August 2, 2008
For the past couple of days, I've been working on my Powerpoint presentation with Dr. Noé. Today I went through a full-on practice run with Marty and everyone else in the lab as spectators. I think it went actually pretty well, considering how bad at public speaking I am! I've got a sheet of notes (well, 2.5 sheets actually) that really came in handy, as I found it much easier to give my talk when I had something prepared. But today is Dr. Noé's last day, which means he won't be able to make it to the REU talk on Friday. It stinks, but I'm sure he's probably heard my talk enough that he could recited it himself! :) I only have 2 more days here myself, because I leave on Saturday. this summer went by crazy fast. Still have to write my paper and web report, so....that'll be the big thing to work on today and tomorrow.
August 3, 2008
Here it is, the final week at Stony Brook - and it's going to be a busy one. Last night Dr. Noé and I were here until about 9:00 working on my abstract after I made two not-so-great attempts. But the final product is pretty nice I think. Now we want to have Marty read it and see what he thinks, just in case we missed something. It's good to have one thing out of the way, because I've still got lots to work on and finish, including my paper, web report, talk, and powerpoint. Today I'm working on making some illustrations for my presentation using xfig ( a cool Linux program that's like MS Paint on steroids). I made a schematic of my experimental setup, and tried to illustrate how the spherical wavefronts create a path (phase) difference across the pinhole. I'll post these here on my site pretty soon.
July 30, 2008
Quick update...yesterday I was able to figure out an offset for the Mathematica model we created. It seems that an addition of ~0.32 mm makes the predicted intensity profiles fit much more nicely to observed data. Again, I do believe that this is an artifact of how I found the zero point in the experiment. One question that I'm almost certain I'll be asked during my talk next Friday is, "Why use a fiber?" The answer is that you can do basically the same experiment using a lens that focuses the beam and creates a divergence similar to fiber, about 0.1 radian. I wanted to make sure that this is possible today, so I put in a microscope objective, because it has a small focal length and thus larger divergence. With this and the 100 micron pinhole, I was able to create the same pattens observed with the optical fiber.
July 28, 2008
Last Friday, Dr. Noé and I were finally able to come up with the correct (very close) mathematical model of the patterns seen. It involved taking the Fourier Transform of the circular aperture illuminated by a Gaussian beam of light. We used Mathematica to integrate over the radius of the pinhole to get a graph of the intensity of the field formed at an angular position, w, on the screen with a fiber-pinhole separation L. The integrand included a Gaussian part, a phase shift part, and a zeroeth order Bessel Function part. We discovered the general solution to a circular aperture in the book "Principles of Optics" by Max Born and Emil Wolf. Dr. Noé calls this book the Bible of optics, and I can see why-it's packed with some deep stuff. The reason I said the model is close is because it gives accurate patterns, but they are not in the exact separations measured experimentally. This may be an artifact of the way I found the zero position of the separation not being very good. I would gently touch the pinhole and gently move the fiber close until I just barely felt it make contact. There is some systematic error associated with this that could throw off the measurements. I will have to figure out just what this error is (Dr. Noé had the idea that it may be due to the thickness of the aperture itself), and attempt to account for it. But anyway, I got something that fits PRETTY well, so we went out for beers that afternoon :)
I also learned today that our REU abstracts are due on the 6th of August, so 7 days from now. I need to get rolling on that I guess, but I'm thinking it shouldn't be too incrdibly difficult.
July 21, 2008
Finally finished scanning the beam from the fiber optic, and fitting the diverence to a hyperbola. This proved a little difficult to do, because I used Excel to plot the points and minimize Chi^2 to achieve the correct fit parameters. Chi^2 is the difference between the theoretical curve and the data collected, squared. For the hyperbola, the fit parameter was half the beam waist, w. After minimizing, the beam waist was found to be 4.8 microns, much smaller than what I had originally found. This is smaller than the fiber, which is around 10 microns.
With the waist size and the wavelength of the light used, one can calculate the divergence of the beam, which is proportional to the wavelength over the waist size. A waist of 4.8 microns produces a divergence of ~0.1 radians. When I graphed the hyperbola with the 3 points I was able to measure, if looked like this.
July 16, 2008
I've decided I probably need to start working towards an end result, as with 3 weeks left, I think it's a good idea to have a good goal in mind. So I've been doing some brainstorming about what exactly I want to have/say in my talk on August 8. Its preliminary title is "Explaining an Accident," in reference to how we accidently discovered the diffraction phenomena I've been studying. In my talk, I'll deffinitely want to include something about the basics of diffraction, while not including TOO much math, because I've learned that equations tend to make the audience lose interest. I'll discuss the whole pinhole phenomenon, and attempt to explain it, using some of the Mathematica graphs that Nityan and I created, as well as actual photos (that I still need to take!). I learned yesterday that a lot of the other REU students deal with Fourier transforms in their projects, so that kind of put me off a little bit about discussing that subject. However, they mostly deal with computer algorithms, while we use lenses and the Beam 2 program. So, I probably will mention it some, and the picture I included in my last post will be in the talk for sure. So with that, a tentative list of things to complete:
1. Finish scanning the beam a few more times and fitting the data to a (hopefully Gaussian) curve.
2. View the Fourier plane of my setup, and attempt to recreate the image by using the 4f setup mentioned earlier.
3. Explain mathematically the diffraction patterns observed, using Fresnel/Fraunhofer ideas.
4. Maybe think of something else related to diffraction to explore/explain.
5. Write up a paper about everything I've done.
6. Write a web paper to post on this site.
7. Make a PowerPoint presentation of "Explaining an Accident."
July 15, 2008
We've been talking a lot about far field approximations and how it deals with Fraunhofer Diffraction, because that seems to be the situation of the pinhole experiment we've been doing. Also, Dr. Noé, Dr. Cohen, and I have spoken about Fourier transforms of the pinhole and how we should use that to develop a mathematical expression for the diffraction pattern. However, I was basically in the dark about what a Fourier transform actually was. There was a really cool website found that explained the basics of FT's without all the difficult math behind it. The link can be found on my links page. Fourier analysis is when you add up all the spatial frequencies of light coming from the source(s). What you get is a Fourier plane, where rays with common angles come together at a spot in the plane. What's really cool though is that if you use this new pattern as a source, you should get the original image out! This means the Fourier transform operation is its own inverse! We read that lenses perform Fourier transforms by themselves (if the source is at the front focal plane, the Fourier plane will be at the back focal plane).I learned how to use the program "Beam 2," which lets you set up optical systems and send in rays at different angles and positions to see what happens. Using Beam2, I made a 2 lens system, with 3 point sources of light, each with rays emitted at 5 different angles. As you can see in this BEAM2 diagram, after the first lens there are 5 spots where the light comes together. These 5 spots correspond to the 5 angles emitted by each source (the common angles converge together), and form the Fourier plane. After this, the second lens essentially "undoes" the Fourier transform, and what results is the image of the original object. This setup is called a "4f system," because the length of the setup is 4 times the focal length of the lenses.
July 7, 2008
So, it's been a while since my last post on here, sorry about that one! It has been a really busy week. Dr. Hal Metcalf has begun to give lectures on quantum mechanics, which I'm actually really excited about. The first couple of talks have concentrated mostly on matrix mathematics. We talked about the easy things like multiplying matrices and also operators such as energy and momentum. We also discussed what eigenvalues/vectors are, and we were given the homework assignment of learning how to find them. Good thing I took a linear algebra class, so I have a little understanding of "eigenstuff." It did take a little time, however, for me to remember certain methods. He wants to try and explain the "elegant" parts before the disgusting math parts, which is the opposite of how most classes are taught. I haven't had much quantum yet, so it'll be cool to learn something new and possibly get a jump on next year's courses. We also had Dr. Dominic Shneble give a talk on his research with Bose-Einstein Condensates, which started out really cool, but got a little bit over my head towards the end! When he went in to how individual atoms can get caught in energy wells (or something like that), he pretty much lost me. Afterwards was nice, because we got to go into his lab and get a tour from some of the students who work there. There were lots of mirrors, lasers and vacuum pumps, and a CCTV camera for seeing the atoms condensed together. The weird part is that it's all done with Rubidium, and I've had experience with experiments with Rubidium spectroscopy and diode lasers. So I've been working on a mini-project looking at the diffraction patterns of light passing through a single mode fiber optic and a pinhole. We discovered some strange phenomenon of a dark spot occurring at the center when the pinhole gets close to the end of the fiber, then a dark ring moves outward as it gets closer. It took a while to set it up properly, because I had to make a 3D translational stage out of 3 1D stages, but afterwards it was way easier to get the beam into the pinhole and line it up correctly. The tough part now is figuring out how to quantify or organize the data to get some kind of final coherent results. I'm still working on that one... Oh! and last weekend we went on an adventurous walk to the movie theatre. I say adventure because it was like a 2 mile walk along the highway, about 4 feet from zooming cars, after taking a wrong turn (of course) getting off campus. I no longer trust Google Maps with my life, as I doubt they planned on people WALKING along the routes they give. But we saw The Hulk, with Edward Norton, and it was pretty good I must say. Always an adventure around here though.
June 26, 2008
It has been decided that Wednesdays will be our official meeting days with Dr. Noé to discuss how things are going, give short talks and possibly have visitors present their topics of interest. Yesterday we decided to go out to lunch, because it was the "Last time we could all fit into one car," as next week the other high school folks get here, and we'll have a larger group. So it was Hamsa, Victor, Dr. Noé and myself at a restaurant called "Raga," an Indian restaurant up the road. I'd actually never had Indian before, and it was really GREAT! Today I was surfing around, reading about optics phenomena, and I discovered a technique called "Total Internal Reflection Microscopy." This ivolves measuring the height of microscopic spheres ( a rough approximation for biologic material that size) above a microscope slide using frustrated internal reflection. The evanescent wave propagates a short distance from the surface of the slide to the sphere, then carries light through the sphere, and you can see it. The intensity seen relates to the height above the surface, as the evanescent wave decays exponentially. I thought this sounded like a really cool experiment to try out/modify in some way. The link is in my links page. Another thing I discovered was in the July/August 2008 issue of Optics & Photonics News. They use photoacoustic imaging to see inside things. Lasers are used to create ultrasonic waves in media (like a rat's ear) by heating it, causing it to expand and send a pressure wave through it. These ultrasonic pressure waves can be amplified and a very good image formed. Anyway, that's about it.
June 22, 2008
This weekend, we decided to take a walk to the beach ("we" being some of my fellow REU students). While it was a nice day, we ended up making many many wrong turns, which resulted in us being horribly lost and taking about twice as long as we were expecting to get there. When we finally arrived, however, the beach was pretty nice, so it was worth the walk. Still don't have a project idea yet, but I've been reading a lot about fiber optics and such, trying to get ideas!
June 19, 2008
So I think I would like to study evanescent waves (NOT ``effervescent,'' as I accidently said once). An evanescent wave (which is not really a wave) is the field that comes out the other side of an interface after total internal reflection. I was under the impression that if something was TOTALLY reflected, there wouldn't be anything on the other side, but apparently there is, though it only comes out to a distance of about 2 wavelengths, so very short! So if you have a prism and create TIR inside it, there will be an evanescent wave into the air on the other side, propagating along the interface. Now supposedly, if you place an object with a higher index of refraction within that field (so very very close), you can get the wave propagating into that object. This is analagous to quantum tunneling, where particles seem to "tunnel" through energy barriers to states that are energetically favorable. I'm trying now to solve Maxwell's equations (or find a solution) for TIR, as it would be really nice to be able to see the evanescent wave come out of the math. So far, it's been really tough, but I haven't given up yet!
June 17, 2008
First day at Stony Brook! I got to meet all the other people participating in the physics REU this summer. It's cool because their projects range from astronomy to high energy physics. Dr. Noé showed me around the building/lab, I got to see some of the projects from past students, and we talked about how things work around here. I also talked to Dr. Cohen about acousto-optics, which I'd never really heard of before. It's cool! There are so many things I could study -- it's going to be tough to narrow it down to a main topic.