Research Journal

Friday, October 19, 2012

Over the weekend, I attended the Frontiers in Optics 2012 / Laser Science conference at Rochester, NY. It was an amazing experience. I arrived Sunday night and left late afternoon Monday. On Monday morning, Melia and I went to a breakfast/ talk titled "Women and Minorities in the Optical Society of America." The hour-long lecture was about how one might become self-employed, and the skills one needs to do so. It was actually very informative. Afterwards, I attended the Plenary lectures. The first one I heard was called "Imaging Single Cells in the Living Retina". The speaker, Dr. David R. Williams, explained how a technique called "adaptive optics" can be used to resolve structure at a cellular level in the living eye! He mentioned that this potentially has a lot of applications in understanding many ailments of the eye. For example, researchers could understand how colour-blindness works using the detailed images of single retinal cells. Dr. Williams also mentioned some studies concerning blindness, and how, aided by the excellent images of the retinal cells, it may be possible to correct blindness. This has apparently been attempted with rats. Dr. Williams showed the audience a video of a rat in a pool of water, enclosed by a high wall. There are several doors in the wall, and the only door that leads outside has light shining through from underneath. In order to choose the correct door, the rat must be able to see the light. The rat that was blind seemed to pick doors at random until it found the right one; however, the rat whose vision had been restored consistently chose the right door on the first try. I thought that was really cool.

The second lecture was themed around the Higgs boson and CERN: "History of the Higgs boson and recent discoveries at the CERN Large Hadron Collider" by Dr. Alfred T. Goshaw. It was also an interesting lecture, though the math went over my head. Unfortunately, I didn't hear much of the last lecture, "Attosecond Photonics: What we learn by transforming many photons into one" by Dr. Paul Corkum, as I had to leave and put up my poster for the poster session. I stood by my poster for a bit, until Dr. Noé came up to me and told me where I was actually supposed to be-- in a room with all the other undergrads and Dr. Metcalf, and quite a few emminent scientists in the field of optics. The undergrads were listening to tips about how to pick graduate schools, among other things. It didn't apply to me much, but it was still an interesting experience. After that, I went back to my poster and stayed there for the next two-and-a-half hours. I was surprised by the number of people that came up to me and asked me to explain the work! Dr. Larry N. Thibos, one of the foremost experts in the area of work in my poster, talked to me for a bit. Another person who was with him told me, "no pressure, but he's the expert in your work". Dr. Thibos also mentioned something that he had done research in: an aberrometer that uses both the moiré and Talbot effects! I've actually read a bit about those aberrometers, and it was nice to know what he was talking about, even if the experience was nerve-wracking.

After the poster session, all the students convened by a grand staircase in the convetion center to take a group photo. Then, I attended several smaller oral presentations given by the remaining students. One lecture was on metamaterials, a really fascinating topic. At the end, the audience members received several "goodies" from Thor Labs: a snack box, a tote bag, and a cap. I was especially appreciative of the snack box, as I hadn't had lunch! I had to leave after that, sadly, as I had to attend class the next day. I'm sorry I missed Melia's poster, but I'm glad I got to see Jonathan and Melia again at the conference. Altogether, I had a really great time, and I'm glad Dr. Metcalf invited me to attend!

Above left: The hotel we stayed in. Above Right: View of the river from outside the hotel.

Saturday, September 8, 2012

Today I went back to the lab to work on my Siemens paper with Dr. Noé and to clarify some things about the collimation tester. First, Marty explained some details about the setup that I didn't know before, namely that without the pinhole, the collimating lens must be moved to a different place than with the pinhole. I will have to study the math behind this much more to fully understand what he was trying to tell me. I also measured the beam radius of another laser at several different places along the beam to understand how a Gaussian beam diffracts over a distance. After that, Dr. Noé took us out to lunch at the Simons Center Cafe-- the food was great, as usual! When we got back to the lab, I measured the beam radius of the laser in the collimation test setup at four different points, for several different placements of the collimation lens. This was done to see how the location of the minimum waist changed as the position of the collimating lens changed. I made a graph of this on Mathematica. It is shown below:

Saturday, September 8, 2012

Today, I went back to the lab to work more on the collimation tester we're working on. You can actually see horizontal fringes when the beam is collimated, just as other papers described. They tilt more and more as you move the collimating lens away from the point where the beam is collimated. Dr. Noé and Marty came up with a clever way of tilting the grating and image of the grating w.r.t each other so that you get horizontal fringes. They tilted the holder with the Ronchi grating about 8 degrees and replaced the mirror a Talbot distance away with a retroreflector. The retroreflector looks like a triangle with mirrors on the inside. The beam hits the inside of one edge of the triangle, is reflected to the other edge, and then comes back parallel to the incoming beam. The result of this is that the image of the grating is reflected twice, which means that if the original grating was tilted +8 degrees, the images is now tilted -8 degrees!

Right now, I'm trying to understand the various equations that will be involved in the model. Basically, from the fringe angle you can tell the difference in period between the Ronchi grating and its self-image. From there, you know the magnification, and from there, using an equation we found in a paper, you can figure out the radius of curvature of the beam. This can tell you how far to move the collimating lens, and in which direction. This, at least, is what I have surmised. Implementing the process is trickier, so I'm still struggling with Mathematica there. Hopefully I can make some progress this weekend.

Here is a quick sketch of the setup:

Friday, August 10, 2012

I'm going to write what I did the last day of the Simons program, so that this page can feel a bit more complete.

Along with the other members of my program, I presented my poster at the poster session in the morning. Dr. Noé, Marty, and Hal all attended, along with my family and the neighbour who had helped me with my project. I brought along the two grids with holes punched out so that people could see the moiré patterns they formed. It's interesting to watch peoples' faces when the rotate the grids with respect to one another and the moirĂ© patterns just form out of nowhere, surreally.

After the poster session, Dr. Noe took us all out to lunch at the Simons café, where, of course, the food was excellent. I showed my parents the moirĂ© patterns on the heater screens. Following the meal, we visited the lab to get my belongings and show my family around. I demonstrated the collimation setup we had. My family and I soon left, because it was starting to rain. Unfortunately, we got caught in the rain-- it was crazy, because the road in front of the dorms had flooded and I had to wade through water past my knees to get to the building.

Anyway, I plan to come back soon, so that we can continue the work on the collimation tester, which I will hopefully present at the Rochester conference in October.

Tuesday, August 7, 2012

Today I gave my moiré presentation to the other members of my program. It was a little scary, but I'm glad I got to do it!

Monday, August 6, 2012

UPDATE 1:32 AM EDT: Captain's log, stardate Aug 6, 2012: Witnessed live NASA JPL telecast of Curiosity's landing. Now, going to bed.

Friday, August 3, 2012

It was a busy week! I'm going to narrate the week's events now, or try to at least.

On Tuesday, I went to a talk (whose name currently escapes me) about some interesting three-dimensional shapes, and how they applied to the art of sculpture. The talk took place in the Simons Center for Geometry and Physics. The speaker spoke about objects like tori (toruses??) and mobius bands; basically, how cutting a torus in special ways could result in interlocked structures, or free-moving pieces. The speaker mentioned a particular way to cut a torus so that it would split into two interlocked mobius bands, and related that a colleague of his had applied that to cutting a bagel! I'm really excited to try that when I get home. It was fascinating, although I hadn't really intended to attend. I thought I was going to an origami talk, but it turned out that it was the next day, so I was very confused at the beginning as to how mobius bands applied to origami!

On Wednesday, Melia, Marissa, Jonathan, and I gave presentations at the group meeting. I had pretty much the same stuff as last week, but I got to talk about the quasiperiodic structures I had made. See previous entries for examples of that.

Here is a PDF of my presentation. Also, this is a PDF I made with LaTex of a proof we did in the lab one day. It shows how to derive the equation λ = d sinθ. We did this a while ago, but I just forgot to put it up!

I also went to the origami talk, the real one this time, and that was amazing! The talk was called "Ocean Beasts." Both Martin and Eric Demaine (father and son team) were supposed to speak, but only Eric Demaine could make the lecture. He talked about how he and his father blow glass and put origami pieces in them, which I find very impressive. He also showed how if you fold concentric circles in a paper alternating mountain and valley folds, the paper will automatically fold into a saddle shape. Their sculptures were created out of these circles. Another thing I found really interesting and intriguing was a proof he mentioned. It is a litle hard to describe, but basically he said if you fold a paper a bunch of times and make one straight cut through it, it is possible to make any shape! Eric Demaine showed us how to make a swan and a star, each in one cut of paper! Of course, complicated shapes would take rather a lot of folds! Demaine also spoke about how it is possible to make any three-dimensional shape out of a bunch of small boxes, the three-dimensional equivalent of pixels on a computer. He showed a clip of a colleague making the Stanford rabbit using steel and a computer-generated folding pattern. It was really cool!

Below is a picture of the cover of the brochure from the origami talk. Source from Stony Brook website.

I also tried out some hexagonally arranged dot patterns on Mathematica. Instead of making squares when overlaid, they make triangles!! I was inspired to do this by an article Dr. Philip Allen, a professor of theoretical solid-state physics, showed me. Te article was called "Water-Mediated Proton Hopping on an Iron Oxide Surface," and it was from the Science magazine. The article had nothing to do with moiré patterns, but it showed a picture of moiré patterns created when a very thin layer of FeO was placed over a layer of Pt(111). This occurs because FeO has a hexagonal structure, as does Pt(111), so of course, the same thing happens here as happens when any two repeating grids are overlaid: moiré patterns. I simulated this in Mathematica, and I had a lot of fun! One thing that really interested me was how to make the dots appear in a hexagonal pattern. Rather than having some complicated length or angle formula to arrange the dots, there is a very simple way. Basically, you can split the whole hexagonal pattern into the superposition and shift of a single rectangular pattern with itself. So, you have one pattern where the dots are laid out in rectangles with the rule y = 2x (height is 2x width). Now all you have to do is shift the same exact pattern half over and half up, and you get hexagons! I'll put up a picture so my meaning becomes clearer. I was really amazed by this-- there's probably some sort of proof for this.

Below are a picture of moiré patterns created when one hexagonal grid was compressed and overlaid by another that was slightly larger. I believe the ratio here is 1:8.

Today were the REU presentations. I was impressed by everyone's work, and Melia, Marissa and Jonathan all did very well. Melia and Marissa presented their work in creating Bessel beams, and Jonathan explained his research in multi-pinhole diffraction. We went out to lunch at the Simons Center café after that for a very delicious meal. Thanks to Dr. Noé for buying us lunch! Melia and Jonathan left after that, so it's just me and Marissa now. Hopefully we'll all see each other again sometime!

Now I'm mostly working on my poster and abstract, as well as learning some more of the math behind various moiré patterns. There's a really great paper for this, which I will put up later.

Monday, July 30, 2012

Update, later in day: I thought I'd go a little more into the math behind the sunflower floret pattern. Scientists have been trying for years to perfect a formula for generating the pattern that florets make in a sunflower. In 2004, H. Vogel proposed a formula that was rooted in the Fibonacci sequence. He based this choice on two criteria that he proposed must always hold true: (verbatim)

    (1) Each new branch (leaf, flower) bears the same spatial relationship to the existing stem and accordingly issues at a fixed angle δ with respect to the preceding branch.

    (2)Each new branch fits into the largest still-existing gap between older branches, cutting a constant fraction off the gap.

As Vogel mentioned, Cond. (2) will make the pattern seem as though it is uniform, although very close up, the florets may be separated by slightly different gap sizes. But which value of δ will satisfy these conditions?

Vogel expresses δ in terms of turns of a circle:

δ = z * 2π

It becomes clear now that z cannot be a rational number. A rational z would eventually lead to a repeated δ, after which gap sizes would not become any smaller and Cond. (2) would be broken. Vogel now proposes that a series zn be created that converges to the real value of z. The series follows the following rule: (verbatim)

z0 = 1/3 --> δ0 = 120°

At a given

zn = pn / qn where GCD(pn,qn) = 1

there is a period of qn branches, which form [in] exactly pn complete turns, the distance zn, between temporally consecutive branches being divided into pn equal parts. Branch qn coincides with branch 0.

I would have paraphrased that last bit had I understood it. As it stands, this marks the place where my comprehension breaks down. For one thing, it is not obvious (to me) at the start why qn should be the period and form the distance zn (how can it form the distance if it goes around the circle several times?) in pn rotations. I tried this with a java program and indeed it holds true, but how? Also, why start with 1/3?

Anyway, Vogel goes on to explain how if one increases zn to zn+1, then part of the old gap between branch 0 and its nearest neighbour is cut off. This somehow ties into the Fibonacci sequence... Okay, I admit, I don't know what I'm talking about. I'll just cut straight to the formula

In polar coordinates (r, θ):

r = c * Sqrt[n] ; θ = 2π n / Φ2

Where n goes from 1 -> any number (~500) and Φ represents the golden ratio. In degrees, the number in front of n in the θ equality is ~137.58 degrees. This is the golden angle, the golden ratio of a circle. Thus, the Fibonacci sequence. I don't think that in real life this can be perfectly quasiperiodic because this is only an approximation of the golden ratio. However, I think the approximation is good enough that δ will not repeat when we are looking.


I spent part of the weekend working on more modeling, and I finally managed to make the sunflower floret pattern! It was actually a lot easier than I thought it would be on Mathematica. I overlapped two patterns of different sizes and moiré patterns showed up! Now I just have to understand the math... not so easy. Here is a picture of the sunflower pattern that I modeled: (n, 0, 500)

Below are two patterns of different sizes superimposed so that they create moiré:

I would have also made a horizontally shifted one to see the moiré produced then... but I find that I can't use polar coordinates. So I'm going to sit here and bang by head against my desk until what should be obvious comes back to me... I'd also like to make a graph of fringe separation vs. angle for linear moié for practice-- I think the math is already worked out somewhere.

Wednesday, July 25, 2012

Today I gave a presentation about moiré patterns at the group meeting, and I think it went well! I'm relieved about that. I spent a looonnng time working on the powerpoint since yesterday. I'll just summarize it here for future reference: The presentation was about the moiré effect and how it cropped up in various places. I started off by showing some of the math for linear gratings and my own Mathematica model for the special case when the periods of the two gratings are equal. The I pointed out the aliasing present in my models because of their intricacy and the computer's pixels, and went off on a tangent about aliasing and moiré. Finally, I went through some of the applications moiré patterns have, such as collimation testing and steganography. I finished with a question I had about quasiperiodic structures used for Glass patterns.

After that, I spent the rest of the day working on my abstract and thinking about my project. I was thinking that perhaps instead of simulating a quasiperiodic structure, perhaps I could simply print a picture out on a transparency. I found a book by Isaac Amidror, and the website included a "moiré demonstration kit" that could be printed out on transparencies. I really want to print out the ones that make Glass patterns and see them for myself! Maybe I'll ask Dr. Noé tomorrow if I can print out some patterns.

What else... we all finally saw Jonathan's diffraction patterns today, and they looked just like they were supposed to! It was really cool! Also, I *think* the patterns were quasiperiodic, so that's interesting as well. Melia showed us some really great pictures of her setup in the lunch meeting, so that was also fun to see!

Monday, July 23, 2012

9:12 AM: Update on the projector. It works! Well, as well as it could with only one grating anyway. The dots from the laser pointer did move as expected, but I only got dots along one line because I only had one grating. Maybe I can borrow another one from the lab to try two next.

Above is a picture of the lego "projector." I will try to get a good picture of the patterns it makes and put it up later.

I spent the rest of the day working on my Mathematica simulations. I made one for circles, finally. Maybe I'll make one for ellipses next. I'm still trying to understand all the math, even for linear gratings. What I observe in my simulation seems compliant with the math I've looked at, but I don't understand why those things happen. Also, I see a lot of patterns in my circle simulation that are the result of aliasing. It's amazing that aliasing happens in such intricate patterns like those I see. I'd like to look into that more and see why it is that the pixels a computer picks to display happen to fall in such a specific manner.

Sunday, July 22, 2012

I spent a good part of yesterday and today working on my Mathematica model of moiré patterns. I think I finally got it working, so yay! It was cool, because I got to verify for myself some of the equations I had seen regarding moiré patterns. For one thing, when the period of the revealing layer is equal to that of the base layer, one sees horizontal moiré fringes, which is what I saw in my simulation! I also observed the optical speedup effect, which was markedly pronounced for the horizontal fringe case. It seemed to me that when I made one period an integer multiple (twice) the other, the fringes remained horizontal, which is unexpected. Actually, it doesn't seem intuitive to me at all that the fringes be horizontal in the first place, so I guess I have to take a closer look at the math. Tomorrow, I'll try and figure that out, and also make my simulation a bit more user-friendly!

Also, forgot to mention, my brother and I finally got around to making the lego diffraction grating projector that I've been meaning to try. I can't say for sure if it works yet-- it certainly looks nice, though. We didn't have enough of the right pieces to use two gratings, though, so our patterns won't be as intricate as those in the video we saw. I can't wait to try it out with a laser pointer tomorrow in the lab!

Friday, July 20, 2012

Yesterday we went to the optical vortex party, and that was an interesting experience. It was in City College, and lots of people gave presentations, including Melia, Marissa, and Jonathan. I thought they did very well! I did learn a lot about optical vortices, a topic on which I had long ago resigned myself to perpetual confusion. Perhaps there's some hope for me now. Afterwards, we looked at the various posters of peoples' research that were scattered around the room, and some of those posters (those that I could somewhat understand) were actually really fascinating! There was one on polarization in shells, and it had color-coded pictures of the different polarization states in gastropods and... something else. Cephalopods, perhaps? It was amazing to see the complex not-quite-patterns in the pictures. They looked sort of like the wavy patterns that appear in the bottom of a swimming pool. Another poster was about quantum computing, and the student was trying to entangle photons, I think. It was nice to see that because we'd just seen the Eberly video on Bell inequalities and entangled photons (see previous entry), so I could understand the poster! We also went down to a lab, where I finally got to see the oft-spoken-of Spatial Light Modulator in action. Giovanni made an optical vortex for us, which was cool because I'd never seen one in "real life" before. So, anyway, the whole thing was a great experience and an enlightening one.

Today, I spent the whole day wrangling with Mathematica, with mixed success. At first, I tried to make moiré patterns with concentric circles, but I couldn't animate them, which is what I wanted to do. So I tried plotting straight lines to make a linear grating instead, and I did manage to make moiré patterns by animating those. I found a sort of paper on the mathematics behind moiré patterns, so I'm going to try and prove the math to myself using the animations. I guess I'll start with making the slope a variable and from there computing the angle between the gratings. I want to eventually plot the diffraction patterns of quasicrystals to see what kind of patterns they make, if any at all. The problem with quasiperiodic structures is that you can't really iterate over them to save time, because they aren't periodic, and you can't generate them randomly either, because they're not random. So I think they take some time to plot. Maybe I'll start with the Fibonacci sequence, which is often seen in nature, because I know I can make that with an iteration. Well, anyway, that's all quite ambitious for someone whose computer can't handle twenty straight lines, and whose skill with Mathematica could be called "passable" by a generous judge. I'll see if I can get that far... but I have hope!

Tuesday, July 17, 2012

I forgot to mention in yesterday's entry that we watched a really interesting video with Dr. Metcalf. The video was a recording of a talk that Joseph Eberly gave on Bell inequalities. Dr. Eberly gave a nice example of a Bell inequality in his talk, which I will attempt to reproduce now...

Say you have 16 cents: a penny, a nickel, and a dime. Each of those has two states, heads (H) or tails (T). Let the coins be represented by the sets

H = { P, N, D }

T = { p, n, d }

Now go up to someone and bet them 100:1 that the following will always hold true:

n( P, d ) + n( p, N ) ≥ n( N, d )

Where n means "number of occurrences." This has nothing to do with probablity-- it is literally counting. To be absolutely certain that you will not lose 100 dollars, see for yourself that this must always be true. Here is how it works:

Notice that in the inequality, only two coins out of the three are included in each relationship. This means that the third one doesn't matter, and you can re-write the various components of the inequality as such:

1. n( P, d ) = n( P, N, d ) + n( P, n, d )

2. n( p, N ) = n( p, N, D ) + n( p, N, d )

3. n( N, d ) = n( P, N, d ) + n( p, N, d )

That means that the total number of, say, Hpenny and Tdime is equal to the number of those occurrences that had Tnickel plus the number of occurrences that had Hnickel. Looking at the equations above, it can be seen that the parts of Eqn. 3 already exist as parts of Eqns. 1, 2. In fact, not only is Eqn. 3 covered in the other two equations, but Eqns. 1, 2 have more to them! This means that, put together in the earlier inequality, the inequality must always hold true! So you win your 1 dollar.

Eberly went on to create another such inequality, but this time he used photons and polarization filters. I'm still trying to understand that part. Basically, he created a Bell inequality for polarization that relied on the knowledge of a photon's polarization. However, he showed that if one tries to do the same thing with photons that one can do with pennies, nickels, and dimes, one runs into some snags along the way. One such snag was the following equation:

cos2(2θ) ≥ cos(2θ)

Clearly, that is not always true... The reason the contradiction comes up is because the Bell inequality relies on our assumption that the photon's polarization exists even though it is not observed. The only way to observe the photon (with a detector) is to destroy it, and Quantum Theory says that if you didn't see it, you can't know for sure. The two photons were in a state called "entanglement," which is now called the "Bell state." Anyway, that's all I have written down, and hopefully I haven't mangled anything too much. It was all very interesting!

Other than that, I spent the day learning more about the mathematics behind moiré patterns. Hopefully once I get Mathematica (the free trial version, at least), I'll be able to model the patterns. I also spent a great deal of time looking through telecentric lenses, which is always a very bewildering experience. Lastly, I updated my ideas page with some more things I've been thinking about.

Monday, July 16, 2012

Last Friday, the REU students and I went to the American Museum of Natural History for some presentations. That was a lot of fun! The presentations covered various topics in astronomy, such as the rovers on Mars, a mysterious green cloud of gas called "Hanny's Voorwerp," and recent solar activity. After the talks, I had a quick lunch in the museum's hugely overpriced cafeteria, and then I went upstairs to see the Bioluminescence special exhibit-- Dr. Simon had given us tickets to see the special exhibits! The Bioluminescence exhibit was really well done-- I learned that different species of male fireflies fly in different patterns when glowing, and luminesce differently as well. Forget fireflies, though, for deep in the ocean there lurk (apparently) all manner of strange bioluminescent creatures. The Vampire Squid, for one, is the queerest animal I've ever seen, apart from a bird called the Frogmouth. Unlike its squid and octopus cousins, the Vampire Squid has adapted to deep sea conditions by emitting a glowing mucus when it is threatened. It's really a rather cute animal: only about six inches long, but it has the largest eye-radius to body size of any animal. Its eyes are about the size of a dog's. When in danger, the Vampire Squid can also cover itself with its arms and hide, which must be a pretty amusing sight. Here is a useful site for information about the squid, and here is a picture.

Aside from the museum, I also talked to an extremely knowledgable neighbor over the weekend about project ideas. He gave me a few intriguing suggestions for project ideas. I will list them below:

  • One effect that Telecentric lenses have is to remove some of the distortion created around edges of objects that appear when a normal lens is used. Can one quantitatively analyze that? As in, show how much distortion is eliminated and perhaps model it?
  • Is it possible to somehow look at the difference between the image of an object produced by a Telecentric lens and that produced by an ordinary lens and from that figure out how far away the object is?
  • Moiré patterns are always produced by periodic gratings. Is it possible to create those patterns using a quasiperiodic structure? (This is actually something I had vaguely pondered before, but I never knew what these sorts of structures, like the Fibonacci sequence, were called.)
  • Can one use moiré patterns to test metal fatigue in a non-invasive way?

Dr. Noé showed me the box of Telecentric lenses today and I had fun playing around with them. They do indeed make objects that are farther away appear larger-- it's very disorienting. Because of the shape of the lens, the images of the ceiling lights reflected in it appear to be floating in mid-air, and the lights are all in various shades of purple. In contrast, other lenses seem to reflect the images of the overheard lights in a myriad of colors, not just limited to one hue. I wonder why the reflections are different colors. Also, what I found interesting was that if you put the lens horizontally on a flat surface and looked through it, you could see that through the top half of the lens, things appeared upside down, and in the lower half, the images were correctly oriented. Somewhere in the middle, things faded to a blurry grey. I could close my right eye and see everything upside down, and then repeat the process with my left eye, and see just the opposite.

I think I found a sort of project idea that involves connecting all the various strange optical phenomena I have thus far researched. It should be fun! Hopefully I find a way to get Mathematica, because then I can try to model the Talbot effect and moiré patterns. It's a good tool to learn.

Wednesday, July 11, 2012

There were a lot of meetings today. I went first to the REU meeting where I was given instructions on meeting at the Natural History Museum, and I listened to the small presentations that each of the REU students gave. I was impressed by the projects! After that, there was a lunch meeting, where people tried to help me come up with an idea. Dr. Metcalf suggested some ideas, so I'll look into those. After that, I spent some time updating my ideas page, which now looks a lot more full than it used to. Dr. Noe sent us an article about a weather phenomenon called a "Glory," and I put some information up about that on the links page as well.

Tuesday, July 10, 2012

Most of the day was spent taking a tour of the Brookhaven National Laboratory, and that was very interesting. I saw their collider, PHENIX, and I was very impressed. Later on, I also got to see their center for functional nanomaterials, and of course that was also amazing. The electron microscopes are built on a separate foundation from the rest of the building so that they aren't jostled, and it's so amazing to think that a piece of dust is like a boulder to a nanomaterial. I also learned that a process similar to something I've done in art class, I forget the name, is used to make very small circuits. Some sort of chemical etching, but unfortunately I don't remember much of the process now. I do remember that they use a lens to make the image appear very small, and something about the wavelength of light being too large to etch such a small circuit-- instead, they use very fast-moving electrons for the same purpose.

Other than the tour, I spent my time reading through more papers that Dr. Noé sent me. They seem interesting! I will summarize them and put them up here when I've finished reading them. Also, I'm almost done with the PDF of the proof we did the other day. I finished the diagram, and I just need to understand some parts of the proof more before I write them.

Monday, July 9, 2012

Again, very long time. I'm still looking for a project idea, maybe something to do with moiré patterns. I spent the first part of the day looking through more papers about moiré patterns and their various applications. I also thought more about a problem Dr. Noé presented last week-- how to use diffraction grating glasses to see the spectral lines of a sodium lamp. I learned about the various components of a spectrometer, and I also found out a lot about sodium lamps, which was a nice side-effect of the problem. I actually found a nice site that detailed the workings of several different kinds of lamps, and I spent an hour looking through that. I also found a really cool lego diffraction grating projector that this guy built, and it was amazing! It projected amazing patterns onto the wall, although I was a bit worried when he shone a green laser into it and the beams went all over the place. I want to build something similar with my brother this weekend.

I began learning LaTex last friday so that I could write up the proof that we did last week in the lab. There are a few things I need to clear up, but it looks pretty nice. There are so many parentheses! I need to label the diagram, somehow, also.

I started figuring out the math behind moiré patterns a while ago, but I'm going to try again now. The papers I'm reading skip a lot of steps, but hopefully I can keep up a little better now.

I also attended a thesis defense and a seminar today. Alas, I couldn't understand either one (a common theme), but it's good to be exposed to ideas that are far above one's head. At least the mind begins to work more quickly, out of sheer desperation.

I found a bunch of interesting papers related to moiré surface contouring and topography, and some other papers as well. See my ideas page for them.

Improved collimation testing using Talbot interferometry

I haven't read all of them yet, but I'll get through them eventually.

Wednesday July 4, 2012

It has been an inordinately long time since I last updated this journal page. I suppose I'll start from most recent events. I woke up at 3:00 this morning to watch the results of CMS and ATLAS live. This morning I read that they had announced within 5 sigma certainty a new particle that might be the Higgs Boson!

Yesterday I read more papers on the Talbot effect... tried to read, that is. It took me a very long time to get past the first sentence, because every word I didn't understand led to an hour's delay looking up all the things associated with that word. I also learned that the bright rainbows on a CD are the result of diffraction-- the small data pits on the disk work like a diffraction grating. I found a bunch of CDs and played around with those, which was fun. I also read more about circular polarization... Actually, yesterday was mostly spent looking up and understanding random concepts.

Wednesday June 27, 2012

Very busy day, despite the fact that I spent most of it sitting down. I attended a seminar by Pietro Faccioli, and that was really interesting! I'm really glad I went. Of course, most of the lecture went way over my head, but the pieces I could puzzle together were really fascinating. Below is the abstract:

    The investigation of the non-equilibrium dynamics of thermally activated reactions of biomolecular systems is a central problem at the interface of physics, chemistry and molecular biology. A few notable examples of this type of processes are the protein and RNA folding and the allosteric transitions. In general, standard molecular dynamics simulations are very inefficient when applied to thermally activated processes, because they waste an exponentially large fraction of the total computational time to simulate thermal oscillations inside a single (meta)stable state. On the other hand, one is mostly interested in the reactive and free-energy barrier crossing part of the dynamics. In this seminar, I will discuss how rare and complex activated biomolecular transitions can be efficiently simulated in atomistic detail using a recently developed path integral based approach denominated Dominant Reaction Pathways (DRP). I will also discuss how in this formalism it is possible to systematically include quantum corrections to the motion of atomic nuclei and to simulate the real-time propagation of quantum excitations (e.g. electrons or excitons) across conformationally evolving macromolecules.

Anyway, it was about protein folding, and though I could only understand the introduction, I still couldn't look away.

After that was the Lab Safety lecture, which covered absolutely nothing I would need to deal with in this lab. Still, it did terrify me, so that's something.

After that was the Group Meeting, which was lots of fun. I did clarify some concepts, and it was fun (and nerve-wracking) to talk about what I had learned over the past few days. Later, in the lab, I asked Melia for help with Fourier series, which I didn't understand at all. She was really helpful, and I am relieved that what little calculus I know hasn't vanished from my mind. It was useful to see what each part of a Fourier series does and why that is so, and also to finally connect seperate concepts into one coherent thought. It was also interesting to see the connection to sound waves! Melia showed me something called an oscilloscope, which shows a sound wave when you play a sound into the microphone. The "mysterious" phenomenon with tuning notes that I mentioned in yesterday's journal entry was resolved- apparently the strange undulating hum is the result of "beats." Beats are the result of constructive and destructive interference when two sound waves of different frequencies are heard. The constructive interference causes the amplitude to suddenly surge up, and the destructive interference causes the amplitude to decrease, which is why the sound varies so much in volume. We tried to observe the beats using two tuning forks of slightly different frequencies, but we didn't get too much of an effect. The oscilloscope is rather difficult to use-- it looks very complicated!

In the oscilloscope, voices show up as very complex waves, but whistling creates a seemingly perfect wave. Melia mentioned an experiment where different Japanese people spoke into an oscilloscope and the complex wave that resulted was modeled with a Fourier series... transform... I don't know if the waves for the voices were periodic... no, they wouldn't be because they're wave packets, not waves, and so it's Fourier Transform? I have to research this more. Anyway, the researchers looked at the different harmonics and found out all sorts of interesting information about Japanese vowels and why those particular sounds became vowels in the first place. It makes me wonder whether languages that use "purer" vowels would have simpler waves. Do we percieve those sounds as purer because we hear that the sounds are simpler? Melia showed me a really interesting looking book titled Who Is Fourier?, and I can't wait to read it tomorrow!

I still have to research "slow light" and optical vortices. I found a paper about someting called "moiré fringes" that related to optical vortices, and I'd like to find out what optical vortices are! Maybe I'll ask Marissa and Jonathan tomorrow.

Tuesday June 26, 2012

The second day went by pretty much the same as the first. I read more about moiré patterns and found out that digital cameras actually have filters to prevent Moiré patterns from occurring. As far as I can tell, moiré patterns show up in a picture when the photographed scene has areas that have repetitive detail (like stripes) that exceed the resolution of the camera. When that happens, the camera "samples" only portions of the pattern. So say a green stripe appears every x stripes and the resolution of the camera only allows it to allot a pixel for every y stripes, then the picture may appear to have a long section of green because each pixel sampled might be part of a green stripe, regardless of how many other stripes there are in between. This is called "aliasing," when pixels are indistinguishable from one another, even though the actual subject may vary greatly.

Digital cameras now have an "antialias filter" built into them. These filters work by purposely giving the camera a lower resolution, so the camera won't try to resolve detail that is too intricate for its lens. Digital cameras like mine (the cheaper ones, ha) have the filter built into them, but higher end cameras have removable ones because removing the filter will give the camera a higher resolution.

Actually, what's really interesting is that the same effect occurs with sound waves. Below is a picture of aliasing in a sound wave.

Two different sine waves defined by 
the same sampling points

If a signal is sampled at less than twice the highest frequency in the signal, aliasing occurs. In the picture above, the red values show what is sampled. The wave created from the sample has a much lower frequency than the original sound wave. In this particular image, the sine wave is approximately one-tenth the frequency of the original wave! The effect of aliasing on sound waves is far greater than its effect on images. Frequencies determine which note is played, and changing the frequency would change the note! Recording would be impossible if there weren't filters in recording equipment that remove all signals with frequencies above half the sampling frequency.

I continued yesterday's "experiment" (if I can really call it that) where I was trying to create moiré patterns with lines of text on a computer, and I actually succeeded today! What I was doing wrong was that I was using the same size, letter, and line spacing for both the upper and lower stripes (these have fancier names, but I don't know what they are). This time I used a bigger font for the lower "sheet." I used Ws for the lower page and Ds for the upper page-- totally random choice-- and lo and behold, wavy white spaces appeared when I began scrolling up and down. It was really cool-- I even observed the optical speedup effect. When I replaced the Ws with Qs, I began to observe straighter moiré patterns, which makes me wonder if Ws cause waves because of their shape or if I'm just seeing straighter lines because I expect to.

I now wonder if moiré patterns are also dependent on contrast between the lines and the spaces. It seems to me that it is the white spaces rather than the black lines that make moiré patterns stand out. In most of the pictures of these patterns that I saw online, the stripes appear to be orange and blue, which also reaffirms the idea of contrast because blue and orange are complimentary colors. Some people hypothesized that the lines were those colors because of the green filter in the camera, so maybe that's the case instead. I also wonder if moiré patterns have anything to do with an effect heard when tuning an instrument. If the instrument holds a note that is only slightly off from the tuning note, the two notes heard together create a sort of undulating sound that is distinct from the two notes. It is hard to describe this without actually presenting the effect here, but I wonder if the two frequencies just displaced from one another can be seen as analogous to two patterns displaced from each other, which is what causes the moiré effect.

Monday June 25, 2012

The first day of working in the lab went fairly well, I think. Dr. Noé and his students showed me a laser setup they were working on. I forgot to ask what it was for, but they spent a good portion of the day trying to fine-tune the mirror positions. I had a try at it, and it was really interesting to see how the light intensity changed due to the mirror positioning. I got the multi-mode laser pretty bright, but the single-mode laser stayed stubbornly dim. It was cool to hear that total internal reflection was the reason that the laser beam could travel down the... I think it was a fiber optic tube?... presumably instead of being emitted through the tube. I remembered learning about total internal reflection when I was learning about Evanescent waves in my science research class, so it was nice to see an application. I also looked at the graph that past students made that showed how positioning the mirrors worked, for lack of a better description, and that was really interesting. I'm sure I've seen a graph like that before, but I don't remember what it was. I also spent some time reading through the optics chapter in a textbook Dr. Noé showed me.

We went out to lunch at a campus cafe after that, and Dr. Noé pointed out something called a Moiré pattern on the screen around some kind of a lamp or a heater. The two screens were slightly out of alignment with one another, and the result was that a wavy sort of pattern appeared on the screens. I spent the time after lunch looking up more on moiré patterns, and I found a lot of really interesting stuff. I'm still trying to understand all the equations associated with the phenomenon, but I'll get there eventually. When I got to my dorm room, I tried to create more moiré patterns using a paragraph of text on my computer, seeing as my resources are pretty limited in a dorm room. I just held down the 'a' key until a paragraph of decent size was generated, and then I highlighted it and dragged a copy of the text until it was slightly displaced from the original. I didn't see much of a difference, so I tried decreasing the spacing between the lines. I did get some sort of striped pattern then, but I'm not sure if that's just due to the shape of the letter 'a' or if it's really a moiré pattern. I'll have to try with something else-- maybe a screen from a window? I don't really want to take a screen out from a window here, though, so I'll have to wait until the weekend so I can try it at home. I know I have moiré fabrics at home, too-- the word moiré actually comes from a french verb meaning "to produce a watered textile by weaving or pressing" (quote from Wikipedia). A watered textile is created when part of a fabric is laid upon itelf and then dampened and pressed, leading to a "water" or wave-like pattern, basically what a moiré pattern looks like.

Aside from all that, I spent the day looking up basic optics vocabulary. I read more about the difference between standing and traveling waves, and about nodes and antinodes. I finally found out what Interferometry was, and I looked up the Michelson-Morley experiment, which I've heard a lot about. So, a pretty productive day, over all.

Here's one source I read on moiré patterns, and here's another. These were very informative.