Analysis of Density of Rb MOT
by Cameron Cook
supervisors: Brett DePaola, Larry Weaver
Week 2: This week I continued learning more about the experiment and why these atoms are acting the way to do concerning their photonic emission.(elaborate more about what I read) We had safety training for the JRM lab and for the wood and metal workshop. Also, I designed a simple mount for a new CCD camera to sit on and view into the MOT.
Week 3: Monday I built my camera mount in the student workshop with supervision. It works and looks great; here’s some pictures. I started some tutorials on the programming language Python. This will be handy later since I will be developing a couple programs later in the summer and I have minimum experience in programming. I’m also reading about BASEX, POP, and the Iterative method. These programs are inversion techniques that pull 2-D plots into 3-D density distributions and should help me determine the MOT’s density. They each have their pros and cons.
Week 4: Vince fixed up my computer so that the digital camera would connect to the computer and so that the image would show in Labview. The MOT was a little shy in its first photo shoot. Bachana and I had to find the little guy in the chamber. There was much distance changing, refocusing, and searching for the MOT. The fluorescence is near infrared, just outside of human vision, so human eyes can’t see the MOT, but a CCD filter is capable of sensing it.
Finally got some decent resolution and size images. Here’s one of them:
This is an image after I’ve prettied it in Origin 8. The axes are the number of pixels. 1 millimeter is equivalent to about 70-80 pixels, so this is pretty huge for atomic standards. The legend to the right is a measure of the fluorescent intensity. Notice the dip in intensity in the middle of the graph. Pretty odd- could be destructive interference of the light, maybe it’s so dense that the outer atoms are absorbing some light that the inner are emitting, or there could actually be a dip in the real atom cloud. I think the second option.
Now, run the image through the BASEX program, and I get this inverted image:
BASEX inverts the image line by line, and so all the noise in the image is pushed inward, creating the blue center line. BASEX concurs that there is a dip in density. The center blue line and the extra red on the left and right sides are artifacts of the program.
Week 5: This week, with help from Brett, I wrote a Python code that takes user input of the number of rows and columns of a designated matrix and it performs an inverse abel transform on the inverted image from BASEX. The MOT contains a cylindrical symmetry. Because of this, one doesn't have to worry much about the z axis due to its symmetry throughout. Therefore, the main concern is summing up all of the pixels in polar coordinates around the middle origin. From an integral of sqrt(x^2+y^2) for all values of radius, one will obtain the deconvolution of the inverted image, i.e. the 2-D intensity plot derived from the 3-d density distribution.
This is Python’s deconstruction that I made.
Also, the program contains a subprogram that takes a fractional error between the deconvoluted image and the raw image from the camera. By subtracting the deconvoluted image plot counts from the raw image and dividing by the raw, it gives a matrix that plots the difference between the two programs so that I can see how accurate BASEX is inverting my images.
This is the error graph. It shows a -30% error in the blue area, about 35% error in the yellow, and about 2%-10% in the middle green.
Doesn't seem ideal.
Week 6: I made another Python program that takes the deconvoluted images made from the program I made last week and puts a running average of any value the user decides. One can input any odd number and the program will put a running average on the values in the matrix in order to smooth out the deconvoluted image. The thought was that this running average would produce a more accurate image that is more similar to the raw image. Its change was negligible.
I measured the spatial calibration of the camera to the MOT. As the camera was 7 cm from the viewing glass of the MOT, I took a picture of the MOT chamber without the laser on. Brett told me the distance between the plates in the chamber. With that knowledge, I measured the pixel distance and determined the spatial ratio is about 85 pixels per millimeter.
Week 7: Tested BASEX with fake matrices, and it proved useless to us.
This is the fake matrix. There is no symmetry between the quadrants.
This is the fake matrix after a run through BASEX. No boxes are checked in the program that would assign some symmetry to the image, yet there is some type of averaged superimposed symmetry from all four quadrants. These results are not good for an original image that is not symmetrical radially, horizontally, nor vertically.
Now I am trying to learn the Vrakking code in FORTRAN so that I can adapt it to my particular data. Vrakking is supposed to not assume any symmetry, is supposed to be better for unsymmetrical images, and suppose to have less error than other deconvoluting programs. It is also slower than other programs, but time is not an important issue to me. It only takes 25 seconds for the program to run, compared to BASEX's 12 second record.
I learned it well enough to run the program I got from De Sankar, a postdoc here. This edition of the Vrakking Iterative method works in a circular manner, whereas BASEX was line by line. This supposedly makes most of the error accumulate in the middle. Within the program it creates several files, one that makes a target image, what the program tries to iterate the image into, a simulated image, the actual 2-D deconvolution the program makes from the target image, an inverse image, the 3-D plot, and an error plot. These matrices are in cartesian coordinates, and the FORTRAN code also makes another set in polar coordinates. After looking at all of the files, especially the error files, I decided Vrakking was unsatisfactory.
This is the raw image again.
This is a slice of Vrakking’s inversion.
This is Vrakking’s deconstruction. After creating the deconstruction, Vrakking compares it to the raw and adjusts itself to improve its deconstruction so that it looks more like the raw. It repeats the inversion process over and over until the deconstruction is very close to the raw.
This is the error graph made from a Vrakking subprogram. This final deconstruction has an average error of less than 5%, which is good.
This week was temporal calibration between the laser and camera. In my setup, the laser first hits a diverging lens. Very far downstream along the laser, the diverged beam encounters an iris. As the beam's Gaussian shape is diverged, the iris serves to allow only the centermost part of the beam pass. This cuts off the maximum of the Gaussian shape and can be approximated as a flat plateau, in order to assume the same changes are being made to all affected pixels on the camera. After the iris, there is a neutral density filter of 3 (so it lets only a thousandth of the intensity of light through; this is so that the camera doesn't become saturated), and I measure the power with a power meter. After the attenuator, the camera is situated for prime viewing of the laser.
With this setup, I took several pictures. One set had a constant gain as I switched the shutter speed. The next set had constant shutter speed as I altered the gain. From each graph, I took the value of a certain pixel. I plotted each respective set with one axis being either gain or shutter speed and the other being the count value of the pixel. The shutter speed showed a linear graph in respect to count number. The gain graph showed an exponential curve with an offset. The graphing program provided me with these parameter values of the exponential curve.
The program that is used to take pictures also provides a total sum of the pixel counts in the picture. One pixel can range from 0 to 255. 255 is the extreme limit of intensity and the camera is most likely saturated if the counts are this high. With all of these values at my disposal, I could relate the sum of the pixel counts, gain value, and shutter speed value, to find a conversion factor and be able to predict the power of the laser. By knowing the power of the laser from this, the MOTRIMS group will be able to measure the intensity of light emitted by the MOT and predict the power that is emitted to the MOT. By relating power to the rate of photons per second, one may determine how many photons are being emitted by the MOT. Then, through another relationship of spontaneous emitted photons to stimulated emitted photons, one may calculate the amount of stimulated photons and the atomic density of the MOT. (The camera only sees spontaneous emission because the stimulated emission follows the path of the laser.)
I go more into detail on my powerpoint presentation and my poster.
I also measured the attenuation of the camera lens. It has an attenuation of .0813.