon is substituted for nitrate
in gallium-nitrate. June is with the atomic, molecular, and optical physics
group, and is currently doing ray tracing with Mathematica in order to
eventually understand how to build a diode laser. Yakov has been working on a
project at the Brookhaven Lab since back in October and is currently using C++
computer programming to figure out the best materials for an electron beam.
Kate and Sarah have so far learned how to create a Linux graph to chart the
luminosity versus effective temperature of different sized protostars
(measured in terms of solar masses) over an extended period of time.
Jonathan
explained how he was interested in optical vortices, especially in conjunction
with their unusual
application of the Maxwell equations, and then Marissa described her
fascination with optical fibers and possibly trying to send a vortex through
one. We’ll be meeting again every Wednesday to report our progress.
During the first weekly pizza lunch Professor Dominik Schneble explained
the process of creating ultracold atoms, which was the basic principle behind
Bryce Gadway’s thesis defense from Monday. The atomic, molecular, and optical
physics group is currently working with Bose-Einstein condensates (BEC): a
phase of matter in which there are bosons (one of the fundamental classes of
subatomic particles) occupying the lowest quantum state. They are created
from laser cooling and magneto-optical trapping (MOT). Then the AMO group
uses optical lattices to study properties of the BECs. An optical lattice is
created from two opposing beams that give the boson a momentum from continuous
absorption and stimulated emission. There is a certain level of uncertainty
in the energy due to the lattice being pulsed on for a very short period of
time; this makes sense in connection with the Fourier transform, since the
shorter the time, the more uncertainty there is in the function. It was
interesting to learn that every time they make a measurement, the BEC is
destroyed and
they have to create another one (which only takes about one minute!) to do the
next measurement. After the lecture, we also got a brief tour of the AMO lab,
which was pretty cool to see all of the actual instrumentation used.
Dr. Noé gave me an article to read that he found in this month’s issue of
Physics Today: Classical votex beams show their discrete side, by
Ashley G. Smart. It reported the invention of a sonic screwdriver, which is
an ultrasound device that can generate high-angular momentum acoustic
vortices. The research group from the University of Dundee in the UK was able
to create a sound wave with three intertwined helical wavefronts by
individually adjusting an array of 32 x 32 transducers. With a water chamber
device that could measure torque exerted by the acoustic vortex and the
radiation pressure, they could determine the relative amounts of orbital
angular momentum and beam energy, respectively. I had to look up orbital
angular momentum (OAM), since it was something I was unfamiliar with. It
describes the actual revolving motion of the beam, whereas the spin angular
momentum (SAM) is a product of the polarization of the beam. As is the usual
case nowadays, there was a connection to the Fourier mathematics I’ve been
studying, since the shape of the overall acoustic vortex is really a
superposition of each wave produced by each individually phased transducer.
Overall it was very interesting stuff! The end of the article suggested
advances in developing complex sound beam shapes (such as the nondiffracting
Bessel beams) could be useful to ultrasound surgery.
I also read through Will’s LTC project: Modeling Diffraction by a Circular
Aperture Illuminated by a Diverging Light Beam. He described the
accidental discovery of an unusual diffraction pattern after passing a beam
from an optical fiber through a pinhole. It started out as a dark spot in the
center, and as the distance between the tip of the fiber and the pinhole
decreased, a more complex pattern of concentric dark rings developed. Will
was able to model the observed intensity distributions at certain optical
fiber-to-pinhole distances by squaring the Fourier transform of the pattern
(which was the product of the Gaussian intensity function, the phase function,
and the zero order Bessel function). His report also contains a very helpful
ray diagram to visualize the diffraction pattern in the Fourier plane of a 4-f
spatial filtering system.
First on my list tomorrow is to read through more of the Bessel beam articles
I printed and also review some of the mathematics behind Bessel functions.
Today Dr. Noé helped us to better understand the Polaroid CP-70 contrast
enhancement filter from last week. When you hold the filter up to a mirror
and look straight through one side, you can see your image clearly in the
mirror. However, when you turn it over to the other side and look straight
through it to the mirror, everything appears dark. The reason the reflection
was blocked only one
way was because the Circular Polarizer (CP) is a combination of two sandwiched
polarizers: a linear and a quarter wave plate. When light travels through the
linear polarizer first, it becomes oriented at 45-degrees, and then after going
through the quarter wave plate, the x and y components are rotated
with a 90-degree phase shift, thus creating circularly polarized light oriented in
a certain direction (it can be either left, right, horizontal, vertical—we don’t
know specifically for this polarizer, though it is possible to figure out with a
few reference polarizers..). After this light bounces off of the mirror, it comes
back circularly polarized in the opposite direction. This means after going
through the quarter wave plate again, the circular polarization is undone and the
linearly polarized light that emerges (oppositely oriented to the original linear
polarization) is blocked. (If you look through the other side of the filter, with
the quarter wave plate in front of your eyes, there is no change in your
reflection, since the
non-linearly polarized light passes through the quarter wave plate unaffected.)
This filter can be used on a computer screen to block reflections from outside
light sources, therefore eliminating screen glare.
The articles I found on phase filtering used to reduce the effects of optical
aberrations turned out to be mainly theoretical and fairly complex. This is what
I’ve come up with though today:
(1) Firstly, I found a project done by Xueqing titled The Aberration Correction
of a Diode Laser after doing a search on the Laser Teaching Center website for
projects that dealt with aberrations. The student’s objective was to make a diode
output beam as round as possible, since the beam normally diverges differently in
different planes and is subject to optical aberrations. The key points from the
project: (A) the aberrations were effects of the diode laser itself; in other
words, they were not caused by an external deformed lens, but rather the imperfect
light source. (B) Correction for these aberrations was done with the use of a
lens, not by filtering. However, in addition to the lens, she did use an
anamorphic prism to allow for the magnification of the beam size along one axis,
but not the other, which I thought was interesting.
(2) Amplitude and Phase filters for mitigation of defocus and third-order
aberrations (Samir Mezouari, 2004) described a theoretical analysis of possible
filter designs. The amplitude filter is easier to create than a phase filter, and
achieves the same correction, however at the expense of light transmission. There
were two amplitude examples discussed: the annular aperture method (which uses a
very small effective pupil) and the use of shaded filters (which is a method that
uses the whole aperture). The publication then discussed that wavefront coding
(carried out by means of an aspherical phase plate) could be used to tag the
wavefront coming in so that it would be possible to restore the image
(with
digital image processing) over a large range of defocus. This method makes it
theoretically possible to have a diffraction-limited resolution, which means that
for the most part diffraction alone determines image quality (since the aberrations
are greatly diminished).
(3) I read through some of Spatial Filtering in Optical data-Processing
(Birch, Rep. Prog. Phys, 1972), which is a publication that Lidiya cited
in her project. The section on phase filters describes how they are used to
advance/retard the relative phase of transmitted light and a few methods of
fabrication. The one that seemed the simplest was the use of Vectograph film,
which produces a phase shift from two sensitive layers separated by a supporting
base layer. Each sensitive layer passes one polarization freely and transmits the
perpendicular polarization depending on the properties of the layer. Usually the
two polarizations will be given a 180-degree phase shift. Besides optical
aberration correction, phase filters can be used for enhancing discontinuities at
slits and edges, while at the same time suppressing the illumination of uniform
areas.
Since Dr. Noé says it’s best to have multiple project ideas, I’ve also started
looking at some articles about Bessel beams. So far what intrigues me is that
these beams are nondiffracting and self-reconstructing.
After reading more about their properties, I’d like to brainstorm new
interesting ways to analyze Bessel beams..
Dr. Noé recommended that I read Lidiya’s report Spatial Filtering in Optical
Image Processing since I was interested in Fourier analysis in connection with
optics. The project was focused on Abbe’s Theory of Image Formation, which states
that objects illuminated by a plane wave form diffraction patterns in the Fourier
plane (back focal plane) of an objective lens. The squared Fourier transform
(squared since our eyes don’t know what a negative light wave is, we just see the
brightness of the light) is the intensity distribution of an image’s diffraction
pattern. In other words, the diffraction pattern is a visual representation of the
optical signal divided in terms of spatial frequencies, all with a different weight
of importance to the overall image.
Through filtering certain parts of the diffraction pattern, Lidiya observed how
different spatial frequencies of the pattern contributed to certain components
of image formation. Obstructing the low spatial frequencies (located on the
inside of the pattern) with a high pass filter enhanced the edges. Blocking
the high spatial frequencies (located on the outer part of the pattern) with a
low pass filter blurred the image details. Lidiya had used a Ronchi grating as
her object. I think it would be interesting to try a similar project with a
more complex object, such as a design or picture printed on transparency paper.
Though now that I think about that again, it would be difficult since the laser
beam would be too small comparatively.. I would have to devise a way to expand the
beam.
I am also interested in Mara’s unrelated project on the Optical Activity in
Sugar Solutions. She investigated the polarization of
light due to chiral molecules as the solution density and
path length were altered. When light beams of varying wavelength were sent
through a sugar solution, a phase difference was introduced to the x and
y components, which rotated the linearly polarized light. As the
solution density increased, so did the rotational angle, and it was found that
the waves with the shorter wavelengths were rotated the most.
While trying to combine a few of the topics I’ve become interested in, (namely
astigmatism, using Fourier mathematics to describe the diffraction pattern
before image formation, and spatial filtering to improve image quality), I
found the following: Circularly symmetric phase filters for control of
primary third-order aberrations: coma and astigmatism (source: Mezouari,
Samir; J. Opt. Soc. Am. A / Vol. 23, No. 5 / May 2006). I haven’t had a chance
to go through the mathematics yet, but the article describes the development of
a quartic filter, which is a phase-mask that makes use of the interference
pattern of phase differences to retard portions of a light beam. This is used
to improve image resolution and light gathering, making it possible to correct
the coma and astigmatic aberrations. Besides this, I found a number of other
publications that discussed similar topics. I’m excited to learn more about it
tomorrow and maybe try to develop a project somehow from this-- that is, from
the use of a phase filter to correct optical aberrations (such as astigmatism,
coma, spherical aberration) based on the Fourier transform of the diffraction
spectrum.
The Bruce W. Shore lectures lasted for about an hour and a half each on Tuesday,
Wednesday,
Thursday of this past week. Bruce Shore is known for his work on the theory of
coherent
atomic excitation in conjunction with multilevel atoms and incoherence. The title
of his lecture series was “Visualizing Quantum State Changes.” For someone who’s
only taken an introductory course on quantum mechanics, I was able to recognize some
concepts but it was still a little hard to follow. The lectures described ways in
which to picture quantum state manipulation (that is, transferring population from
one state to another) in Hilbert space (referring to different energy levels instead
of an orbital atomic structure).
The first day he described a simple two-state example, in which pulsed energy was
used to create a population transfer. A gradual turn-on/turn-off of the pulse
resulted in the excited population returning to their original state. However an
abrupt pulse left some electrons in that second state. This was all based on the
time-dependent Rabi frequency: the frequency at which there were oscillations
between states. The second day he discussed a vector model of the situation and how
a full population transfer could be achieved with a sequence of two pulses. And
then on the third day he discussed the slightly more complicated three-state system,
which had two separate Rabi frequencies.
The part of the lecture that really sparked my attention was on the second day when
he began discussing the change in the vector orientations based on the pi and pi/2
pulses, which reminded me of the pulse sequence used in NMR imaging I learned about
last semester in my Medical Physics course. I’m not sure if during his lecture he
had mentioned the application to nuclear spins being oriented in a magnetic field,
but if he had I guess I had missed it. Bruce Shore was very good at explaining
every small detail and term he used, but at the same time some of the material was
hard to digest with the continuous speed he was moving at, so I found myself getting
caught behind numerous times.
But now after sitting down with the material on my own time and coming to the
initial realization, it all started to click into place! The whole principle of NMR
is moving between two states: equilibrium and excitation of the nuclear magnetic
moments (which are proportional to the nuclear spins). This is achieved through a
series of radiofrequency pulses, pi and pi/2. Based on the sequence and timing of
pulses, information about the part of the body being imaged is gained both through
the desynchronization and relaxation of the spins. The Larmor frequency is the
quantized frequency of precession of the transverse nuclear magnetic moments about a
static magnetic field, which is along the same lines of the Rabi frequency.
Now that it became so clear and obvious, I feel kind of silly for not making the
connection myself during the lecture. However, I guess it was partially due to the
fact that in my Medical Physics class, we only briefly mentioned the Bloch
equations, and we didn’t use the Rabi frequency, the time-dependent Schrödinger
equation, or really any linear algebra for that matter.
I scanned through Bruce Shore’s article Coherent manipulation of atoms using
laser light [from Acta Physica Slovaca 58, No.3, 243-486 (2008)] and sure enough
he mentioned nuclear magnetic resonance! If I have any spare time this week, I’d
like to read more of the publication. Now that I’ve recognized a basic application
of the material, I feel like it will be easier to teach myself the parts I didn’t
understand about the lecture.
Since it was sunny today, we spent some time out of the lab to do a few
experiments outdoors. Dr. Noé showed us multiple demonstrations: how a shadow
becomes blurrier as the object is moved farther away from the screen (which was what
brought forth Marissa’s project last semester), how the sky is polarized from
Rayleigh scattering (which can be seen through a circular polarizer), the different
focal lengths of various sized lenses, and how the distance between a mirror and
screen changes the size of the magnified reflection of light.
(1) Image magnification with a mirror:
We used a mirror was that completely covered with the exception of a small hole in
the center. Marissa then focused the reflected light onto my notebook, and together
we adjusted the distance until the reflected spot had a 1 cm diameter (the size of
the spot increased as we increased the distance between the mirror and notebook).
The distances we calculated from the mirror to the image were 86.4 cm, 91.4 cm, and
81.3 cm. Marissa’s project from last semester determined that the diameter of the
image and distance from mirror to image (along with the diameter of the hole for the
mirror) could be used to solve for the angular size of the sun with a hyperbolic
function.
(2) Using magnifying glasses to burn a piece of paper:
Dr. Noé started out by explaining how the scene in The Lord of the Flies
where the boys use Piggy’s glasses to start a fire is not physically possible.
Since Piggy was nearsighted, that means he would have had concave lens for seeing
far distances, and concave lenses don’t focus light to a point. That being said,
even with a pair of reading glasses (which are made from convex lens that do
focus light rays to a point), there wasn’t enough intensity in the focused beam to
ignite a piece of black paper. The focal length was 80 cm and the convex lens was
+1.25 diopters. A diopter is the unit of measurement of optical power and is the
reciprocal of the focal length. Optical power is the degree to which the lens
converges/diverges light.
There are a couple of factors that come into play: the area of the lens (which
determines the intensity of the focused light) and the focal length (which is a
function of the index of refraction of the lens, the thickness, and the radii of
curvature). With the smallest lens we were able to focus the sunlight to a tiny
point (at a focal length of 5 cm), but the small area of the lens meant there wasn’t
much intensity being concentrated on the paper. With the largest lens, there was
plenty of intensity in the focused light, however the focal length was so long (262
cm) that the projected image was a lot larger than that of the smaller lenses. The
magnifying glass had the perfect area and focal length to focus an intense amount of
sunlight onto a small spot, successfully burning a hole in the black paper.
(*) Interesting extra research: Just a note about optical power- I thought it was
interesting that the optical power of two or more lenses close together is
approximately equal to the sum of each. In addition, the optical power changes when
the lens is immersed in a refractive medium, which therefore means the focal length
changes. This reminded me of my time on the swim team at my high school and how
everything always seemed slightly magnified when I went underwater with my goggles.
(*) When I was looking up different types of glasses, since personally I don’t wear
them
and therefore don’t know much about them, I came across astigmatism (which was a
condition I’ve heard about but never fully understood). I found it fascinating that
an irregular curvature of the cornea causes the formation of multiple focal points
along different planes (making the overall image blurry). Further more, it was
interesting that a toric lens could be used to correct this condition.
Today after getting through more of the Fourier book I came to understand Fourier
mathematics in a whole new way. When I first learned about Fourier analysis, to me it
simply meant a way to decompose a complicated wave form into its simpler components. I
had learned the different forms for the Fourier Series with its separate coefficient
formulas, the concise complex versions of both of these, and then Fourier Transform
coefficient formula and its inverse. But after going through the entire derivations
again, I realized that I hadn’t actually grasped the conceptual differences that well the
first time around. (This may contain a little repetition from my last journal, but I
just wanted to set everything straight in the same place.)
The Fourier Series formula does exactly what I remembered: it is used to quantify a
complicated periodic wave (the key point is that the wave is periodic- it repeats
itself in a finite amount of time), to show how it is the sum of simple waves. It
contains three important terms which represents the combination of three types of
simple waves, a0, cosine, and sine.
To find the individual coefficient formulas, it’s a matter of finding the area under the
curve of that specific wave and then dividing by the period (since the area is the
amplitude times the period). So we take the integral of one period after multiplying the
function by either cosine, sine, or nothing (depending on whether you are looking to find
an, bn, or a0) in order to cancel out all of the
net areas of the other coefficients.
The Fourier spectrum creates a graph of the discrete frequencies and their amplitudes
contained in the complicated waveform. (Example application: This is an important tool
for analyzing which frequencies make up the defining characteristics of a certain sound.
For instance, the first 2 peaks of a vowel, known as “formants,” are what define the vowel
sound).
Now after using Euler’s formula to create a simplified complex number representation of
the Fourier series and its coefficients, we don’t end up with an easier way to do the
calculations, but rather an easier way to understand the relationship between a
complicated waveform and the simple waves it contains.
Fourier Transform, used to analyze non-periodic waves, is derived from the
complex number representation of the coefficients for a wave with an infinite period. It
no longer incorporates the integral multiple “n” into the formula because we aren’t
calculating discrete
amplitude values; we’re just looking at a function of the possibilities, which is still
informative about the relative amplitudes of each frequency in the overall function. To
do calculations, we have to define a finite period of time; the longer the period of time,
the more closely the graph will represent the true shape of the relative amplitudes. In
other words, it declares with more certainty the frequency of the wave. The fact that the
Fourier Transform incorporates the uncertainty of waves is important to quantum mechanics
applications of the wave-like properties of quanta, since their behavior at the subatomic
level is uncertain and we use probabilities to quantify the possibilities.
Today, after setting up my bio page, Dr. Noé gave me one of his books to read, Who is Fourier? a
Mathematical Adventure, since he knew I was interested in sound as well as optics. While I had
already learned about Fourier analysis in my sophomore year Vibrations, Waves, and Optics course,
this proved to be a very useful refresher of the Fourier series equation and coefficients. I hope to
finish up the book with the chapter on Fourier Transforms tomorrow..
What I read so far brought up some interesting points regarding the
application of Fourier analysis to the way languages are learned. I had never really stopped
to think about the fact that babies learn how to talk just from listening to others speak
around them constantly, and not in the conventional way languages lessons are taught in
schools, beginning with basic vocabulary lists and such. This means that in the complex mix
of sounds a baby hears, he is able to pick out a simple regularity among them, which can be
analyzed through Fourier analysis. The Transnational College of LEX actually did a study
where they realized that the first two frequency peaks on the Fourier spectrum of every vowel
are its defining characteristics. So by altering these “formants” as they’re called, it
transforms the sound into a different vowel. The study also found that there is a
symmetrical pattern formed when the spectrums of each of the vowels are all analyzed
together, known as the Formant Diamond.
Another interesting side note was the way the book approached teaching logarithms. It
pointed out that logarithms express the perception of things in proportion, and that this
actually reflects how humans perceive certain quantities, such as the brightness of light or
the spacing of notes on a music scale. For instance, we are under the impression that there
are equal intervals between octaves, however the interval actually doubles each time.
Today we met up with the summer REU students and mentors for an informal breakfast at the Simons
Center, and then afterwards we broke up into our individual research groups. In the Laser
Teaching Center, Dr. Noé started us out with a few basic optics demonstrations.
The first dealt with a “mirage toy” that projected an image on top of a central
hole in the apparatus of two small pig figurines placed on the inside of two
concave mirrors. When he shined a laser at the image of the pigs, it appeared
that the light was somehow interacting with the image. However this was not
actually the case. After a little thought, we realized that the beam of light
went straight through the image and into the central hole of the apparatus
where it bounced off the concave mirror inside and shined on the actual object.
So when we saw the laser light “hitting” the image, we were really just seeing
the projection of the laser light hitting the actual object below.
Dr. Noé also explained how, if you were to change the distance between these
two concave mirrors, it changed whether the image was a true image or inverted.
After briefly reviewing ray diagrams for concave mirrors, I understood that
this was due to the fact that the inversion of the image depends on where the
object is in relation to the focal points of the two mirrors. With concave
mirrors, when the object’s distance from the mirror is closer than the focal
point length, the image is enlarged but not inverted. Therefore, initially
when the two mirrors are placed together, the image is inverted. However as
the second mirror is moved farther away from the first, the image will flip
back to its true orientation once the object is farther than the focal point.
The other main project we learned about was the Michelson Interferometer, which consisted of a
laser beam being sent through a beam splitter to two mirrors. The light was then reflected off of
each mirror, through the same beam splitter, and each was then further split so that now there
were two beams reflecting back to the laser and two beams sent on a perpendicular path through a
lens to a counter. When the two beams were overlapped, they created an interference pattern that
shifted as the path length of the beam changed. We used this change in path length (the distance
one of the mirrors was moved closer) and the number of passing fringes the counter recorded to
determine the wavelength of the laser beam.
Random New Fact of the Day-
(1) Birefringence: when the refractive index of a material depends on the polarization and
propagation direction of the light ray penetrating it. In other words, the speed of light in a
material is different along different axes.
Monday 28 July 2014
Thursday 24 July 2014
Wednesday 23 July 2014
Tuesday 22 July 2014
Monday 21 July 2014
Friday 18 July 2014
Thursday 17 Juy 2014
Wednesday 16 July 2014
Tuesday 15 July 2014
Monday 14 July 2014
We found a list of Jeffrey Davis’s (San Diego State University) publications,
which is good to go through for different ideas since a lot of his work
has been about these different beam modes. There’s also this article
about making an Airy beam from a tilted lens (Papazoglou 2010).
doppler AND
velocimetry
Friday 11 July 2014
Thursday 10 July 2014
Wednesday 9 July 2014
Tuesday 8 July 2014
Monday 7 July 2014
Thursday 3 July 2014
Wednesday 2 July 2014
select Secure Shell (ssh)
Tuesday 1 July 2014
Monday 30 June 2014
Friday 16 August 2013
Thursday 15 August 2013
(pg. 9 – 68)
Wednesday 14 August 2013
Tuesday 13 August 2013
Monday 12 August 2013
Friday 9 August 2013
Thursday 8 August 2013
Wednesday 7 August 2013
Tuesday 6 August 2013
Monday 5 August 2013
Sunday 4 August 2013
Saturday 3 August 2013
Friday 2 August 2013
Thursday 1 August 2013
Wednesday 31 July 2013
Tuesday 30 July 2013
Monday 29 July 2013
(a) walk it? (b) jog it? (c) sprint
it?
Friday 26 July 2013
Thursday 25 July 2013
Wednesday 24 July 2013
Tuesday 23 July 2013
Monday 22 July 2013
Friday 19 July 2013
Thursday 18 July 2013
Wednesday 17 July 2013
Tuesday 16 July 2013
Monday 15 July 2013
Friday 12 July 2013
(assuming constant, unobstructed
sunlight during this period) 
Thursday 11 July 2013
Wednesday 10 July 2013
Tuesday 9 July 2013
Monday 8 July 2013
Friday 5 July 2013
Wednesday 3 July 2013
Tuesday 2 July 2013
Monday 1 July 2013
Friday 28 June 2013
Thursday 27 June 2013
Wednesday 26 June 2013
Tuesday 25 June 2013
Monday 24 June 2013
Friday 21 June 2013
Thursday 20 June 2013
(1π phase shift for 800-nm light)
Wednesday 19 June 2013
Tuesday 18 June 2013
Monday 17 June 2013
Friday 14 June - Sunday 16 June 2013
Thursday 13 June 2013
Wednesday 12 June 2013
Tuesday 11 June 2013
Monday 10 June 2013
Friday 3 August 2012
Thursday 2 August 2012
Wednesday 1 August 2012
Tuesday 31 July 2012
Monday 30 July 2012
Friday 27 July 2012 - Sunday 29 July 2012
Thursday 26 July 2012
Wednesday 25 July 2012
Tuesday 24 July 2012
Monday 23 July 2012
Friday 20 July 2012
Thursday 19 July 2012
Wednesday 18 July 2012
Tuesday 17 July 2012
Monday 16 July 2012
Friday 13 July 2012
Thursday 12 July 2012
Wednesday 11 July 2012
Tuesday 10 July 2012
Monday 9 July 2012
Sunday 8 July 2012
Friday 6 July 2012
Thursday 5 July 2012
Wednesday 4 July 2012
Tuesday 3 July 2012
Monday 2 July 2012
Axicon Lens (to create a zero-order or higher order Bessel beam)
Spherical Aberration (to create a zero-order, possibly higher order beams
too?)
Thin Ring Light Source (Bessel beam created through Fresnel diffraction)
from:
4-f Spatial Filtering, using:
Ring Photo
Friday 29 June 2012
Thursday 28 June 2012
Wednesday 27 June 2012
Tuesday 26 June 2012
Monday 25 June 2012
Sunday 24 June 2012
Friday 22 June 2012
Thursday 21 June 2012
Wednesday 20 June 2012
Tuesday 19 June 2012
Monday 18 June 2012
Sunday 17 June 2012
Friday 15 June 2012
Thursday 14 June 2012
Wednesday 13 June 2012
Tuesday 12 June 2012
