Friday, April 29, 2011

After the hectic college application season, I am glad to say that I will be going to the Cornell University College of Engineering. I am also extremely excited about receiving the Hunter R. Rawlings III Presidential Research Scholarship, because of the possiblities it opens up for doing research during my time at Cornell.

Also for future Cornell applicants, I found this page extremely helpful.

Tuesday, November 23, 2010

I finally finished my Intel report, which is now available on the website. Since leaving Stony Brook University after the summer, I have been busy with huge workload of my senior year.

I am extremely happy with the way my report turned out. Although, after turning it in and reflecting for a while, I am hoping for another chance to collect better data. Hopefully I can go back at some point and try my hand at the data again, especially the sinusoidal zone plate with the &pi -phase jump.

The Simons fellowship was a great experience, I enjoyed being able to experience a real research experience. I am also grateful for being able to work in the LTC, which really gave me an opportunity to work on a research project of my own design. Dr.Noe, showed me how to think like a scientist, how to analyze scientific phenomena, and how to comminucate my ideas effectively.

I would like to thank the Dr. Noe, Prof. Metcalf, Dr. Cohen, my fellow Simons students, the REU students, and the Simons foundation for making this summer enjoyable and enlightening.

Sunday, November 14, 2010

I finished wirting a draft of the research report on Friday, and sent it to Dr. Noe. Now I have the abstract to work on.

Sunday, November 7, 2010

Today I continued analyzing the data. I did this by using XV image editor to compress the pictures to a height of one pixel. Then I converted these images to .pgm files and later .dat files. These files contain a long list of the average intensity values along each column of pixels on the CCD. I began to plot the data using GNUplot in order to visualize the intensity distribution in the focal plane. I also later used GNUplot to fit the data to the curves that represent the theoretical intensity distributions in the focal planes of the zone plates.

Monday, October 25, 2010

I sent my very primitive research report to Dr.Noe, When I called him, he emphasized that I needed to clearly explain the ideas that I understand well. He also stressed the importance of a great introduction. I also hope to share my research with Dr. Michael Raymer from the University of Oregon, who helped me find the photography service that helped me make the zone plates.

Friday, October 8, 2010

I have not had too much time to work on my project recently, but I have a holiday today, So, I continued working on the draft of the research report and I plotted some data using XV and Gnuplot. I plan to send it to Dr. Noe if I make significant progress.

Monday, August 23, 2010

I continued taking pictures of the focal lines of the zone plates on Thursday. I wish I had stayed back on Friday to get some more pictures, but I had to come home because my father had important business. It took me an entire weekend to install Ubuntu Linux operating system on my Mac. First I installed VirtualBox on my Mac and installed Ubuntu in the VirtualBox. VirtualBox creates a virtual machine which runs the Ubuntu operating system while I am running the regular Mac OSX operating system. So I installed XV image editor and GNUplot, so now I am prepared to properly analyze all of the pictures that I took.

Wednesday, August 18, 2010

Today, I continued working on taking pictures of the focal lines of the zone plates. I got 11 pictures of each of the zone plates' focal lines at different distances from the zone plates. Tomorrow, I plan to continue with this experiment by analyzing the intensity distributions of the diffraction patterns.

Tuesday, August 17, 2010

Today I came back to the lab, and continued experimenting with my zone plates. At first, I simply decided to traverse the diffraction pattern, but when Dr. Noe, said that this method would lead to a large error, I realized it was time was time to find a new method of quantitatively mapping the diffraction pattern of each zone plate. So eventually Dr. Noe suggested that I use a CCD camera on a rail to accurately see how the diffraction pattern changes axially.

Friday, August 13, 2010

Today is the last day of the Simons Summer Program. All of the Simons fellows presented posters about their projects. After saying final goodbyes to the other Simons fellows, I gave my father a tour of the lab. However, after a short rest at home I plan to come back to the lab on Tuesday to traverse the diffraction pattern created by the zone plates with a razor blade. Later, I also hope to try aligning the HeNe laser using the pi-phase jump zone plates. Here are the diffraction patterns produced by the different zone plates.

Diffraction pattern caused by binary linear zone plate

Diffraction pattern caused by
a binary linear zone plate.

Diffraction pattern caused by sinusoidal linear zone plate

Diffraction pattern caused by
a sinusoidal linear zone plate.

Diffraction pattern caused by binary linear zone plate with a
π-phase jump

Diffraction pattern caused by
a binary linear zone plate
with a π-phase jump.

Diffraction pattern caused by sinusoidal 
linear zone plate with a π-phase jump

Diffraction pattern caused by
a sinusoidal linear zone plate
with a π-phase jump.

Wednesday, August 11, 2010

This has been a very eventful week. Today, I finally received my zone plates and was able to test them. The zone plates without a pi-phase jump indeed created bright lines and the zone plates with the pi-phase jump created dark lines. It was very exciting to see that the zone plates behaved as predicted. However, I will continue testing them on Thursday. Most of Monday and Tuesday was spent crafting abstracts, which in the end still proved to be incomplete as we spent most of lunch today correcting minor errors. Dr. Noe took us out to lunch at an Indian restaurant, where we saw a story on the news about a solar concentrator based on the anatomy of fly eyes.

Linear binary zone
Binary linear zone plate.

Linear sinusoidal
zone plate
Sinusoidal linear zone plate.

Linear binary zone plate with a π-phase jump
Binary linear zone plate with a π-phase jump.

Linear sinusoidal zone plate with a π-phase jump
Sinusoidal linear zone plate with a π-phase jump.

Sunday, August 8, 2010

On Saturday, I attempted to print my zone plates on to paper and take photographs of them using a disposable film camera, only to find that the SINC sites on campus were all closed. Therefore, I will have to rely on the zone plates that I gave to Gene Lewis for printing. I also found a mathematical error in my equations for determing the focal length of a zone plate. The calculation was off by a factor of 2, but this should not change my possible experiment too drastically. I was thinking that I could use the zone plates to align lasers to show the possible applications in optical alignments. Also I could possibly use the pinhole method to chart the beam profile across the focal plane of the zone plate.

Thursday, August 5, 2010

Today Mr. Walt O'Brien informed me that he no longer prints onto 35mm film, so he gave me the contact information for one of his colleagues, Mr. Gene Lewis. However, I am still waiting for Mr. Lewis to respond to my email. Today I modified all of my zone plates so that they would fit on 35mm film. Also I created binary zone plates that have the same focal lengths as the sinusoidal zone plates I had already created. I also used various Mathematica functions to improve the quality of the zone plates. At the end of this process I found that the quality of the binary zone plates improved tremendously, and the quality of the sinusoidal zone plates improved moderately. In addition, if Mr. Lewis doesn't respond to my email by tommorow morning, I plan to try printing the zone plates myself with one of the laser printers on campus. Perhaps I could use the printer in the library, or the printer in the TLT(Teaching Learning Technology) center.

Wednesday, August 4, 2010

We spent most of the day editing our Simons abstracts and listening REU students practice for final talks. With only a little more than a week left in the Simons Program there is a still a lot to be done. I must finish the abstract, the poster, and I must send the zone plate design for printing. After the zone plate is printed I can set up my experiment and finally collect some data.

Tuesday, August 3, 2010

Today, I created a zone plate, which I believe I can use in my experimental setup, perhaps I can create a series of zone plates of varying focal lengths and plot the intensity distribution in the focal plane for each plate. Also, I got the contact information of a transparency printing service through Professor Michael Raymer at the University of Oregon.

Monday, August 2, 2010

Today, I finally started working on creating zone plates using Mathematica. I found that the transparency or opacity of a sinusoidal zone plate are described by the general function,

Transmittance equation

So by adjusting the parameter k, it is possible to create a zone plate that meets certain specifications for wavelength and focal length. The parameter k, can be found by using the equation,

Binary zone plate equation

where n is an integer, f is the focal length and λ is the wavelength. By setting n equal to an arbitrary value and setting f and w equal to the desired focal length and wavelength, you get a value for r, which can then be plugged into the equation

Transmittance equation

This equation can then be used to find the value of k. Once a value for k is obtained the varying opacity of the desired zone plate can be determined. I think that I will be working with linear zone plates, because they are easier to generate and the math involved with them is simpler. I also found that by ignoring the time dependence in the wave equation and having two waves that are out of phase by pi, you can prove that destructive interference occurs. If you have the equation,

Equation for two wavefronts out of

then you can prove that the resulting amplitude is zero, by using Euler's Formula.

Thursday, July 29, 2010

Today, I spent most of the day studying the math behind zone plates. However, the problem is that I must still figure out how to apply the math that governs binary, circular zone plates, to sinusoidal zone plates which have top halves with an even configuration and bottom halves with an odd configuration. This change in the configuration across the diameter of the plate is what causes the destructive interference at the focus.

Wednesday, July 28, 2010

Today, I began reading some more about zone plates. When I expressed an interest in this Dr. Noe, spent quite some time explaining how zone plates work. This discussion really elucidated the details involved in the fabrication of zone plates. I found an interesting paper that outlined possibilities for how to create destructive interference at the the focal point of a zone plate. This can be done by introducing a pi-phase shift.

Tuesday, July 27, 2010

Today, I found that I probably have to find a new project, because Dr. Noe suggested that working with the solar concentrators could be too complex. There is not enenough time left in the program to finish this project. So, this was certainly discomforting, but I had to move on, so I decided to go back to square one and re-analyze my interests. Therefore, I think I am going to be doing a project involving gradient index lenses, or perhaps zone plates. I am not entirely sure yet, but I think I am going to work on creating a diverging grin lens.

Monday, July 26, 2010

Today Ben, Annie, and I were able to give a presentation on our mini project as well as listen to others such as Dr. Kiko Galvez, Giovanni Milione, and other high school students give talks about optical vortices and cylindrical vector beams. Over the weekend I actually figured out how the flat waveguide used in the solar concentrator of the UC San Diego student worked. It was actually not flat. It had small prisms at the focal point of each lens, thus allowing total internal reflection to occur. I also came up with designs for solar concentrators over the weekend. One is similar to the one using the waveguide however in my design, the waveguide is not flat. Also, I came up with a solar concentrator that uses a Fresnel lens and a mirror whose cross-section resembles two hyperbolic curves placed next to each other. The Fresnel lens is used to steer the light onto the mirror, and focus it. Then the mirror essentially funnels the light to the Stirling Engine.

Thursday, July 22, 2010

Today we spent most of the day working some more on the report. However, we were able to use Vince's spectrum analyzer to find the beat frequency of the laser. Using the beat frequency and the equation, f=c/2L, we calculated the length of the laser cavity. This further helped to confirm the validity of our calculations.

Wednesday, July 21, 2010

Today we continued to fit the data to theoretical erf curves. By the end of the day we finally calculated the location of the beam waist, which we found to be 3.6 cm behind the laser. This measurement is consistent with the mirrors inside the laser cavity. Then later on we also got to meet with Greg Caravelli and Rebekah Schiller, who used to both work at the LTC, but then became high school physics teachers.

Tuesday, July 20, 2010

Once more, Ben, Annie, and I spent most of the day perfecting our report, but then we got to attend a talk given by Marty Ligare from Bucknell University on thermodynamics, who explained his unique approach to deriving the thermodynamic equations involved in describing what happen in a trap.

Monday, July 19, 2010

Today, we spent the majority of the day collecting more data and further working on our report. However, after a short discussion with Dr. Noe following dinner it became perfectly clear that Ben, Annie, and I all needed to study the properties of Gaussian beams more, because none of us could even write the standard form that describes the radius of the laser beam at various distances.

Friday, July 16, 2010

We collected more data for the mini project and finally have enough data points to get an accurate number for the location of the beam's waist. We also started on the report for the mini project. By monday we should have the results for the beam's waist, and the report should be nearly complete. Also I saw some interesting new design concepts for solar concentrators. One design uses an acrylic and glass optic to capture the light and redirect it to the center where the receiver is located. Another design uses lenses all located on a single section of glass which send the light to a waveguide, which then redirects the light to a single receiver.

Thursday, July 15, 2010

Today we continued in our search to find the waist of the HeNe laser beam. We did this by moving the razor blade across the beam at various distances from the laser and plotting the changing intensity. By finding the curve of best fit for the data from each distance, it is possible to derive the width of the beam by looking at the equation for the best fit curve. By plotting each of these widths, it is then possible to find the curve of best fit, which will allow us to determine where the beam's waist is located. However, we did not locate enough data points today to definitively determine how the beam's width changes as the beam propagates. Therefore, we will wait until tomorrow to find the beam's width.

Wednesday, July 14, 2010

Today we took some more data using the HeNe laser, although we did some more measurements as to how the beam's intensity changes as you move a razor blade across, we also tried to find the beam's waist by estimating the beam's width at various points along the beam's axis. We did this by measuring the distance the razor blade had to move to decrease the beam's signal from its maximum to zero. However, by the end of the day, Marty Cohen told us that this was completely pointless because this could cause major inaccuracies and indeed our data incorrectly showed that the beam had multiple waists, so therefore we will have try the experiment again tomorrow with a new method.

Tuesday, July 13, 2010

All of the Simons fellows took a tour of the Brookhaven National Laboratory today. We were able to see the detector used in the PHENIX experiment to detect collisions created by the Relativistic Heavy Ion Collider (RHIC). Then we learned more about particle accelerators and how they function. Later, after lunch we received a short presentation on how supercomputers worked and their role in science. After this we were able to see IBM's New York Blue supercomputer in person. New York Blue is currently ranked as the 67th fastest computer in the world, although in 2007 it was ranked 5th. But, the most interesting part of the day was definitely being able to see the detector at PHENIX in person.

Monday, July 12, 2010

Ben, Annie, and I finally started our mini-project today. We were essentially measuring how the intensity of the laser changes as you move a razor blade across it. We accomplished this by using a HeNe laser, which was lined up with a converging lens and a photodetector. The photodetector was used to measure the intensity of the laser beam, and the converging lens was simply used to make the beam smaller, allowing the photodetector to measure its intensity more accurately. We ran the experiment twice, once from a distance of 3.5 meters, and another from a shorter distance of 15 centimeters. Once we got our data we had to calculate what the graph of the distance of the razor blade across the laser beam versus the beam's intensity would look like. We found that it would theoretically follow the error function. But, I was surprised when Dr. Noe said that the error function could not be expressed without the use of an integral sign, because there is no way to truly find a function which describes the antiderivative of the Gaussian function. The Gaussian function models a laser beam's intensity when nothing is impeding the beam.

Friday, July 9, 2010

Today we discussed a possible mini-project with Dr. Noe. It essentially consisted of moving a razor blade across a laser beam, and seeing how its intensity changes. So we discussed what a graphical representation of this experiment would look like. When examined the data of a student who had done the experiment on beam diffraction before, we found that in fact the graph of the beam's diffraction does not follow a linear pattern, but rather a hyperbolic pattern. It only appears to be linear because as a hyperbola approaches infinity it begins to resemble a line. This led us to the derivation of the equation for a hyperbola from the simple fact that a hyperbola consists of all the points, such that the difference between the distance from each foci to a point on the hyperbola remains constant.

Thursday, July 8, 2010

First, we started off the day with a discussion with Ewuin on lasers, their profiles, and their various modes. However, when we sat down for lunch with Dr. Noe and Mr. Goldwasser, they quickly became convinced that we needed some real hand-on work to really get a feel for how lasers work and a feel for how to do deal with numbers without a calculator. So, we took a laser pointer and used it in hallway outside of the lab to measure the dispersion of the laser beam. However, we momentarily found that our tape measure was stolen until Vince suddenly appeared and said he just found it in the men's bathroom. However, despite all of that excitement we still got our data and then spent some time using Excel to make a plot of our data , the only problem was that our data suggested that at the source of the laser, the diameter of the beam was a negative number. But, after Dr. Noe showed us how exactly to find a line of best fit, the data seemed a little bit more reasonable. However, the way Dr. Noe explained how to find the line of best fit was amazing. You subtract the experimental data from the theoretical numbers and square each difference, and the sum of the squares is a measure of the error. Then by adjusting the slope of the line and looking for where the sum of squares is the lowest, you can find the line of best fit. However, I also found a paper that describes a new design for a solar concentrator, which I never saw before.

Wednesday, July 7, 2010

Today we attended a great presentation by “Laser Sam” on the different types of lasers, laser safety, and finally the stabilization of lasers. Mr. Goldwasser explained the difference between diode lasers, gas lasers, solid state lasers, and dye lasers. However, the majority of the time was spent discussing HeNe (Helium Neon) lasers, which no doubt are Sam's favorite. However, today was also rather uneventful. But, I did come across an interesting paper that looked at the optimal solar reflector for cylindrical absorbers. This paper will no doubt be extremely helpful, because the Stirling engine's absorber is in fact cylindrical.

Tuesday, July 6, 2010

Today was quite uneventful, aside from cleaning up inside the lab and attending a talk during lunch by Dr. Carlos Simmerling, I read some interesting papers on solar concentrators. One paper explained an algorithm that can be used to create solar reflectors for a receiver of any shape. However, this algorithm dealt with where to place simple plane mirrors in order to concentrate the sunlight rather than using one continuous mirror. This would certainly help to cut the cost of making a Stirling engine, as well as make it easier to mass produce. Then I read another interesting paper that compared Fresnel lenses and parabolic mirrors as solar concentrators.

Monday, July 5, 2010

Today was extremely enlightening mathematically, we learned more about parabolas osculating spheres, but it truly became interesting when we examined an ellipse osculating a parabola. When two functions osculate, they have the same value at x=0, but they also have the same value for the first and second derivative at x=0. Therefore, for a parabola and an ellipse to osculate their second derivatives must be equal. If you have the parabola y=Ax^2, then the second derivative, which is 2A, must be equal to the second derivative of the ellipse. By equating the two and solving for A, you find the parabola that osculates with a certain ellipse. But, then what really surprised me was when Dr. Noe showed us that in fact when a projectile is thrown close to the surface of the Earth, it seems to follow a parabolic path, but in fact it only follows an approximation of a parabola. It actually follows an elliptical path where one of the ellipse's foci is located at the center of the Earth. Here is a picture of an ellipse osculating a parabola:

An ellipse osculating with a parabola

Friday, July 2, 2010

The Stirling engine finally worked today, and to think all it needed was some polish and some lubricant. So after a quick polishing of the mirror, and a small spray of lubricant on the flywheel, the Stirling engine worked great. I would definitely be excited about doing a project on the Stirling engine. Perhaps creating a feedback system to keep the Stirling engine focused towards the sun would be a good project. Dr. Noe suggested that it would be possible to use a quadrant photodetector to find the brightest area in the sky and have the Stirling engine position itself to that area of the sky. Or I could still test different solar concentrators as I originally planned. Unfortunately, the Stirling engine would not run for quite as long or quite as efficiently later on in the day. The sun was probably too weak or perhaps the entire engine became overheated, and there was no real temperature difference to drive the pistons. Therefore, we decided to let it cool down overnight and try again later.

Thursday, July 1, 2010

Today we really witnessed how mathematics and optics are interconnected. It started with just a simple question by Dr. Noe about how we know that the focal length of spherical mirror is half the radius of curvature, which everyone seemingly had taken for granted. But, after the application of the small angle approximation we saw that indeed in an ideal situation, the focal length is half the radius of curvature. But, even more interesting is that a series of ray trace diagrams is completely unnecessary in describing a series of lenses separated by a certain distance, rather one can simply describe where the light will travel using a series of matrices. Later as we discussed the solar optics phenomena more, we found that indeed the difference between the reading and prescription glasses is the shape of their lenses. But, this later led into a small discussion about the properties of different thin films, and some of their optical properties, which I plan on doing some research about.

Wednesday, June 30, 2010

Soon after going to the lab today we discussed the wave properties of light. We mathematically derived the results when two slits act as point sources for two waves. After spending quite a bit of time with the derivations, we finally found the pattern of the interference between the two waves. However, the real surprise came when we discovered that even a simple single slit can create an interference pattern. After eating pizza, we listened to an interesting talk by Professor Metcalf, who described the superposition of waves, specifically how that related to acoustics and harmonics, starting simply with the question of what makes the same note on two different instruments sound different. Then later we went outside to see various phenomenon that puzzled us, such as why a pinhole, independent of its size, always produces a circle of light of a constant size, and why reading glasses cannot be used to burn paper like a magnifying glass, I suspect it has to do with the shape of the lenses.

Tuesday, June 29, 2010

Today we first reviewed some math, from basic geometry to the connection between exponentials, imaginary numbers, and the trigonometric functions. It was truly eye-opening that real phenomenon can be mathematically explained using real numbers. It was equally surprising to see that when i is part of the exponent of an exponential it starts to osciallate much like a sinusoidal wave. After which we were lucky enough to attend a talk where we saw some interesting optics demonstrations, such as how lasers behave when shined through a space with a gradient refractive index, and how a laser can be used to measure the linear expansion of a heated copper wire. I was mostly fascinated by the fact that you need nothing more than a gradual distribution of any refractive material in water to manipulate light. Then we spent the rest of the day learning more math, such as the general form of the wave equation, and updating our webpages.

Monday, June 28, 2010

Today was our first day at the Laser Teaching Center. We got to meet Dr. Noe and talk about various optics subjects. First we took a tour of the LTC, seeing the posters for various projects throughout the years at the LTC. Of course, as soon as we arrived at the lab, we dived right into the optics. First we looked at a toy which has two pigs inside of it and uses mirrors to make it appear as though the two pigs were resting on top of the toy. After spending about an hour, we determined how the image was formed, and we determined that in fact that it was a real image. After a discussion at lunch with Dr. Noe and making diagrams on pizza boxes, we went back to the lab and had a discussion about the importance of keeping a detailed and organized notebooks. Then after we went back to the lab, we tried to see if we could get the Stirling engine to work, unfortunately it ≈was cloudy outside, so we went back inside to observe the graduate students work on making a Mach-Zehnder interferometer.