Journal

April 24th 2012

One possible reason for why I was having some bad luck resolving the past couple tries was that the pictures were in fact taken from too far away. I had originally done this to maximize the resolution from the diffraction grating, but doing so might have reduced the D-lines in size so as to make them too small for the camera to pick up. To remedy this, I began by making the slit size even smaller by using two razor blade edges placed closely together, held by a magnet. The slit width is now on the order of 0.5 mm. I took pictures from distances varying between 1 and 4 meters. I also tried using a black and white setting to maximize the contrast between the light from the slit and the background. Also, the Mavica's lens is one the order of 3 cm wide, so I apertured it to the previously calculated 2 mm width. After running these through the older image processing software on the old LTC server, we were still unable to resolve the D-lines. We hypothesized that this was due to the size of of the Mavica's pixels. By using this older piece of technology, we were able to get more reliable focus, but didn't have enough resolving power in the camera to detect the D-lines individually.

April 22nd 2012

After a couple more unsuccessful shots with the more modern digital camera, Dr. Noe suggested I use a different imaging device. The digital camera that he produced for me was a Mavica, a beautiful piece of slightly older technology that records onto floppy disks. I'm quite a fan of older technology, so this was a pretty neat new approach to the problem. I took a few trial shots and quickly realized one of the downsides to the Mavica was it's display. When previewing the pictures I had taken, even at full zoom, the diffracted D-lines took up only one pixel on the display. To check if they were even resolved, we had to plug the floppy drive into the lab's computer. Upon first inspection, it looked like we were in the clear and had successfully resolved the D-lines, but it was a very close call. We couldn't get a definitive view due to the image processing softwares default zoom behavior of pixel blur when zoomed in to closely. With this in mind, I plan to take some more pictures with the Mavica next meeting and to run it through a software that Dr. Noe suggests will be more helpful for analysis.

April 21st 2012

Yet another relatively unsuccessful day. I attempted to vary the distance between the camera and the sodium lamp to see if the focus of the digital camera could do any better. I also experimented with some smaller slits. Unfortunately, each of these attempts were met with similar results. I was only able to stay for a short while, so I will give it another in the next couple days.

April 20th 2012

Now that we know it's possible to resolve the D-lines with the previous set up, I attempted to do so with the camera as is. This is, of course, a more difficult of a task due to the zoom limitations of the camera. After a few quick pictures, it became apparent that I was going to need to spend some time today changing various parameters to see if we could get a resolved picture. I tried multiple different slit widths and varied the distance between the camera and the sodium lamp, as well as using a different slide of diffraction grating, also 500 lines/mm. Unfortunately I was limited by a rapidly depleting battery, and I was unable to get any pictures of the D-lines. Dr. Noe said he would grab the battery charger from his house and, with that, I will go about the task again tomorrow.

April 18th 2012

Dr. Noe sent me an email couple days after our last meeting saying he was able to see the doublet, so today's goal was to successfully image it. To begin, I attempted to see it myself using the toy diffraction glasses and a small handheld telescope. It was a bit difficult to make out the lines out exactly, primarily because I don't have the steadiest hands in the world, so I did some scrounging around and put together a stand for both the glasses and the telescope. When I peered through, there they were, clear as day! After quickly setting the camera up on a tripod, I was able to take some photos, as shown below. Initially, the shots were a little blurry, so on Dr. Noe's suggestion we apertured the telescope opening from roughly an inch to 2 mm in diameter. After doing so, the picture came out very well, with the two lines fully resolved. The final image and setup are pictured below, as well.

Friday, 13 April 2012

Today I was able to spend some time talking to another student doing research with Dr. Noe, Marissa Romano. I chatted with her about our respective projects, hers being about measuring certain aspects of sunlight. I've always felt that explaining a topic out loud to another person greatly helps with my own understanding of it, so this brief exchange was definitely worthwhile in that respect.

After this, I approached another issue that would affect the resolution of our setup: the size of the image in the camera. As stated before, we need a resolution of roughly 1 part in 1000. To accomplish this, our camera would need to be able to resolve 1 mm from 1 m away. I needed to fully zoom in, without engaging the digital zoom, but was ultimately able to get a picture that clearly shows the 1 mm demarkations. So, from this, we know for sure that we will not be limited by the resolution of our camera.

Returning to the issue in the previous journal entry, I gathered a few more measurements to find the slit spacing of our diffraction grating. I used a HeNe laser that emits light with a wavelength of 632.8 nm, rather than the green handheld laser from before. I took three measurements of the distance between the zeroth and first diffraction order with respect to the grating's distance to a projection screen, making sure the light was diffracted at a different point on the grating in each case. With these results we should be able to better determine if the grating is regular.

Wednesday, 28 March 2012

When I first stopped by, Dr. Noe took some time to format last week's entry for this webpage and handed me the most recent copy of Optics & Photonics News to read while he did. In it was an article on Max Planck's life and his contributions to physics. I've never read a lot about the history of the man, so what I was able to read provided some interesting insight. One thing that struck me as pretty neat was his interaction with Albert Einstein, the two having played music together. I'm quite the music-nut, so reading about two of the greatest minds in physics hanging around jamming brought these almost mythical figures in my mind into a new, and very humanizing, light.

When he had finished with the journal entry, Dr. Noe mentioned that the writing in it and the previous ones could use a little work. Partially, it was a matter of simple errors, but more fundamentally, the language needed some tweaking. I've been told in the past that my writing is "intentionally esoteric," and this certainly shows in a number of my previous entries. Dr. Noe mentioned that this was a concern for another student he was working with, but assured me that she, and I, should be able to do better. Thus, we spent a good amount of time going through my previous entry so that it read a bit more clearly. After that, we talked about the HTML formatting of my webpage and also some logistical issues regarding the recent upgrades to the computers in the Laser Lab.

As we were reading through my last entry, I went into a bit more detail about my calculations. I had made a couple of incorrect assumptions when working the numbers, namely with the wavelength of the laser pointer's light, and replacing it in the calculations lead to a line spacing value of 1.98 microns, even closer to 2 microns as written on the glasses. We also talked about the error that I calculated using the website mentioned below. I used the phrasing "there is an error of" and Dr. Noe quickly mentioned that this neglected to recognize the importance of error calculation. What I had found was a range of possible values, given the accuracy of our measurements. Considering the glasses are a toy, the data written on the side isn't necessarily reliable, so comparing the range I calculated to that value doesn't yield anything particularly helpful. All that could be accomplished by that is seeing how accurate the company that made the glasses cared to be. The next step in finding the spacing of the diffraction grating is taking multiple measurements, and seeing how much they vary. This will tell us how regularly spaced they are.

Thursday, 8 March 2012

It had been much to long since I had been to the lab, and today marked the end of that dry-spell. Dr. Noe and I had a lengthy discussion about my responsibilities as a student enrolled in independent research class. When we had finished this part of the conversation, we attempted to get back in gear and make some progress. As it had been a while since our last meeting, a back-to-basics approach was necessary to establish a framework that I would use to go forward. But, after a very short amount of time, it became clear that I didn't have much to contribute to the conversation. So, I was tasked with looking into some fundamentals of photon optics for my own edification.

One primary issue is that I have not fully internalized some of the fundamental terminology of optics. For example, I misspoke and uttered the phrase "low wavelength," which is patent nonsense. I intended this to be a differentiation between long and short wavelengths, but obviously failed to, as I can't even recall which I meant. Another fundamental relationship that escaped me at the time is that between the energy of a photon and its frequency, which is E = hν. A topic related to this, which I haven't had much formal education about as yet, is black-body radiation. [I did some looking into this and found some interesting stuff out.] The basic idea is that an object that absorbs all wavelengths of radiation that fall onto it will give off a certain spectrum of wavelengths which depends only on its temperature.

After I was done with my time in the lab, I attempted to develop some ideas for the diffraction grating project. Ideally, I am going to work on figuring if sodium's "famous" D line doublet [link] can be resolved using a simple toy diffraction grating [link]. Earlier, I took some measurements of a green laser pointer [wavelength] aimed through diffracting glasses, and used these to find an value for the distance between the slits of the grating. This value turned out to be 1.96 microns, in remarkably good agreement with the nominal 500 lines/mm value printed on the glasses. I also looked into resolvance, or ability to resolve two nearby wavelengths using a diffraction grating. The formula is rather simple: R = λ/Δλ. The sodium D lines have wavelengths of 589 nm and 589.59 nm, so we'd need a resolving power of about 1000 to be able to distinguish the two. It is also important to note that R = mN, where m is the order number and N is the number of slits illuminated. So, we'd need to illuminate 2 mm worth of our diffraction grating to get this level of resolvance, which is entirely possible.

Tuesday, 22 November 2011

We had a short meeting today where I presented my solutions for the two short problems involving spectroscopy and mirror measurements. For the latter problem, I worked out a method for calculating the radius of curvature of a mirror from the radius of the outer rim and the depth of the mirror, as noted on page 9 of my computation notebook. This formula turned out to be r = (l^2 + s^2)/2s, where l is the radius of the mirror's outer rim and s is the length of the sagitta, which in this case was depth of the mirror. More information about the sagitta can be found here: http://en.wikipedia.org/wiki/Sagitta_(geometry). The next step was to take measurements of the mirror that inspired this curiosity. I began by taking two lengths of string, taping them to the edge of the mirror to form two arbitrary chords, finding their midpoints, and perpendicularly bisecting them. The resulting line segments were two radii of the of the small circle defined by the outer rim of the mirror. Measuring the distance from the center of the outer rim, located at the intersection of these two lines, to the closest point on the mirror's surface gave the length of the sagitta. These lengths were l = 41.25 inches and s = 23.5 inches, thus the radius of curvature of the mirror was r = 48.0 inches. The solution to the spectroscopy problem I presented turned out to be incorrect, so I will attempt again to determine why spectral lines are more spaced out the further from the source one is. To be better prepared to solve this problem, we took a few pictures of the He-Ne laser which are below. Note the more apparently distinct spectral lines in the right image, which was taken at a farther distance than the left.

      

Friday, November 4th

Today, I started my time in the lab by familiarizing myself with the available systems of the Laser Teaching Center. We begun by going over the fundamental HTML I'd need to keep this, my journal, and the other sections of my web page up to date with progress made in the lab and my thoughts and ideas. The computer in the lab runs Linux, so I picked up a couple shortcuts to allow for more efficient terminal navigation. I also was briefly introduced to a number of different useful pieces of software installed on the system, such as xfig, gnuplot, and pico (which I'm using right now for this entry!). Finally, we put the finishing touches on my account at the LTC by entering my unique password.

After the logistical issues were handled, we went on to getting some solid science done. Primarily, we talked about the optical properties of lenses and mirrors, but the topic of spectroscopy was briefly brought up. Namely, I learned that the laser I observed and wrote about last week is referred to as a He-Ne laser.

We continued to discuss some of the fundamental behaviors of mirrors and lenses. In particular, we clarified what was observed at the concave reflecting dish in the math tower's basement. At first, I assumed that the point that my image flipped was at the same point that my changed tone, but this is not the case. In order to detect a difference in the direction my voice seems to be coming from when speaking into the reflecting dish, I would have to be passing the center of curvature. At this point, my voice would be reflected directly back at me, bouncing perpendicularly to the curve. This means that my hypothesis that the change in the apparent direction of the sound does not occur at the same point an image flips.

One could record these important locations (focal point/center of curvature) by these acoustic and optical properties, or one could calculate them mathematically. In this case, where we only have a portion of the curve, it pays to have some mathematical tools in order to appropriately use the limited information available. With a length of a chord and the sagitta, it is possible to determine the radius of curvature, and thus the focal point, with a simple application of the Pythagorean theorem.

Friday, 28 October 2011

Today, my first day in the lab, was an exciting one. Two topics that had recently caught my interest were the fundamentals of spectroscopy (from my the introduction to quantum mechanics in PHY 251), the similarities between the behavior of sound and light (from a parabolic mirror in Stony Brook University's Math Tower, which demonstrates that the focal point can be determined by optics and acoustics), and Fourier analysis (from MAT 341).

To begin, I observed some of the behaviors of a neon-helium laser through a diffraction grating. This produced a series of images of the laser that were of varying colors. When viewed from a distance, the lines of light were farther apart, showing well-defined images of different wavelengths of light. This was because the gases in the tube emit light in a finite spectrum, whereas less controlled light, such as the one emitted by a green LED, exhibited a continuum of colors. Additionally, the image of the laser was displaced by a certain angle θ, the sine of which is equal to d (the distance between slits in the diffraction grating) over λ (the wavelength of the light). It was very interesting to see that there was a particular point where two adjacent lines blurred into one. This is apparently a similar phenomena to that described by the Raleigh criterion, which limits the imaging of distance stars that are in close proximity.

In addition to observing the diffraction of the Ne-He laser, we went over some acoustic principles and sound interacting with light. A setup was used to demonstrate sympathetic vibration that occurs when an object vibrates with a tone similar to the resonant frequency of another object. It is interesting to note that these frequencies need not be absolutely equal, and can be off be a couple of Hz. When the two tuning forks used in this equipment were not exactly equal, one can hear beat frequencies, or a swelling sound that is related to the difference in these frequencies. Following this, we observed a setup which demonstrated the possibility of beat frequencies occurring in light and how a laser shown through a region that is disturbed by sound waves can be manipulated to interfere with itself in order to find the frequency of the sound it traveled through.