April 29th, 2015
Today was URECA, and things went well! I got caught up in everything else and didn't spend too much time by my own poster, but everything was great. I was there to show a few of the classic LTC demonstrations to passerbys, and people, as expected, love that illusory pig. This was a great opportunity to meet people and network.
April 24-27, 2015
These days were spent on deciding what would be going on the poster, setting up the format, creating a draft, and going through multiple rounds of revision. All in all, it was a really fun experience, and I'm glad I got to do it. We also stumbled upon a previously unseen relationship in our data. The prediction line on our 1/L vs F graph was thought to be dependent on the parameter L, however, it turned out to be a constant. The data points depended on L. This resulted in us including a considerably sized explanation of this parameter on the poster, and rightfully so, as this whole topic of distance with respect to the objective lens in interesting. This, as a whole, gave us a better understanding on how this parameter works, and how significant it was in the spreadsheet analysis and consistency of our data. Very slight changes in the set value of L resulted in values that were widely off from the prediction lines.
April 20th, 2015
Today, Dr. Noe and I constructed the final set up we would be using for the project. We placed the 500 micron aperture 1 meter away from the laser and fixed it to the table. We tested several different objective lenses and finally settled on the 10x rather than our original 20x. I threw together a screen made of two tall posts and a piece of graph paper and after a long time of aligning everything, we began to photograph. We translated the objective lens a total of 1.5 inches and took about 9 pictures, each at the clearest bright or dark center seen during the transition. We also took pictures of the unmagnified airy pattern, as well as the image of the aperture by moving the lens as close as we could to it. We discussed ways in which we could graphically display this data and predicted that a 1/L vs. F (Fresnel number) would give a neat, positive, and linear relationship.
April 16th, 2015
There's not too much to say for today other than that the 500 micron diameter pinhole will be offering us the best images. We also began looking at a 20x objective lens so we could sample the near-field. We will need to set up a more precise system to quantitatively categorize our images. This will probably feature a set position for the aperture, and the objective lens being fixed to a one inch translation stage. It will be important to give the laser light an ample space to expand since 500 microns is relatively large compared to what we have been using.
April 15th, 2015
Today, we scrapped the mirror set up. Marty came by, talked some theory with Dr. Noe and me, and helped set up the objective lens that will now be the main coordinator for our photographic success (thanks!). We tried several diffrent pinholes to enhance spatial coherence but ran into a new problem of pinhole distortion. The aluminum cast pinholes, mainly the 200 micron one we really wanted to use, are showing hexagon-esque diffraction patterns with noncontinuous rings. We tried a 100 micron, different model, pinhole and had slightly better results, but they're by no means great. A 200-400 micron pinhole would be optimal at this point considering the dimensions of our table and the fresnel numbers we wish to achieve. I'm on the task now of checking out our options and seeing if anything is worth ordering. On a side note, there are 5 +/- 1 micron apertures available which is fascinating considering what seems to be such a massive relative range of uncertainty. Tomorrow, I'll hopefully be able to try some larger sizes a see if they give favorable results. There's a 500 micron pinhole ready and waiting to be tested.
April 14th, 2015
We started off today getting some materials together, and Dr. Noe showed me where some "building" peices were (posts, mounts, clamps, etc.). We picked out a random metal disk with symmetric holes, estimated at 2mm, as my aperture to test. I did some reading on past bessel beam projects to gather a grasp on how I could use Bessel functions to determine the radius of this aperture by measuring its diffraction pattern. I was left to my own devices for quite a while and started setting everything up. I took the metal disk and set it to the height of the laser using cutting-edge height gaining technology, physics textbooks and individual magazine pages for precision. I used a silver and a gold mirror to turn the beam around, guiding it into the camera. To my dismay, the camera was not producing quality images. Apart from circular diffraction pattern on the image caused by what was likely dust, there were two primary diagonal distortions on the image. Imagine taking a perfect circle of paint and running two diagonal, parallel lines through it with a brush. This was incredibly problematic as the bright central spot that was being distorted greatly outshined the surrounding rings we really wanted to see. This ruined the whole image, really. We'll have to shift the focus of the apparatus unfortunately since the same problem was present in the second camera. I was looking forward to this method, unfortunately. The plan now is to enhance the images of fresnel diffraction to take pictures with our own cameras.
April 13th, 2015
Today, I began configuring the camera for my project. I downloaded the necessary software which took considerable time given the blazing speed of WolfieNet Guest (tens of kb/s for a 230Mb file). In the mean time, Brandon, Dr. Noe and I went to the Math Tower's dish mirror and took a plethora of measurements. We tried for a while to get decent pictures from far away of a candle being held at the focal point. We didn't manage to fill the dish with light, but saw some interesting ring patterns and we did fill a significant portion of the center. After walking back, my download was finally complete and we began testing what the camera could do. Being easily saturated by ambient light, we attached a filter and shined a green laser pointer into the lens. We managed some blurry, circular, central blobs but we certainly need a more formal apparatus before we can get some clear diffraction patterns. We discussed how I could set my experiment up, and I'll most likely be doubling the beam back on the same table as the laser, so I'll finally be able to employ my beam walking skills.
April 8th, 2015
I had a one on one meeting with Dr. Noe today and we began planning the apparatus and procedure for my project. We put together a good idea for the rail system which would allow the distance L to be varied, and we began to test different apertures using a HeNe laser. We tested square and triangular apertures like we discussed in the last meeting. We attempted to find critical points along the span of the near field but had difficulty doing so since the laser was just too bright. Using a polarized film we managed to dim the light to tolerable amounts in order to locate a fresnel number of approximately 1 by sight alone after approximating our aperture size to be 2mm. We traced the diffracted laser light out and observed its characteristics during its transition to the far field, eventually seeing barely any change in the pattern (even opening the LTC doors and going to the end of the hall resulted in no change to the image). We've finalized the idea that a 2mm aperture will be optimal for the experiment. Next time, I need to start figuring out what I'll be doing with the lens in order to make the transition into the far field more favorable.
April 6th, 2015
Today we resolved the final directions of our projects. For me, this began with a discussion of the fresnel number, and what it means to be in the near and far field based on this. Given by the equation w^2 / (lambda)L, a fresnel number much less than 1 is a characteristic of the far field, meaning that the distance between the aperture and the image plane multiplied by the wavelength of incident light is much greater than the radius of the aperture squared.
We discussed the progression of images as the distance, L, increased while all other conditions remained constant. Moving from near to far field, one would observe a shadow of the aperture, which would soon begin to show hints of the far field diffraction pattern. At a far field distance, we would see the shape of the aperture as a bright central point, and radiating outwards from its edges would be progressively dimmer points, as one would see in a typical diffraction pattern, but corresponding to the aperture space in this case. A triangular aperture would radiate in 6 main directions, two, opposite facing patterns for each point. A rectangular or square aperture will form a cross-type shape which would be made up of many aperture shaped points. Now that I have a greater understanding of what exactly my project should be comprised of, I can begin writing my abstract. We will really be showing the procedure of "Reaching the Far Field."
March 30th, 2015
Today, I showed Brandon and Jay the derivation of the intensity Dr. Noe and I went over last week that I now (hopefully) understand well. We worked through some bumps and discussed other ways one could represent this intensity via either trigonometric identities or hanging onto the radicals in the derivation for its use in Fresnel Diffraction.
Brandon briefly went over the sagitta (which is NOT someone's name) method of finding the radius of curvature for circles that are incomplete. Focusing on his project idea about the dish mirror, we then began trying to demonstrate what we have previously diagrammed several times in our discussions of geometric optics. For this demonstration Dr. Noe grabbed some candles, some matches, the parabolic mirror from the pig illusion toy, and the half-circle mirror. When he held the lit candle at precisely the right point, Dr. Noe was able of shining a very bright light on our faces from across the room. This is essentially the same technique applied to headlights/searchlights. To say my face lit up is an understatement. The parabolic mirror was optimal for demonstrating this effect.
From this, we segued into an interesting discussion about our projects in general. We all believed Brandon would be analyzing the dish mirror in the math tower as if it was a circle, but that was a complacent notion. We truly have no idea what shape it may be and this idea can be extrapolated onto likely any situation. Question everything! We also discussed how to write an abstract since our deadline is quickly approaching. We've got a lot of work ahead of us, and it should be fun.
March 23rd 2015
Today's meeting down in the LTC was very fruitful, as I had an opportunity to have a more project focused talk, one-on-one with Dr. Noe. We began with a quick overview of Huygens Principle and what it means for diffraction. The ultimate takeaway is that each point along the wavefront acts as a new source of waves. Then things got a little more math oriented. We went over the way to represent a wave via a complex equation.
We spent a fair amount of time analyzing the relationship between the variables in this equation and formulated conditions that would allow a single point to remain at a fixed position on the wave as it spanned its position, z.
The discussion moved towards Young's Experiment, the famous experiment that showcases the diffraction of light through two slits to create an interference pattern on the image plane. We then began deriving a formula to represent the intensity at any given point along the image plane. Knowing that the intensity is the amplitude of the wave (in our complex representation) multiplied by its complex conjugate, we were able to use Euler's equation to create a simple and concise function of intensity with respect to the distances between the two slits and the point in question. The fluidity of the math was also dependent on understanding the first order of the binomial expansion, which represented the two distances in an algebraically friendly manner. (I will get pictures of this stuff soon!)
March 9th 2015
We've been granted access to the server today, and we spent most of our time recapping commands and how we can navigate around the SSH client.
We also began discussing how we could take our ideas and put them into the format of a project. We discussed a geometric analysis of the dish mirror, and how we could use the sagitta method to locate its center of curvature even though it is merely an arc of a whole circle.
We were also directed towards some online references to further our own search into topics and our areas of interest. I will continue my pursuit of Fourier optics, spatial frequencies, and imaging with these. I have nearly completed the book Dr. Noe has given me on Fourier, and I am coming closer to understanding the mathematics behind the transform. I still don't quite understand how the math on paper can be readily applied to a realistic situation in which one would be confronted with a very complex wave. I hope that I soon will, however.
March 6th 2015
Today, Jay Rutledge and I visited the center to talk a little about our writing, and a lot about maintaining our web pages. Dr. Noe walked us through the downloading of the SSH secure shell client to access the server, and also how to use numerous commands in the Linux environment. He briefly reviewed my writing and offered some advice for further clarity. I hope to begin working on the web page at some point in this coming week once I receive the information needed to connect through SSH shell.
We also perused some pages on the LTC's site that concerned any topics involving Fourier. I'm excited to keep learning about these things since, as we continue our discussions, it seems to be rather ubiquitous. I want to begin focusing on applications so that I can begin to formulate some general ideas for projects, perhaps.
March 2nd 2015
Today, Jay, Brandon, and I visited Dr. Noe in the LTC to continue our general discussions. We began by talking about geometry in optics, focusing a lot on the dish mirror in the basement of the math tower and sound as examples. We showed how and why speaking at the approximate focal point of the mirror would result in a convergence of sound at your position, and so you would hear yourself very clearly. However, an interesting thing occurs once you move your head beyond the plane of the wall and begin to speak; you hear very little, while someone standing far behind you can hear your whispers! Light and sound alike will be reflected in parallel lines when they are emitted halfway between the focal point and the mirror/wall. We then discussed the geometry of the infinitely thin lens. We considered the small angle approximation in this situation, which closely related the radius of the lens, the focal length and the angle between them, and got a bit of an insight into matrix optics. We then considered a lens with some thickness and analyzed how varying degrees of strength are required to converge light at the focal point as you move farther away from the central axis.
We followed this up with a discussion about complex numbers, stemming from the wonder that is Euler's identity. We briefly discussed De Moivre's theorem, Euler's formula, and the graphical representation of complex numbers, demonstrating why they're represented as they are, due to exponents and roots.
February 23rd 2015
Today was the first day we began to discuss project-related topics in depth with Dr. Noé and Dr. Marty Cohen. I began the discussion by reporting what I had recently found out about Fourier Transforms and Fourier Transform spectroscopy from past projects in the LTC and other sources. I explained how these transforms are applied in electronics and signal processing since they can decompose square, non-sinusoidal waves, into their constituent frequencies. Since I only gathered some general knowledge about these transforms, and do not yet understand the mathematics behind them. Dr. Nolent me a book titled Who is Fourier? It seems very low level, and easily accessible, so I should be able to come to a more holistic insight of how the Fourier series and expansion are derived. I see a lot of potential use for Fourier transforms in my time here because of my interest in the interferometer. It seems that the raw data of an interferogram can be analyzed using Fourier Transforms.
Jay Rutledge brought up some ideas concerning optical vortices. The concept of bent and curved light then dominated the conversation as we derived the law of reflection geometrically and discussed an experiment using corn syrup and water to gradually bend a ray of light. We are interested in recreating this setup that involves a solution of water and corn syrup in a tank to sit for a few days which results in a variety of indices of refraction along the depth. We were fascinated and confused by the illustrated parabolic curvature of the light if it was to be emitted at an upward angle into the tank. Hopefully, as we study light further, well gain a better understanding as to how light decides to move and why. The led us into the consideration of Fermats principle, the idea that the path between two points of a ray of light is the path that will take the shortest amount of time for the light to traverse (The apparent anthropomorphizing of light in these two cases is making it increasingly difficult for me to believe its not in fact sentient). This seems obvious, but it helps define what a ray of light means.
Finally, Brandon Yalin brought up the field of ellipsometry. We managed to construct a, more-or-less, definition of it, being the measurement of the properties of thin films, however, Dr. Noe and Marty do not seem to have ever used it much and so its likely a dead end pursuit.