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ID Date Author Typedown Category Subject
  90   Tue Aug 17 16:31:55 2010 AidanThings to BuyLaserBought a laser diode from Thorlabs for HWS

http://www.thorlabs.com/thorProduct.cfm?partNumber=CPS180

I bought this laser diode from Thorlabs today to try the current modulation trick Phil and I discussed last Friday. 

That is:

  1. Accept that there will be interference fringes on the Hartmann sensor probe beam with a laser diode source (especially if the probe beam is the retro-reflection from a Michelson interferometer with a macroscopic arm length difference)
  2. Modulate the current of the laser diode source to vary its wavelength by a few hundreds on nm. Do this on a time scale that is much faster than the exposure time for a Hartmann sensor measurement
  3. The contrast of the interference fringes should average out and the exposure should appear to be the sum of two incoherent beams.

 

 

 

  93   Mon Aug 23 08:43:16 2010 AidanThings to BuyLaserBought a laser diode from Thorlabs for HWS

It arrived on Friday.

Quote:

http://www.thorlabs.com/thorProduct.cfm?partNumber=CPS180

I bought this laser diode from Thorlabs today to try the current modulation trick Phil and I discussed last Friday. 

That is:

  1. Accept that there will be interference fringes on the Hartmann sensor probe beam with a laser diode source (especially if the probe beam is the retro-reflection from a Michelson interferometer with a macroscopic arm length difference)
  2. Modulate the current of the laser diode source to vary its wavelength by a few hundreds on nm. Do this on a time scale that is much faster than the exposure time for a Hartmann sensor measurement
  3. The contrast of the interference fringes should average out and the exposure should appear to be the sum of two incoherent beams.

 

 

 

 

  106   Fri Feb 18 13:26:23 2011 AidanThings to BuyDelivery NoteFirst parts of Bosch framing have arrived from Valin

The first pieces of the Bosch framing have arrived from Valin Corporation. These are just small pieces such as the fasteners and the gussets. There are no custom lengths of framing yet.

The details are in the attached Packing List. [1:25PM] I haven't verified that everything is there yet.

 

Attachment 1: Packing_List_01.pdf
Packing_List_01.pdf Packing_List_01.pdf
  108   Wed Feb 23 18:04:38 2011 AidanThings to BuyDelivery NoteFirst parts of Bosch framing have arrived from Valin

Quote:

The first pieces of the Bosch framing have arrived from Valin Corporation. These are just small pieces such as the fasteners and the gussets. There are no custom lengths of framing yet.

The details are in the attached Packing List. [1:25PM] I haven't verified that everything is there yet.

 

 Another box of Bosch stuff arrived in my office. The packing list is attached

Attachment 1: Packing_List_02.pdf
Packing_List_02.pdf Packing_List_02.pdf
  111   Thu Feb 24 13:35:41 2011 AidanThings to BuyDelivery NoteBosch framing has arrived

 The custom pieces of the Bosch framing have arrived. Transportation is currently moving them downstairs to the lab. The packing list is attached.

 

 

Attachment 1: Packing_List_03.pdf
Packing_List_03.pdf Packing_List_03.pdf
  117   Tue Mar 1 11:19:34 2011 AidanThings to BuyDelivery NoteMFF001 flipper mirror has arrived

 The Thorlabs MFF001 flipper mirror recommended by Bram has arrived. The delivery note is attached.

Attachment 1: Flipper_mirror_delivery_notice.pdf
Flipper_mirror_delivery_notice.pdf
  118   Tue Mar 1 11:21:37 2011 AidanThings to BuyDelivery NoteMore Bosch framing parts - angle connectors

 Another box of Bosch framing parts arrived today. The delivery note is attached.

Attachment 1: Packing_List_04.pdf
Packing_List_04.pdf
  124   Tue Mar 8 18:57:50 2011 AidanThings to BuyDelivery NoteFiber optics cable and Bosch Fastener
Attachment 1: deliveries_2011-03-08.pdf
deliveries_2011-03-08.pdf deliveries_2011-03-08.pdf
  133   Mon Apr 4 13:13:23 2011 AidanThings to BuyDelivery NoteNewfocus 5102 mirrors and Firewire extension cable have arrived

 See attached delivery note ...

Attachment 1: receipt_mirrors.pdf
receipt_mirrors.pdf receipt_mirrors.pdf
  136   Sun Apr 17 14:59:36 2011 AidanThings to BuyDelivery NoteL-Com patch panel, Newport lenses, Thorlabs fibers delivery notes
Attachment 1: newport_lenses_2011-03.pdf
newport_lenses_2011-03.pdf
Attachment 2: L-Com_patch_panel_-_2011-03.pdf
L-Com_patch_panel_-_2011-03.pdf
Attachment 3: thorlabs_fiber_optic_cables_2011-03.pdf
thorlabs_fiber_optic_cables_2011-03.pdf thorlabs_fiber_optic_cables_2011-03.pdf
  139   Mon Apr 18 15:06:53 2011 AidanThings to BuyHartmann sensorOrdered 2" optics from Newport

 Given that the HWS requires several 2" optics to handle the big beam size, I've ordered the following items from Newport:

  • 2x 2" 50/50 beam splitter: 20B20BS.2
  • 6x 2" NIR mirrors: 5122
  • 8x 2" Ultima mirror mounts: U200-A2K
  232   Mon Jul 22 18:44:53 2019 Edita BytyqiThings to BuyGeneralNeed to Order Gloves

Small/Medium size gloves need to be ordered in order to handle the optics carefully.

  235   Thu Jul 25 09:13:36 2019 JonThings to BuyGeneralNeed to Order Gloves

New gloves are ordered for the TCS and QIL labs. They arrive tomorrow (Friday).

Quote:

Small/Medium size gloves need to be ordered in order to handle the optics carefully.

 

  9   Thu Feb 4 19:45:56 2010 AidanMiscRing HeaterRing heater transfer function - increasing collection area

I mounted the thinner Aluminium Watlow heater inside a 14" long, 1" inner diameter cylinder. The inner surface was lined with Aluminium foil to provide a very low emissivity surface and scatter a lot of radiation out of the end. ZEMAX simulations show this could increase the flux on a PD by 60-100x. 

There was 40V across the heater and around 0.21A being drawn. The #9005 HgCdTe photo-detector was placed at one end of the cylinder to measure the far-IR. (Bear in mind this is a 1mmx1mm detector in an open aperture of approximately 490 mm^2), The measured voltage difference between OFF and the steady-state ON solution, after a 5000x gain stage, was around 270mV. This corresponds to 0.054mV at the photo-diode. Using the responsivity of the PD ~= 0.05V/W then this corresponds to about 10mW incident on the PD.

 

Attachment 1: low-emissivity-tube.jpg
low-emissivity-tube.jpg
  44   Wed May 26 14:58:04 2010 AidanMiscHartmann sensorHartmann sensor cooling fins added

14:55 -  Mindy stopped by with the copper heater spreaders and the cooling fins for the Hartmann sensor. We've set them all up and have turned on the camera to see what temperature above ambient is achieves.

17:10 - Temperature of the HWS with no active cooling( Digitizer = 44.1C, Sensor = 36.0C, Ambient = 21.4C)

 

Attachment 1: HWS_CONFIG1.jpg
HWS_CONFIG1.jpg
  49   Tue Jun 15 16:30:10 2010 Peter VeitchMiscHartmann sensorSpot displacement maps - temperate sensitivity tests

Results of initial measurement of temperature sensitivity of Hartmann sensor

"Cold" images were taken at the following temperature:
| before | 32.3 | 45.3 | 37.0 |
| after  | 32.4 | 45.6 | 37.3 |

"Hot" Images were taken at the following temperature:

| before | 36.5 | 48.8 | 40.4 |
| after  | 36.4 | 48.8 | 40.4 |

"before" are the temperatures just before taking 5000 images, and "after" are
the temperatures just after taking the images. First column is the temperature
measured using the IR temp sensor pointed at the heat sink, the second column the
camera temperature, and the third column the sensor board temperature.

Temperature change produced by placing a "hat" over the top of the HP assembly and the top of the heatsinks.

Averaged images "cool" and "hot" were created using 200 frames (each).

Aberration parameter values are as follows:

Between cool and hot images (cool spots - hot spots)

     p: 4.504320557133363e-005
    al: 0.408248504544179
   phi: 0.444644135542724
     c: 0.001216006036395
     s: -0.002509569677737
     b: 0.054773177423349
    be: 0.794567342929695
     a: -1.030687344054648

Between cool images only

     p: 9.767143368103721e-007
    al: 0.453972584677992
   phi: -0.625590459774765
     c: 2.738206187344315e-004
     s: 1.235384158257808e-006
     b: 0.010135170457321
    be: 0.807948378729832
     a: 0.256508288049258

Between hot images only

     p: 3.352035441252169e-007
    al: -1.244075541477539
   phi: 0.275705676833192
     c: -1.810992355666772e-004
     s: 7.076678388064736e-005
     b: 0.003706221758158
    be: -0.573902879552339
     a: 0.042442307609231

Attached are two contour plots of the radial spot displacements, one between
cool and hot images, and the other between cool images only. The color
bars roughly indicate the values of maximum and minimum spot
displacements.

Possible causes:

1. anisotropy of the thermal expansion of the invar foil HP caused by the rolling

2. non-uniform clamping of the HP by the clamp plate

3. vertical thermal gradient produced by the temperature raising method

4. buckling of the HP due to slight damage (dent)

Attachment 1: spot_displacements_same_temp_0611.jpg
spot_displacements_same_temp_0611.jpg
Attachment 2: spot_displacements_diff_temp_0611.jpg
spot_displacements_diff_temp_0611.jpg
  50   Wed Jun 16 11:47:11 2010 AidanMiscHartmann sensorSpot displacement maps - temperate sensitivity tests - PRISM

I think that the second plot is just showing PRISM and converting it to its radial components. This is due to the fact that the sign of the spot displacement on the LHS is the opposite of the sign of the spot displacement on the RHS. For spherical or cylindrical power, the sign of the spot displacement should be the same on both the RHS and the LHS.

I've attached a Mathematica PDF that illustrates this.

 


Quote:

Results of initial measurement of temperature sensitivity of Hartmann sensor

"Cold" images were taken at the following temperature:
| before | 32.3 | 45.3 | 37.0 |
| after  | 32.4 | 45.6 | 37.3 |

"Hot" Images were taken at the following temperature:

| before | 36.5 | 48.8 | 40.4 |
| after  | 36.4 | 48.8 | 40.4 |

"before" are the temperatures just before taking 5000 images, and "after" are
the temperatures just after taking the images. First column is the temperature
measured using the IR temp sensor pointed at the heat sink, the second column the
camera temperature, and the third column the sensor board temperature.

Temperature change produced by placing a "hat" over the top of the HP assembly and the top of the heatsinks.

Averaged images "cool" and "hot" were created using 200 frames (each).

Aberration parameter values are as follows:

Between cool and hot images (cool spots - hot spots)

     p: 4.504320557133363e-005
    al: 0.408248504544179
   phi: 0.444644135542724
     c: 0.001216006036395
     s: -0.002509569677737
     b: 0.054773177423349
    be: 0.794567342929695
     a: -1.030687344054648

Between cool images only

     p: 9.767143368103721e-007
    al: 0.453972584677992
   phi: -0.625590459774765
     c: 2.738206187344315e-004
     s: 1.235384158257808e-006
     b: 0.010135170457321
    be: 0.807948378729832
     a: 0.256508288049258

Between hot images only

     p: 3.352035441252169e-007
    al: -1.244075541477539
   phi: 0.275705676833192
     c: -1.810992355666772e-004
     s: 7.076678388064736e-005
     b: 0.003706221758158
    be: -0.573902879552339
     a: 0.042442307609231

Attached are two contour plots of the radial spot displacements, one between
cool and hot images, and the other between cool images only. The color
bars roughly indicate the values of maximum and minimum spot
displacements.

Possible causes:

1. anisotropy of the thermal expansion of the invar foil HP caused by the rolling

2. non-uniform clamping of the HP by the clamp plate

3. vertical thermal gradient produced by the temperature raising method

4. buckling of the HP due to slight damage (dent)

 

Attachment 1: Prism_as_radial_vector.pdf
Prism_as_radial_vector.pdf Prism_as_radial_vector.pdf Prism_as_radial_vector.pdf
  51   Thu Jun 17 07:40:07 2010 James KMiscHartmann sensorSURF Log -- Day 1, Getting Started

 For Wednesday, June 16:

I attended the LIGO Orientation and first Introduction to LIGO lecture in the morning. In the afternoon, I ran a few errands (got keys to the office, got some Computer Use Policy Documentation done) and toured the lab. I then got Cygwin installed on my laptop along with the proper SSH packets and was successfully able to log in to and interact with the Hartmann computer in the lab through the terminal, from the office. I have started reading relevant portions of Dr. Brooks' thesis and of "Fundamentals of Interferometric Gravitational Wave Detectors" by Saulson.
  52   Thu Jun 17 22:03:51 2010 James KMiscHartmann sensorSURF Log -- Day 2, Getting Started

For Thursday, June 17:

Today I attended a basic laser safety training orientation, the second Introduction to LIGO lecture, a Summer Research Student Safety Orientation, and an Orientation for Non-Students living on campus (lots of mandatory meetings today). I met with Dr. Willems and Dr. Brooks in the morning and went over some background information regarding the project, then in the afternoon I got an idea of where I should progress from here from talking with Dr. Brooks. I read over the paper "Adaptive thermal compensation of test masses in advanced LIGO" and the LIGO TCS Preliminary Design document, and did some further reading in the Brooks thesis.

I'm making a little bit of progress with accessing the Hartmann lab computer with Xming but got stuck, and hopefully will be able to sort that out in the morning and progress to where I want to be (I wasn't able to get much further than that, since I can't access the Hartmann computer in the lab currently due to laser authorization restrictions). I'm currently able to remotely open an X terminal on the server but wasn't able to figure out how to then be able to log in to the Hartmann computer. I can do it via SSH on that terminal, of course, but am having the same access restrictions that I was getting when I was logging in to the Hartmann computer via SSH directly from my laptop (i.e. I can log in to the Hartmann computer just fine, and access the camera and framegrabber programs, but for the vast majority of the stuff on there, including MATLAB, I don't have permissions for some reason and just get 'access denied'). I'm sure that somebody who actually knows something about this stuff will be able to point out the problem and point me in the right direction fairly quickly (I've never used SSH or the X Window system before, which is why it's taking me quite a while to do this, but it's a great learning experience so far at least).

Goals for tomorrow: get that all sorted out and learn how to be able to fully access the Hartmann computer remotely and run MATLAB off of it. Familiarize myself with the camera program. Set the camera into test pattern mode and use the 'take' programs to retrieve images from it. Familiarize myself with the 'take' programs a bit and the various options and settings of them and other framegrabber programs. Get MATLAB running and use fread to import the image data arrays I take with the proper data representation (uint16 for each array entry). Then, set the camera back to recording actual images, take those images from the framegrabber and save them, then import them into MATLAB. I should familiarize myself with the various settings of the camera at this stage, as well.

 

--James

  53   Sat Jun 19 17:31:46 2010 James KMiscHartmann sensorSURF Log -- Day 3, Initial Image Analysis
For Friday, June 18:
(note that I haven't been working on this stuff all of Saturday or anything, despite posting it now. It was getting late on Friday evening so I opted to just type it up now, instead)

(all matlab files referenced can be found in /EDTpdv/JKmatlab unless otherwise noted)

I finally got Xming up and running on my laptop and had Dr. Brooks edit the permissions of the controls account, so now I can fully access the Hartmann computer remotely (run MATLAB, interact with the framegrabber programs, etc.). I was able to successfully adjust camera settings and take images using 'take', saving them as .raw files. I figured out how to import these .raws into MATLAB using fopen and display them as grayscale images using the Imshow command. I then wrote a program (readimgs.m, as attached) which takes inputs a base filename and number of images (n), then automatically loads the first 'n' .raw files located in /EDTpdv/JKimg/ with the inputted base file name, formatting them properly and saving them as a 1024x1024x(n) matrix.

After trying out the test pattern of the camera, I set the camera into normal operating mode. I took 200 images of the HWS illuminated by the OLED, using the following camera settings:

 
Temperature data from the camera was, unfortunately, not taken, though I now know how to take it.
 
The first of these 200 images is shown below:
 
hws0000.png

As a test exercise in MATLAB and also to analyze the stability of the HWS output, I wrote a series of functions to allow me to find and plot the means and standard deviations of the intensity of each pixel over a series of images. First, knowing that I would need it in following programs in order to use the plot functions on the data, I wrote "ar2vec.m" (as attached), which simply inputs an array and concatenates all of the columns into a single column vector.

Then, I wrote "stdvsmean.m" (as attached), which inputs a 3D array (such as the 1024x1024x(n) array of n image files), which first calculates the standard deviation and mean of this array along the 3rd dimension (leaving, for example, two 1024x1024 arrays, which give the mean and standard deviation of each pixel over the (n) images). It then uses ar2vec to create two column vectors, representing the mean and standard deviation of each pixel. It then plots a scatterplot of the standard deviation of each pixel vs. its mean intensity (with logarithmic axes), along with histograms of the mean intensities and standard deviation of intensities (with logarithmic y-axes).

"imgdevdat.m" (as attached) is simply a master function which combines the previous functions to input image files, format them, analyze them statistically and create plots.

Running this function for the first 20 images gave the following output:

(data from 20 images, over all 1024x1024 pixels)

Note that the background level is not subtracted out in this function, which is apparent from the plots. The logarithmic scatter plot looks pretty linear, as expected, but there are interesting features arising between the intensities of ~120 to ~130 (the obvious spike upward of standard deviation, followed immediately by a large dip downward).

MATLAB gets pretty bogged down trying to plot over a million data points at a time, to the point where it's very difficult to do anything with the plots. I therefore wrote the function "minimgstat.m" (as attached), which is very similar to imgdevdat.m except that before doing the analysis and plotting, it reduces the size of the image array to the upper-left NxN square (where N is an additional argument of the function).

Using this function, I did the same analysis of the upper-left 200x200 pixels over all 200 images:

(data from 200 images, over the upper-left 200x200 pixels)

The intensities of the pixels don't go as high this time because the upper portion of the images are dimmer than much of the rest of the image (as is apparent from looking at the image itself, and as I demonstrate further a little bit later on). Do note the change in axis scaling resulting from this when comparing the image. We do, however, see the same behavior in the ~120-128 intensity level region (more pronounced in this plot because of the change in axis scaling).

I was interested in looking at which pixels constituted this band, so I wrote a function "imgbandfind.m" (as attached), which inputs a 2D array and a minimum and maximum range value, goes through the image array pixel-by-pixel, determines which pixels are within the range, and then constructs an RGB image which displays pixels within the range as red and images outside the range as black.

I inputted the first image in the series into this function along with the range of 120-129, and got the following:

(pixels in intensity range of 120-129 in first image)

So the pixels in this range appear to be the pixels on the outskirts of each wavefront dot near the vertical center of the image. The outer circles of the dots on the lower and upper portions of the image do not appear, perhaps because the top of the image is dimmer and the bottom of the image is brighter, and thus these outskirt pixels would then have lower and higher values, respectively. I plan to investigate this and why it happens (what causes this 'flickering' and if it is a problem at all) further.

The fact that the background levels are lower nearer to the upper portion of the image is demonstrated in the next image, which shows all intensity levels less than 70:
(pixels in intensity range of 0-70 in first image)

So the background levels appear the be nonuniform across the CCD, as are the intensities of each dot. Again, I plan to investigate this further. (could it be something to do with stray light hitting the CCD nonuniformly, maybe? I haven't thought through all the possibilities)
 
The OLED has been turned off, so my next immediate step will be to investigate the background levels further by analyzing the images when not illuminated by the OLED.
 
In other news: today I also attended the third Intro to LIGO lecture, a talk on Artificial Neural Networks and their applications to automated classification of stellar spectra, and the 40m Journal Club on the birth rates of neutron stars (though I didn't think to learn how to access the wiki until a few hours right before, and then didn't actually read the paper. I fully intend to read the paper for next week before the meeting).
 
Attachment 2: ar2vec.m
function V = ar2vec(A)
%AR2VEC V=ar2vec(A)
%concenates the columns of 2D array A into a single column vector V

sz = size(A);
n=sz(1,2);
i=1;
V=[];

while i<(n+1)
... 7 more lines ...
Attachment 3: readimgs.m
function arr = readimgs(imn,n)
%readimgs('basefilename',n) 
%- A function to load a series of .raw files outputted by 'take'
%and stored in /opt/EDTpdv/JKimg/
%  Inputs: 'basefilename' is a string input (for example, for series of
%   images "testpat####.raw" input 'testpat'). "n" is the number of images,
%   so for testpat0000-testpat0004 input n=5

i=0;
arr=[];
... 32 more lines ...
Attachment 4: stdvsmean.m
function M = stdvsmean(A)
%STDVSMEAN takes a 3D array of image data and computes
%stdev vs. mean for each pixel

%find means/st devs between each image
astd = std(double(A),0,3);
armn = mean(double(A),3);

%convert into column vectors of pixel-by-pixel data
asvec=ar2vec(astd);
... 33 more lines ...
Attachment 5: imgdevdat.m
function imgdevdat(basefilename,imgnum)
%IMGDEVDAT Inputs base file name and number of images stored as .raw files
%in ../EDTpdv/JKimg/, automatically imports as 1024x1024x(n) matrix, finds
%the mean and standard deviation of each pixel in each image and plots
A=readimgs(basefilename,imgnum);
stdvsmean(A)
end

Attachment 6: minimgstat.m
function imgdevdat(basefilename,imgnum,size)
%IMGDEVDAT Inputs base file name and number of images stored as .raw files
%in ../EDTpdv/JKimg/, automatically imports as (size)x(size)x(n) matrix, finds
%the mean and standard deviation of each pixel in each image and plots
A=readimgs(basefilename,imgnum);
smA=A(1:size,1:size,:);
stdvsmean(smA)
end
Attachment 7: imgbandfind.m
function [HILT] = imgbandfind(img,minb,maxb)
%IMGBANDFIND inputs an image array and minimum and maximum value,
% then finds all values of the array within that range, then plots with
%values in range highlighted in red against a black background

img=double(img);
maxv=max(max(img));
sizm=size(img);
rows=sizm(1,1);
cols=sizm(1,2);
... 20 more lines ...
  54   Tue Jun 22 00:21:47 2010 James KMiscHartmann sensorSurf Log -- Day 4, Hartmann Spot Flickering Investigation

 I started out the day by taking some images from the CCD with the OLED switched off, to just look at the pattern when it's dark. The images looked like this:

 
Taken with camera settings:

The statistical analysis of them using the functions from Friday gave the following result:

 
At first glance, the distribution looks pretty Poissonian, as expected. There are a few scattered pixels registering a little brighter, but that's perhaps not so terribly unusual, given the relatively tiny spread of intensities with even the most extreme outliers. I won't say for certain whether or not there might be something unexpected at play, here, but I don't notice anything as unusual as the standard deviation 'spike' seen from intensities 120-129 as observed in the log from yesterday.
 
Speaking of that spike, the rest of the day was spent trying to investigate it a little more. In order to accomplish this, I wrote the following functions (all attached):
 
-spotfind.m -- inputs a 3D array of several Hartmann images as well as a starting pixel and threshold intensity level. analyzes the first image, scanning starting at the starting pixel until it finds a spot (with an edge determined by the threshold level), after which it finds a box of pixels which completely surrounds the spot and then shrinks the matrix down to this size, localizing the image to a single spot
 
-singspotcent.m -- inputs the image array outputted from spotfind, subtracts an estimate of the background, then uses the centroiding algorithm sum(x*P^2)/sum(P^2) to find the centroid (where x is the coordinate and P is the intensity level), then outputs the centroid location
 
-hemiadd.m -- inputs the image from spotfind and the centroid from singspotcent, subtracts an estimate of the background, then finds the sum total intensity in the top half of the image above the centroid, the bottom half, the left half and the right half, outputs these values as n-component vectors for an n-image input, subtracts from each vector its mean and then plots the deviations in intensity from the mean in each half of the image as a function of time
 
-edgeadd.m -- similar to hemiadd, except that rather than adding up all pixels on one half of the image, it inputs a threshold, determines how far to the right of the centroid that the spot falls past this treshold and uses it as a radial length, then finds the sum of the intensities of a bar of 3 pixels on this "edge" at the radial length away from the centroid.
 
-spotfft.m -- performs a fast fourier transform on the outputs from edgeadd, outputting the frequency spectrum at which the intensity of these edge pixels oscillate, then plotting these for each of the four edge vectors. see an example output below.
 
--halfspot_fluc.m and halfspot_edgefluc.m -- master functions which combine and automate the functions previous
 
Dr. Brooks has suggested that the observed flickering might perhaps be an effect resulting from the finite thickness of the Hartmann Plate. The OLED can be treated as a point source and thus can be approximated as emitting a spherical wavefront, and thus the light from it will hit this edge at an angle and be scattered onto the CCD. If the plate vibrates, then (which it certainly must to some degree) the wavefront will hit this edge at a different angle as the edge is displaced temporarily through vibration, and thus this light will hit the CCD at a different point, causing the flickering (which is, after all, observed to occur near the edge of the spot). This effect certainly must cause some level of noise, but whether it's the culprit for our 'flickering' spike in the standard deviation remains to be seen.

Here is the frequency spectrum of the edge intensity sums for two separate spots, found over 128 images:
Intensity Sum Amplitude Spectrum of Edge Fluctuations, 128 images, spot search point (100,110), threshold level 110

128 images, spot search point (100,100), threshold level 129
At first glance, I am not able to conclude anything from this data. I should investigate this further.

A few things to note, to myself and others:
--I still should construct a Bode plot from this data and see if I can deduce anything useful from it
--I should think about whether or not my algorithms are good for detecting what I want to look at. Is looking at a 3 pixel vertical or horizontal 'bar' on the edge good for determining what could possibly be a more spherical phenomenon? Are there any other things I need to consider? How will the settings of the camera affect these images and thus the results of these functions?
--Am I forgetting any of the subtleties of FFTs? I've confirmed that I am measuring the amplitude spectrum by looking at reference sine waves, but I should be careful since I haven't worked with these in a while
 
It's late (I haven't been working on this all night, but I haven't gotten the chance to type this up until now), so thoughts on this problem will continue tomorrow morning..

Attachment 1: spotfind.m
function [spotM,r0,c0] = spotfind(M,level,rs,cs)
%SPOTFIND Inputs a 3D array of hartmann spots and spot edge level
%and outputs a subarray located around a single spot located near (rs,cs)
cut=level/65535;
A=double(M(:,:,1)).*double(im2bw(M(:,:,1),cut));

%start at (rs,cs) and sweep to find spot
r=rs;
c=cs;
while A(r,c)==0
... 34 more lines ...
Attachment 2: singspotcent.m
function [rc,cc] = singspotcent(A)
%SINGSPOTCENT returns centroid location for first image in input 3D matrix
MB=double(A(:,:,1));
[rn cn]=size(MB);
M=MB-mean(mean(min(MB)));
r=1;
c=1;
sumIc=0;
sumIr=0;
while c<(cn+1)
... 26 more lines ...
Attachment 3: hemiadd.m
function [topsum,botsum,leftsum,ritsum] = hemiadd(MB,rcd,ccd)
%HEMIADD inputs a 3D image matrix and centroid location and finds the difference of
%the sums of the top half, bottom half, left half and right half at each time
%compared to their means over that time

%round coordinates of centroid
rc=round(rcd);
cc=round(ccd);

%subtract approximate background
... 51 more lines ...
Attachment 4: edgeadd.m
function [topsum,botsum,leftsum,ritsum] = edgeadd(MB,rcd,ccd,edgemax)
%HEMIADD inputs a 3D image matrix and centroid location and finds the difference of
%the sums of 3 edge pixels at radial distance "radial" from centroid for
%the top half, bottom half, left half and right half at each time
%compared to their means over that time

%round coordinates of centroid
rc=round(rcd);
cc=round(ccd);

... 59 more lines ...
Attachment 5: spotfft.m
function spotfft(t,b,l,r)
%SPOTFFT Does an fft and plots the frequency spectrum of four input vectors
%Specifically, this is to be used with halfspot_edgefluc to find the
%frequencies of oscillations about the edges of Hartmann spots
[n,m]=size(t);
NFFT=2^nextpow2(n);
T=fft(t,NFFT)/n;
B=fft(b,NFFT)/n;
L=fft(l,NFFT)/n;
R=fft(r,NFFT)/n;
... 30 more lines ...
Attachment 6: halfspot_fluc.m
function [top,bot,lft,rgt] = halfspot_fluc(M,spotr,spotc,thresh)
%HALFSPOT_FLUC Inputs a 3D array of Hartmann sensor images, along with an
%approximate spot location and intensity threshhold. Finds a spot on the
%first image near (spotc,spotr) and defines boundary of spot near an
%intensity of 'thresh'. Outputs fluctuations of the intensity sums of the
%top, bottom, left and right halves of the spot about their means, and
%graphs these against each other automatically.

[I,r0,c0]=spotfind(M,thresh,spotr,spotc);
[r,c]=singspotcent(I);
... 7 more lines ...
Attachment 7: halfspot_edgefluc.m
function [top,bot,lft,rgt] = halfspot_edgefluc(M,spotr,spotc,thresh,plot)
%HALFSPOT_FLUC Inputs a 3D array of Hartmann sensor images, along with an
%approximate spot location and intensity threshhold. Finds a spot on the
%first image near (spotc,spotr) and defines boundary of spot near an
%intensity of 'thresh'. Outputs fluctuations of the intensity sums of the
%top, bottom, left and right edges of the spot about their means, and
%graphs these against each other automatically.
%
%For 'plot', specify 'time' for the time signal or 'fft' for the frequency

... 10 more lines ...
  55   Tue Jun 22 22:30:24 2010 James KMiscHartmann sensorSURF Log -- Day 5, more Hartmann image preliminary analysis

 Today I spoke with Dr. Brooks and got a rough outline of what my experiment for the next few weeks will entail. I'll be getting more of the details and getting started a bit more, tomorrow, but today I had a more thorough look around the Hartmann lab and we set up a few things on the optical table. The OLED is now focused through a microscope to keep the beam from diverging quite as much before it hits the sensor, and the beam is roughly aligned to shine onto the Hartmann plate. The Hartmann images currently look like this (on a color scale of intensity):

hws.png

Where this image was taken with the camera set to exposure time 650 microseconds, frequency 58Hz. The visible 'streaks' on the image are believed to possibly be an artifact of the camera's data acquisition process.

I tested to see whether the same 'flickering' is present in images under this setup.

For frequency kept at 58Hz, the following statistics were found from a 200x200 pixel box within series of 10 images taken at different exposure times. Note that the range on the plot has been reduced to the region near the relevant feature, and that this range is not being changed from image to image:

750 microseconds:

750us.png

1000 microseconds:

1000us.png

1500 microseconds:

1500us.png

2000 microseconds:

2000us.png

3000 microseconds:

3000us.png

4000 microseconds:

4000us.png

5000 microseconds. Note that the background level is approaching the level of the feature:

5000us.png

6000 microseconds. Note that the axis setup is not restricted to the same region, and that the background level exceeds the level range of the feature. This demonstrates that the 'feature' disappears from the plot when the plot does not include the specific range of ~115-130:

8000us.png

 

When images containing the feature intensities are averaged over a greater number of images, the plot takes on the following appearance (for a 200x200 box within a series of 100 images, 3000us exposure time):

hws3k.png

This pattern changes a bit when averaged over more images. It looks as though this could, perhaps, just be the result of the decrease in the standard deviation of the standard deviations in each pixel resulting from the increased number of images being considered for each pixel (that is, the line being less 'spread out' in the y-axis direction). 

 

To demonstrate that frequency doesn't have any effect, I got the following plots from images where I set the camera to different frequencies then set the exposure time to 3000us (I wouldn't expect this to have any effect, given the previous images, but these appear to demonstrate that the 'feature' does not vary with time):

 

Set to 30Hz:

f30Hz.png

Set to 1Hz:

f1Hz.png

 

To make sure that something weird wasn't going on with my algorithm, I did the following: I constructed a 10-component vector of random numbers. Then, I concatenated that vector besides itself ten times. Then, I concatenated that vector into a 3D array by scaling the 2D vector with ten different integer multiples, ensuring that the standard deviations of each row would be integer multiples of each other when the standard deviation was found along the direction of the random change (I chose the integer multiples to ensure that some of these values would fall within the range of  115-130). Thus, if my function wasn't making any weird mistakes, I would end up with a linear plot of standard deviation vs. mean, with a slope of 1. When the array was inputted into the function with which the previous plots were found, the output plot was indeed observed to be linear, and a least squares regression of the mean/deviation data confirmed that the slope was exactly 1 and the intercept exactly 0. So I'm pretty certain that the feature observed in these plots is not any sort of 'artifact' of the algorithm used to analyze the data (and all the functions are pretty simple, so I wouldn't expect it to be, but it doesn't hurt to double-check).

 

I would conjecture from all of this that the observed feature in the plots is the result of some property of the CCD array or other element of the camera. It does not appear to have any dependence on exposure time or to scale with the relative overall intensity of the plots, and, rather, seems to depend on the actual digital number read out by the camera. This would suggest to me, at first glance, that the behavior is not the result of a physical process having to do with the wavefront.

 

EDIT: Some late-night conjecturing: Consider the following,

I don't know how the specific analog-to-digital conversion onboard the camera works, but I got to thinking about ADCs. I assume, perhaps incorrectly, that it works on roughly the same idea as the Flash ADCs that I dealt with back in my Digital Electronics class -- that is, I don't know if it has the same structure (a linear resistor ladder hooked up to comparators which compare the ladder voltages to the analog input, then uses some comb logic circuit which inputs the comparator outputs and outputs a digital level) but I assume that it must, at some level, be comparing the analog input to a number of different voltage thresholds, considering the highest 'threshold' that the analog input exceeds, then outputting the digital level corresponding to that particular threshold voltage.

Now, consider if there was a problem with such an ADC such that one of the threshold voltages was either unstable or otherwise different than the desired value (for a Flash ADC, perhaps this could result from a problem with the comparator connected to that threshold level, for example). Say, for example, that the threshold voltage corresponding to the 128th level was too low. In that case, an analog input voltage which should be placed into the 127th level could, perhaps, trip the comparator for the 128th level, and the digital output would read 128 even when the analog input should have corresponded to 127.

So if such an ADC was reading a voltage (with some noise) near that threshold, what would happen? Say that the analog voltage corresponded to 126 and had noise equivalent to one digital level. It should, then, give readings of 125, 126 or 127. However, if the voltage threshold for the 128th level was off, it would bounce between 125, 126, 127 and 128 -- that is, it would appear to have a larger standard deviation than the analog voltage actually possessed.

Similarly, consider an analog input voltage corresponding to 128 with noise equivalent to one digital level. It should read out 127, 128 and 129, but with the lower-than-desired threshold for 128 it would perhaps read out only 128 and 129 -- that is, the standard deviation of the digital signal would be lower for points just above 128.

This is very similar to the sort of behavior that we're seeing!

Thinking about this further, I reasoned that if this was what the ADC in the camera was doing, then if we looked in the image arrays for instances of the digital levels 127 and 128, we would see too few instances of 127 and too many instances of 128 -- several of the analog levels which should correspond to 127 would be 'misread' as 128. So I went back to MATLAB and wrote a function to look through a 1024x1024xN array of N images and, for every integer between an inputted minimum level and maximum level, find the number of instances of that level in the images. Inputting an array of 20 Hartmann sensor images, along with minimum and maximum levels of 50 and 200, gave the following:

levelinstances.png

Look at that huge spike at 128! This is more complex of behavior than my simple idea which would result in 127 having "too few" values and 128 having "too many", but to me, this seems consistent with the hypothesis that the voltage threshold for the 128th digital level is too low and is thus giving false output readings of 128, and is also reducing the number of correct outputs for values just below 128. And assuming that I'm thinking about the workings of the ADC correctly, this is consistent with an increase in the standard deviation in the digital level for values with a mean just below 128 and a lower standard deviation for values with a mean just above 128, which is what we observe.

 

This is my current hypothesis for why we're seeing that feature in the plots. Let me know what you think, and if that seems reasonable.

 

  56   Wed Jun 23 06:49:48 2010 AidanMiscHartmann sensorSURF Log -- Day 5, more Hartmann image preliminary analysis

Nice work!

 

Quote:

 Today I spoke with Dr. Brooks and got a rough outline of what my experiment for the next few weeks will entail. I'll be getting more of the details and getting started a bit more, tomorrow, but today I had a more thorough look around the Hartmann lab and we set up a few things on the optical table. The OLED is now focused through a microscope to keep the beam from diverging quite as much before it hits the sensor, and the beam is roughly aligned to shine onto the Hartmann plate. The Hartmann images currently look like this (on a color scale of intensity):

hws.png

Where this image was taken with the camera set to exposure time 650 microseconds, frequency 58Hz. The visible 'streaks' on the image are believed to possibly be an artifact of the camera's data acquisition process.

I tested to see whether the same 'flickering' is present in images under this setup.

For frequency kept at 58Hz, the following statistics were found from a 200x200 pixel box within series of 10 images taken at different exposure times. Note that the range on the plot has been reduced to the region near the relevant feature, and that this range is not being changed from image to image:

750 microseconds:

750us.png

1000 microseconds:

1000us.png

1500 microseconds:

1500us.png

2000 microseconds:

2000us.png

3000 microseconds:

3000us.png

4000 microseconds:

4000us.png

5000 microseconds. Note that the background level is approaching the level of the feature:

5000us.png

6000 microseconds. Note that the axis setup is not restricted to the same region, and that the background level exceeds the level range of the feature. This demonstrates that the 'feature' disappears from the plot when the plot does not include the specific range of ~115-130:

8000us.png

 

When images containing the feature intensities are averaged over a greater number of images, the plot takes on the following appearance (for a 200x200 box within a series of 100 images, 3000us exposure time):

hws3k.png

This pattern changes a bit when averaged over more images. It looks as though this could, perhaps, just be the result of the decrease in the standard deviation of the standard deviations in each pixel resulting from the increased number of images being considered for each pixel (that is, the line being less 'spread out' in the y-axis direction). 

 

To demonstrate that frequency doesn't have any effect, I got the following plots from images where I set the camera to different frequencies then set the exposure time to 3000us (I wouldn't expect this to have any effect, given the previous images, but these appear to demonstrate that the 'feature' does not vary with time):

 

Set to 30Hz:

f30Hz.png

Set to 1Hz:

f1Hz.png

 

To make sure that something weird wasn't going on with my algorithm, I did the following: I constructed a 10-component vector of random numbers. Then, I concatenated that vector besides itself ten times. Then, I concatenated that vector into a 3D array by scaling the 2D vector with ten different integer multiples, ensuring that the standard deviations of each row would be integer multiples of each other when the standard deviation was found along the direction of the random change (I chose the integer multiples to ensure that some of these values would fall within the range of  115-130). Thus, if my function wasn't making any weird mistakes, I would end up with a linear plot of standard deviation vs. mean, with a slope of 1. When the array was inputted into the function with which the previous plots were found, the output plot was indeed observed to be linear, and a least squares regression of the mean/deviation data confirmed that the slope was exactly 1 and the intercept exactly 0. So I'm pretty certain that the feature observed in these plots is not any sort of 'artifact' of the algorithm used to analyze the data (and all the functions are pretty simple, so I wouldn't expect it to be, but it doesn't hurt to double-check).

 

I would conjecture from all of this that the observed feature in the plots is the result of some property of the CCD array or other element of the camera. It does not appear to have any dependence on exposure time or to scale with the relative overall intensity of the plots, and, rather, seems to depend on the actual digital number read out by the camera. This would suggest to me, at first glance, that the behavior is not the result of a physical process having to do with the wavefront.

 

EDIT: Some late-night conjecturing: Consider the following,

I don't know how the specific analog-to-digital conversion onboard the camera works, but I got to thinking about ADCs. I assume, perhaps incorrectly, that it works on roughly the same idea as the Flash ADCs that I dealt with back in my Digital Electronics class -- that is, I don't know if it has the same structure (a linear resistor ladder hooked up to comparators which compare the ladder voltages to the analog input, then uses some comb logic circuit which inputs the comparator outputs and outputs a digital level) but I assume that it must, at some level, be comparing the analog input to a number of different voltage thresholds, considering the highest 'threshold' that the analog input exceeds, then outputting the digital level corresponding to that particular threshold voltage.

Now, consider if there was a problem with such an ADC such that one of the threshold voltages was either unstable or otherwise different than the desired value (for a Flash ADC, perhaps this could result from a problem with the comparator connected to that threshold level, for example). Say, for example, that the threshold voltage corresponding to the 128th level was too low. In that case, an analog input voltage which should be placed into the 127th level could, perhaps, trip the comparator for the 128th level, and the digital output would read 128 even when the analog input should have corresponded to 127.

So if such an ADC was reading a voltage (with some noise) near that threshold, what would happen? Say that the analog voltage corresponded to 126 and had noise equivalent to one digital level. It should, then, give readings of 125, 126 or 127. However, if the voltage threshold for the 128th level was off, it would bounce between 125, 126, 127 and 128 -- that is, it would appear to have a larger standard deviation than the analog voltage actually possessed.

Similarly, consider an analog input voltage corresponding to 128 with noise equivalent to one digital level. It should read out 127, 128 and 129, but with the lower-than-desired threshold for 128 it would perhaps read out only 128 and 129 -- that is, the standard deviation of the digital signal would be lower for points just above 128.

This is very similar to the sort of behavior that we're seeing!

Thinking about this further, I reasoned that if this was what the ADC in the camera was doing, then if we looked in the image arrays for instances of the digital levels 127 and 128, we would see too few instances of 127 and too many instances of 128 -- several of the analog levels which should correspond to 127 would be 'misread' as 128. So I went back to MATLAB and wrote a function to look through a 1024x1024xN array of N images and, for every integer between an inputted minimum level and maximum level, find the number of instances of that level in the images. Inputting an array of 20 Hartmann sensor images, along with minimum and maximum levels of 50 and 200, gave the following:

levelinstances.png

Look at that huge spike at 128! This is more complex of behavior than my simple idea which would result in 127 having "too few" values and 128 having "too many", but to me, this seems consistent with the hypothesis that the voltage threshold for the 128th digital level is too low and is thus giving false output readings of 128, and is also reducing the number of correct outputs for values just below 128. And assuming that I'm thinking about the workings of the ADC correctly, this is consistent with an increase in the standard deviation in the digital level for values with a mean just below 128 and a lower standard deviation for values with a mean just above 128, which is what we observe.

 

This is my current hypothesis for why we're seeing that feature in the plots. Let me know what you think, and if that seems reasonable.

 

 

  57   Wed Jun 23 22:57:22 2010 James KMiscHartmann sensorSURF Log -- Day 6, Centroiding

 So in addition to taking steps towards starting to set stuff up for the experiment in the lab, I spent a good deal of the day figuring out how to use the pre-existing code for finding the centroids in spot images. I spent quite a bit of time trying to use an outdated version of the code that didn't work for the actual captured images, and then once I was directed towards the right version I was hindered for a little while by a bug.

The 'bug' turns out to be something very simple, yet relatively subtle. In the function centroid_images.m in '/opt/EDTpdv/hartmann/src/', the function was assuming a threshold of 0 with my images, even though it has not long before been working with an image that Dr. Brooks loaded. Looking through the code, I noticed that before finding the threshold using the MATLAB function graythresh, several adjustments were made so as to subtract out the background and normalize the array. After estimating and subtracting a background, the function divides the entries of the image array by the maximum value in the image so as to normalize this. For arrays composed of numbers represented as doubles, this is fine. However, the function that I wrote to import my image arrays into MATLAB outputs an image array with integer data. So when the function divided my integer image arrays by the maximum values in the array, it rounded every value in the array to the nearest integer -- that is, the "normalized" array only contained ones and zeros. The function graythresh views this as a black and white image, and thus outputs a threshold of 0.

To remedy this, I edited centroid_images.m to convert the image array into an array of doubles near the very beginning of the function. The only new line is simply "image=double(image);", and I made a note of my edit in a comment above that line. The function started working for me after I did that.

 

I then wrote a function which automatically centroids an input image and then plots the centroids as scatter-plot of red circles over the image. For an image taken off of the Hartmann camera, it gave the following:

centroidplot_nozoom.png

Zoomed in on the higher-intensity peaks, the centroids look good. They're a little offset, but that could just be an artifact of the plotting procedure; I can't say for certain either way. They all appear offset by the same amount, though:

centroidplot_zoom.png

One problem is that, for spots with a much lower relative intensity than the maximum intensity peak, the centroid appears to be offset:

centroidplot_zoom2.png

Better centering of the beam and more even illumination of the Hartmann plate could mitigate this problem, perhaps.

 

I also wrote a function which inputs two image matrices and outputs vector field plots representing the shift in each centroid from the first to the second images. To demonstrate that I could use this function to display the shifting of the centroids from a change in the wavefront, I translated the fiber mount of the SLED in the direction of the optical axis by about 6 turns of the z-control knob  (corresponding to a translation of about 1.9mm, according to the user's guide for the fiber aligner). This gave the following images:

 

Before the translation:

6turn_before.png

After:

6turn_after.png

 This led to a displacement of the centroids shown as follows:

6turnDisplacementVectors.png

Note that the magnitudes of the actual displacements are small, making the shift difficult to see. However, when we scale the displacement vectors up, we can get much more readily visible Direction vectors (having the same direction as the actual displacement vectors, but not the same magnitude):

6turnDirectionVectors.png

This was a very rough sort of measurement, since exposure time, focus of the microscope optic, etc. were not adjusted, and the centroids are compared between single images rather than composite images, meaning that random noise could have quite an effect, especially for the lower-magnitude displacements. However, this plot appears to show the centroids 'spreading out', which is as expected for moving the SLED closer to the sensor along the optical axis.

 

The following MATLAB functions were written for this (both attached):

centroidplot.m -- calls centroid_image and plots the data

centroidcompare.m -- calls centroid_image twice for two inputs matrices, using the first matrix's centroid output structure as a reference for the second. Does a vector field plot from the displacements and reference positions in the second output centroids structure.

Attachment 5: 6turn_before.png
6turn_before.png
Attachment 9: centroidplot.m
function centroiddata=centroidplot(M,N)
%a function to read the image matrix M and plot the centroids of each plot
%on the image
H=M(:,:,N);
cd /opt/EDTpdv/hartmann/src/
centroiddata = centroid_image(H);
cd /opt/EDTpdv/JKmatlab/

v=centroiddata.current_centroids;
r=v(:,1);
... 6 more lines ...
Attachment 10: centroidcompare.m
function centroiddata=centroidcompare(A,B,M,N)
%compares the Mth image in 3D image matrix A to Nth in B
H=A(:,:,M);
I=B(:,:,N);
cd /opt/EDTpdv/hartmann/src/
cent0=centroid_image(H);
centroiddata=centroid_image(I,cent0);
cd /opt/EDTpdv/JKmatlab
v=centroiddata.reference_centroids;
dv=centroiddata.displacement_of_centroids;
... 16 more lines ...
  58   Fri Jun 25 00:11:13 2010 James KMiscHartmann sensorSURF Log -- Day 7, SLED Beam Characterization

BACKGROUND:


In order to conduct future optical experiments with the SLED and to be able to predict the behavior of the beam as it propagates across the table and through various optics, it is necessary to know the properties of the beam. The spot size, divergence angle, and radius of curvature are all of interest if we wish to be able to predict the pattern which should appear on the Hartmann sensor given a certain optical layout.

It was therefore necessary to conduct an experiment to measure these properties. The wavefront emanating from the SLED is assumed to be approximately Gaussian, and thus has an intensity of the form:

 

where A is some amplitude, w is the spot size, x and y are the coordinates transverse to the optical axis, and x0 is the displacement of the optical axis in the x-direction from the optical axis. The displacement of the optical axis in the y-direction is assumed to be zero (that is, y0=0). A and w are both functions of z, which is the coordinate of displacement parallel to the optical axis.

 

Notice that the total intensity read by a photodetector reading the entire beam would be the double integral from negative infinity to infinity for both x and y. If a opaque plate was placed such that the the beam was blocked from some x=xm to x=inf (where xm is the location of the edge of the plate), then the intensity read by a photodetector reading the entire non-blocked portion of the beam would be:

 

Mathematica was used to simplify this integral, and it showed it to be equivalent to:

where Erfc() is the complementary error function. Note that for fixed z, this intensity is a function only of xm. If an experiment was carried out to measure the intensity of the beam blocked by a plate from x=-inf to x=xm for multiple values of xm, it would therefore be possible via regression analysis to compute the best-fit values of A, w, and x0 for the measured values of Ipd and xm. This would give us A, w and x0 for that z-value. By repeating this process for multiple values of z, we could therefore find the behavior of these parameters as a function of z.

Furthermore, we know that at z-values well beyond the Rayleigh range, w should be linear with respect to z. Assuming that our measurements are done in the far-field (which, for the SLED, they almost certainly would be) we could therefore find the divergence angle by knowing the slope of the linear relation between w and z. Knowing this, we could further calculate such quantities as the Rayleigh range, the minimum spot size, and the radius of curvature of the SLED output (see p.490 of "Lasers" by Milonni and Eberly for the relevant functional relationships for Gaussian beams).


EXPERIMENT:

An experiment was therefore carried out to measure the intensity of of beam blocked from x~=-inf to x=xm, for multiple values of xm, for multiple values of z. A diagram of the optical layout of the experiment is below:

 

(top view)


The razor blade was mounted on a New Focus 9091 Translational Stage, the relative displacement of which in the x-direction was measured with the Vernier micrometer mounted on the base. Tape was placed on the front of the razor so as to block light from passing through any of its holes. The portion of the beam not blocked by the razor then passed through a lens which was used to focus the beam back onto a PDA1001A Large Area Silicon Photodiode, the voltage output of which was monitored using a Fluke digital multimeter. The ruler stayed securely clamped onto the optical table (except when it was translated in the x-direction once during the experiment, as described later).

The following is a picture of this layout, as constructed:

 

 
The procedure of the experiment was as follows: first, the translational stage was clamped securely with the left-most edge of its base lined up with the desired z-value as measured on the ruler. The z-value as measured on the ruler was recorded. Then, the translational stage was moved in the negative x-direction until there was no change in the voltage measured on the DMM (which is directly proportional to the measured intensity of the beam). When no further DMM readout change was yielded from -x translation, it was assumed that the the razor was no longer blocking the beam. Then, the stage was moved in the +x direction until the voltage output on the DMM just began to change. The micrometer and DMM values were both recorded. The stage was then moved inward until the DMM read a voltage which was close to the nearest multiple of 0.5V, and this DMM voltage and micrometer reading were recorded. The stage was then translated until the DMM voltage dropped by approximately 0.5V, the micrometer and DMM readings were recorded, and this process was repeated until the voltage reached ~0.5V. The beam output was then covered by a card so as to completely block it, and the voltage output from the DMM was recorded as the intensity from the ambient light from that measurement. The stage was then unclamped and moved to the next z-value, and this process was repeated for 26 different values of z, starting at z=36.5mm and then incrementing z upwards by ~4mm for the first ten measurements, then by increments of ~6mm for the remaining measurements.
 
The data from these measurements can be found on the attached spreadsheet.
 
A few notes on the experiment:
 
The vernier micrometer has a measurement limit of 13.5mm. After the tenth measurement, the measured xm values began to exceed this limit. It was therefore necessary to translate the ruler in the negative x-direction without translating it in the z-direction. Plates were clamped snugly to either side of the ruler such that the ruler could not be translated in the z-direction, but could be moved in the x-direction when the ruler was unclamped. After securing these plates, the ruler was moved in the negative x-direction by approximately 5mm. The ruler was then clamped securely in place at its new x location. In order to better estimate the actual x-translation of the ruler, I took the following series of measurements: I moved the stage to z-values at which sets of measurements were previously taken. Then, I moved the razor out of the beam path and carefully moved it back inwards until the output on the DMM matched exactly the DMM output of the first measurement taken previously at that z-value. The xm value corresponding to this voltage was then read. The translation of the stage should be approximately equal to the difference of the measured xm values for that DMM voltage output at that z-value. This was done for 8 z-values, and the average difference was found to be 4.57+-0.03mm, which should also be the distance of stage translation (this data and calculation is included in the "x translation" sheet of the attached excel workbook).
 
At this same point, I started using two clamps to attach the translational stage to the table for each measurement set, as I was unhappy with the level of secureness which one clamp provided. I do not, however, believe that the use of one clamp compromised the quality of previous sets of measurements.

 

RESULTS:


A MATLAB function 'gsbeam.m' was written to replicate the function:

and then another function 'beamdata.m' was written to input each dataset, fit the data to a curve of the functional form of the previous function for each set of data automatically, and then output PDF files plotting all of the fit curves against each other, each individual fit curve against the data from that measurement, and a plot showing the widths w as a function of z. Linear regression was done on w against z to find the slope of the w(z) (which, for these measurements, is clearly shown by the plot that the beam was measured in the far-field and thus w is approximately a linear function of z). An array of the z-location of the ruler, the fit parameters A, x0, x, and the 2-norm of the residual of the fit is also outputted, and is shown below for the experimental data:

 

z(ruler) A x0 w 2normres
36.5 7.5915 11.089 0.8741 0.1042
39.9 5.2604 11.1246 1.048 0.1013
44 3.8075 11.1561 1.2332 0.1164
48 2.777 11.1628 1.4479 0.0964
52 2.1457 11.1363 1.6482 0.1008
56 1.6872 11.4206 1.858 0.1029
60 1.3831 11.2469 2.0523 0.1021
64 1.1564 11.1997 2.2432 0.1059
68 0.972 11.1851 2.4483 0.0976
72 0.8356 11.1728 2.6392 0.1046
78 0.67 6.8821 2.9463 0.0991
84 0.5559 6.7548 3.2375 0.1036
90 0.4647 6.715 3.5402 0.0958
96 0.3993 6.7003 3.8158 0.1179
112 0.2719 6.8372 4.6292 0.0924
118 0.2398 6.7641 4.925 0.1029
124 0.2117 6.7674 5.2435 0.1002
130 0.189 6.8305 5.5513 0.0965
136 0.1709 6.8551 5.8383 0.1028
142 0.1544 6.8243 6.1412 0.0981
148 0.1408 6.7993 6.4313 0.099
154 0.1286 6.8062 6.7322 0.0948
160 0.1178 6.9059 7.0362 0.1009
166 0.1089 6.904 7.3178 0.0981
172 0.1001 6.8817 7.6333 0.1025
178 0.0998 6.711 7.6333 0

 

All outputted PDF's are included in the .zip file attached. The MATLAB functions themselves are also attached.The plots of the fit curves and the plot of the widths vs. the ruler location are also included below:

 

(note that I could probably improve on the colormap that I chose for this. note also that the 'gap' is because I temporarily forgot how to add integers while taking the measurements, and thus went from 96mm on the ruler to 112mm on the ruler despite going by a 6mm increment otherwise in that range. Also, note that all of these fit curves were automatically centered at x=0 for the plot, so they wouldn't necessarily intersect so neatly if I tried to include the difference in the estimated 'beam centers')

(note that the width calculated from the 26th measurement is not included in the regression calculation or included on this plot. The width parameter was calculated as being exactly the same as it was for the 25th measurement, despite the other parameters varying between the measurements. I suspect that the beam size was starting to exceed the dimensions blocked by the razor and that this caused this problem, and that would be easy to check, but I have yet to do it. Regardless, the fit looks good from just the other 25 measurements)

These results are as expected: that the beam spot-size should increase as a function of z and that it should do so linearly in the far-field. My next step will be to use the results of this experiment to calculate the properties of the SLED beam, characterizing the beam and thusly enabling me to predict its behavior within further optical systems.

 

Attachment 1: BeamData.xlsx
Attachment 2: beam_pdfs.zip
Attachment 3: beamdata.m
function D=beamdata(M,guess)
%Imports array of beam characterization measurements. Structure of M is 
% [z, x, I, a] where z is the displacement of the beam blockage along
% the optical axis, x is the coordinate of razor edge, I is the measured
% output of the photodetector and a is the ambient light level
%and guess is an estimate of the parameters [Amplitude x0 width] for the
%first measurement
%Output Structure [z A x0 w residual_2norm]
thisfile=mfilename('fullpath');
thisdir=strrep(thisfile,mfilename(),'');
... 105 more lines ...
Attachment 4: gsbeam.m
function I=gsbeam(x,xdat)
I=pi/4*x(1)*x(3)^2*erfc(sqrt(2)*(x(2)-xdat)/x(3));
end
  59   Fri Jun 25 10:47:08 2010 AidanMiscaLIGO ModelingUploaded aLIGO axicon+ITM COMSOL model to the 40m SVN

I added a COMSOL model of the aLIGO ITM being heated by an axicon-formed annulus to the 40m SVN. The model assumes a fixed input beam size into an axicon pair and then varies the distance between the axicons. The output is imaged onto the ITM with varying magnitudes. The thermal lens is determined in the ITM and added  to the self-heating thermal lens (assuming 1W absorption, I think - need to check). The power in the annulus is varied until the sum of the two thermal lenses scatters the least amount of power out of the TEM00 mode of the IFO.

https://nodus.ligo.caltech.edu:30889/svn/trunk/comsol/TCS/aLIGO/

The results across the parameter space (axicon separation and post-axicon-magnification) are attached. These were then mapped from this space to the space of annulus thickness vs annulus diameter, (see elog here).

 

 

Attachment 1: aLIGO_axicon_spacing_post-magnification_optimization.jpg
aLIGO_axicon_spacing_post-magnification_optimization.jpg
  60   Fri Jun 25 10:59:43 2010 AidanMiscaLIGO ModelingUploaded aLIGO axicon+ITM COMSOL model to the 40m SVN

Here are the results in the annulus thickness vs annulus diameter space ...

Quote:

I added a COMSOL model of the aLIGO ITM being heated by an axicon-formed annulus to the 40m SVN. The model assumes a fixed input beam size into an axicon pair and then varies the distance between the axicons. The output is imaged onto the ITM with varying magnitudes. The thermal lens is determined in the ITM and added  to the self-heating thermal lens (assuming 1W absorption, I think - need to check). The power in the annulus is varied until the sum of the two thermal lenses scatters the least amount of power out of the TEM00 mode of the IFO.

https://nodus.ligo.caltech.edu:30889/svn/trunk/comsol/TCS/aLIGO/

The results across the parameter space (axicon separation and post-axicon-magnification) are attached. These were then mapped from this space to the space of annulus thickness vs annulus diameter, also attached.

 

 

 

Attachment 1: Screen_shot_2010-06-25_at_11.01.38_AM.png
Screen_shot_2010-06-25_at_11.01.38_AM.png
  62   Thu Jul 1 09:40:13 2010 James KunertMiscHartmann sensorSURF Log 8 -- more SLED characterization

As I started setting up my next experiment, I noticed that the beam size from the SLED appeared to be larger than expected from previous analysis. It was therefore necessary to conduct further experiments to characterize the divergence angle of the beam.

First, I set up the photodetector attached to an SLED and mounted a razor blade on a translational stage, in the same manner as done previously. All of these components were the exact same ones used in the previous beam size experiment. The only differences in the components of the apparatus were as follows: first, the photodetector was placed considerably closer to the SLED source than was done previously. Second, a different lens was used to focus the light onto the photodetector. Lens LX082 from the lenskit was used, which is a one-inch lens of focal length f=50.20mm.

Experiment 1: Columnated Beam Size Measurement

Before repeating the previous experiment, the following experiment was done: the beam was columnated by placing the lens 50.20mm away from the source and then adjusting until columnation was observed. Columnation was confirmed by setting a mirror in the optical path of the beam directing it to the other side of the room. The position of the lens along the optical axis was adjusted until the beam exiting the lens did not change in size across the length of the table and appeared to be roughly the same size as the spot on the opposite side of the room (as gauged roughly by the apparent size on an IR card and through an IR viewer).

Then,the translational stage onto with the laser was mounted was placed after the lens against the ruler clamped to the table, and beam size was measured using the same experimental procedure used to find the width in the previous experiment. The only variation in the experimental procedure was that measurements were not taken strictly at 0.5V intervals; rather, intensity readings were taken for 28 different intensity outputs. The following measurements were collected:


x(mm)   V(V)
13.00  7.25
12.00  7.24
10.80   7.18
10.15   7.09
9.50   6.92
9.30   6.86
9.00   6.74
8.75   6.61
8.50   6.47
8.25   6.31
8.00   6.12
7.75   5.92
7.50   5.69
7.30   5.49
7.15   5.33
7.00   5.17
6.75   4.88
6.50   4.58
6.25   4.27
6.00   3.95
5.75   3.63
5.50   3.32
5.25   3.02
5.00   2.729
4.60   2.306
4.50   2.205
4.25   1.981
4.00 1.770
ambient 0.585

When fit to gsbeam.m using lsqcurvefit, this yielded a width of 4.232mm. Since the beam is columnated through the lens, we know that it is approximately f=50.2mm from the source. Thus the divergence angle is approximately 0.084.

At this point, to double-check that the discrepency between this value and the previous experiment was not a result of a mistake in the function, I wrote a simpler function to go through the steps of using lsqcurvefit and plotting the fit curve versus the data automatically, 'manualbeam.m' (attached), which simply fits a curve to one set of data from a constant z-value. Using this one-by-one on each z-value in the previous experiment, it was shown that the slope of the widths was still ~0.05, so this discrepency was not the result of a mistake in the previous function somewhere.

Experiment 2: Blocked Beam Analysis 2

I then placed the razor before the lens in the beampath and repeated the previous experiment exactly. See the previous eLog for details on experimental procedure. Sets of measurements were taken at 6 different z-values, and widths were found using manualbeam.m in MATLAB. A curve of the calculated widths versus the z-position of the stage on the ruler is below:

BeamSpot_Exp3.tif

Note that this appears to be consistant with the first experiment.

Experiment 3: Direct Beam Measurements on CCD

The front-plate of the Hartmann sensor was replaced with the new invar design (on a related note, the thread on the front plate needs a larger chamfer). In doing this, the Hartmann plate was removed. The sensor was moved much closer to the SLED along the optical axis, and an optical filter of OD 0.7 was screwed into the new frontplate. This setup allows for the direct imaging of the intensity of the beam, as shown below:

directbeam.PNG

The spots and distortions on the image are from dust and other blemishes on the optical filter, as was confirmed by rotating the filter and observing the subsequent rotation of each feature.

Note that in some images, there may be a jump in intensity in the middle of the image. This is believed to be due to a inconsistant gain between the two sides of the image.

The means of the intensities of each row and each column will be Gaussian, and thus can be fit to a Gaussian using lsqcurvefit. Function 'gauss_beam1D.m' was written and this function was fit to using function 'autogaussfit1', which automatically imports the data from .raw files, fits Gaussians to the means of each row and column, and plots everything.

An example of the fit for the means of the columns of one image is as follows:

beamfit100mm.PNG

 And for the rows:

beamfit100mmRows.PNG

Note that for all the fits, the fitting generally looks a little better along the row than along the column (which is true here, as well).

The following procedure was used to calculate the change of the beam width as a function of distance: the left edge of the base of the Hartmann sensor was measured against a ruler which was clamped to the table. The ruler position z was recorded. Then, preliminary images would be taken and the exposure time would be adjusted as needed. The exposure time was then noted. Then, an image was taken and curves were fit to it, and the width was calculated. This was done for 15 different positions of the Hartmann sensor along the optical axis.

The calculated widths vs. displacements plot from this can be seen below:

DirectBeams1.tif

Note that the row width and column width are not the same, implying that the beam is not circularly symmetric and is thusly probably off alignment by a little bit. Also, the calculated slopes are different than the value of 0.085 acquired from the previous two measurements. Further investigation into the beam size and divergence angle is required to finally put this question to rest.

Attachment 6: manualbeam.m
function x=manualbeam(M,guess)
    x=lsqcurvefit(@gsbeam,guess,M(:,2),M(:,3)-M(:,4));
    figure
    hold
    grid on
    xlabel('Stage Translation (mm)')
    ylabel('Photodetector Output (V)')
    text(0.8,0.2,['A = ' num2str(x(1))],'FontSize',12,'Interpreter','none','Units','normalized');
    text(0.8,0.15,['x0 = ' num2str(x(2))],'FontSize',12,'Interpreter','none','Units','normalized');
    text(0.8,0.1,['w = ' num2str(x(3))],'FontSize',12,'Interpreter','none','Units','normalized');
... 7 more lines ...
Attachment 7: gauss_beam1D.m
function result = gauss_beam1D(x0, xdata)
% x0(1) = offset
% x0(2) = amplitude
% x0(3) = x centroid location
% x0(4) = x width

result = x0(1) + x0(2).*exp(-2.0.*( ...
                           ((xdata - x0(3)).^2)/(x0(4).^2)));
                       
Attachment 8: autogaussfit1.m
function [x y wx wy]=autogaussfit1(imgname,guess,imgdetails)
%guess = [offset amplitude centroidlocation width]
%imgdetails = [HWSrulerlocation exp.time]
%output vectors same format as guess
thisfile=mfilename('fullpath');
thisdir=strrep(thisfile,mfilename(),'');

rulerz = imgdetails(1,1);
exposure = imgdetails(1,2);

... 56 more lines ...
  64   Tue Jul 6 21:57:19 2010 James KunertMiscHartmann sensorSURF Log -- SLED fiber output temporal analysis

In the previous log, I describe the direct measurement of the fiber output beam using the Hartmann sensor with the plate removed. In order to analyze how these properties might change as a function of time, we left the camera running over the holiday weekend, Dr. Brooks having written a bash script which took images from the sensor every 500 seconds. This morning I wrote a MATLAB script to automatically analyze all of these images and plot the fit parameters as a function of time (weekendbeamtime.m, attached). Note that the formatiing of a few of the following graphs was edited manually after being outputted by the program (just to note why the plots look different than the code might imply).

The following plots were made:

Amplitude as a function of time:

Amplitude.png

Amplitude again, focused in with more analysis:

Amplitude2.png

 

Offset level:

Offset.png

 

Beam Size:

BeamSize.png

 

Centroid Displacement (note the axis values, it's fairly zoomed in):

CentroidDisplacement.png

Note that these values were converted into radians by approximating the fiber-output/CCD distance and dividing this from the displacement in mm (after converting from pixels). This distance was approximated by assuming a divergence angle of 0.085 and a beam size of ~5.1mm (being a value inbetween the horizontal and vertical beam sizes calculated). This gave a value of ~60mm, which was confirmed as plausible by a quick examination in the lab.

In the first three plots, there are obvious temporary effects which seem to cause the values to fluctuate much more rapidly than they do for the rest of the duration. It is suspected that this could be related to temperature changes within the sensor as the camera begins taking images. Further investigation (tomorrow) will investigate these effects further, while collecting temperature data.

Attachment 1: weekendbeamtime.m
function [X Y wX wY]=weekendbeamtime(basename,guess,N)
%fits 1D gaussian curve to N images in sequence of basename basefile
thisfile=mfilename('fullpath');
thisdir=strrep(thisfile,mfilename(),'');

i=0;
X=[];
Y=[];
wX=[];
wY=[];
... 82 more lines ...
  65   Thu Jul 15 20:06:37 2010 James KMiscHartmann sensorSURF Log: Thermally Induced Defocus Experiments

A quick write-up on recent work can be found at: Google Docs

 

I can't find a Tex interpreter or any other sort of equation editor on the eLog, is why I kept it on Google Docs for now instead of transferring it over.

 

--James

 

Attachment 1: pydefoc.m
function slopes=pydefoc(mainout,N,tol)
[x,y,dx,dy,time,M,centroids]=pyanalyze(mainout,N);
slopes=xdxslope(x,dx,time,tol);
Attachment 2: pyanalyze.m
function [x,y,dx,dy,time,M,centroids]=pyanalyze(mainout,N)
n=0;
centroids=[];
while n<N
    display(['Image Number ' num2str(n)])
    if n==0
        I=pyimportsingle(mainout,n);
        cent=centroid_image(I);
    else
        I=pyimportsingle(mainout,n);
... 22 more lines ...
Attachment 3: pyimportsingle.m
function I=pyimportsingle(mainoutbase,Nimg)
%Imports mainoutbase.raw generated by python framesumexport2 and outputs
%Nth image matrix I

mainout=['/opt/EDTpdv/' mainoutbase '.raw'];
%open main output array
fid = fopen(mainout,'r');
fseek(fid,4*1024*1024*(Nimg-1),'bof');
arr = fread(fid,1024*1024,'float');

... 16 more lines ...
Attachment 4: pyimportM.m
function M=pyimportM(mainoutbase,N)
maintxt=['/opt/EDTpdv/' mainoutbase '.txt'];
fid=fopen(maintxt);
str=fread(fid,'*char');
fclose(fid);
str=str';
str=strrep(str,'Camera Temperature on Digitizer Board:','');
str=strrep(str,'Camera Temperature on Sensor Board:','');
str=strrep(str,' Celsius','');
str=strrep(str,'Start Time','');
... 14 more lines ...
Attachment 5: framesumexport2.py
#!/bin/python

import array
import os
import time
#Number of loops LoopN over which to sum SumN images of dim num_H by num_W
LoopN=100
SumN=200
num_H = 1024
num_W = 1024
... 94 more lines ...
  69   Thu Jul 22 21:46:55 2010 James KunertMiscHartmann sensorHartmann Sensor Thermal Defocus Measurement Noise & Ambient Light Effects

As discussed during the teleconference, a series of experiments have been conducted which attempt to measure the thermally induced defocus in the Hartmann sensor measurement. However, there was a limiting source of noise which caused a very large displacement of the centroids between images, making the images much too noisy to properly analyze.

The general setup of this series of experiments is as follows: the fiber output from the SLED was mounted about one meter away from the Hartmann sensor. No other optics were placed in the optical path. Everything except for the Hartmann sensor was enclosed (a box was constructed out of wall segments and posterboard, with a hole cut in the end which allowed the beam to propagate into the sensor. The sensor was a short distance from the end of the box, less than a centimeter. There was no obvious difference in test images taken with the lights on and the lights off, which previously suggested to me that ambient light would not have a large effect). Temperature variations in the sensor were induced by changing the set temperature of the lab with the thermostat. A python script was used to take cumulative sums of 200 images (taken at 11Hz) every ~5 minutes.

This overly large centroid displacement appeared only in certain areas of the images. However, changing the orientation of the plate appeared to change the regions which were noisy. That is, if the orientation of the Hartmann plate was not changed between measurements, the noise would appear in the same regions in consecutive experiments (even in experiments conducted on different days). However, if the orientation of the Hartmann plate was changed between measurements, the noise would appear in a different region in the next experiment. This suggests that the noise is perhaps due to a physical phenomenon which would change with the orientation of the plate.

There were a few hypotheses which attempted to explain this noise but were shown to not be the likely cause. I hypothesized that the large thermal expansion coefficient of the aluminum camera housing could be inducing a stress on the invar frontplate, causing the Hartmann plate to warp. This hypothesis was tested by loosening the screws which attach the front and back portion of the frontplate (such that the Hartmann plate was not strongly mechanically coupled with the rest of the frontplate) and running another iteration of the experiment. The noisy regions were seen to still appear, indicating that thermally induced stress was not the cause of the distortion. Furthermore, experiments done while the sensor was in relative thermal equilibrium over long periods still showed noisy regions, and there was no apparent correlation between noise magnitude and sensor temperature for any experiment, indicating that thermal effects in general were not responsible.

Another suspected cause was the increased noise at intensity levels of 128 (as discussed in a previous eLog). However, it was observed that there was no apparent difference in the prevalence of 128-count pixels between the noisy regions and the cleaner regions, indicating that this was not the cause either.

A video was made which shows vector plots of centroid displacements for each summed image relative to the first image taken in an experiment, and was posted as an unlisted youtube video at: http://www.youtube.com/watch?v=HUH1tHRr98I

The length of each vector in the video is proportional to the magnitude of the displacement. The localization of the noise can be seen. Notice also the sudden appearance and disappearance of the noise at images 19 and 33, indicating that the cause of the noise is relatively sudden and does not vary smoothly.

Another video showing a logarithmic plot of the absolute value of the difference of each image from the first image (for the same experiment as previous) can be seen here: http://www.youtube.com/watch?v=_CiaMpw9Ig0

Notice there are jumps in the background level which appear to correspond with the disappearance and appearance of the noisy regions in the centroids (at images 18 and 32) (I forgot to manually set the framerate on these last three .avi's, so they go by a little too quickly, but it's still all there). The one-image delay between the intensity shift and centroid noise shift is perhaps related to the fact that the analysis uses the previous image centroids as the reference to find the new image centroid locations.

A video showing histograms of the intensity of each pixel in an image (within the intensity range of 50 and 140 in the averaged summed-image) for this same experiment can be seen at: http://www.youtube.com/watch?v=MogPd-vaWn4

Notice that the peak of the distribution corresponding to the background appears to shift by ~5 counts at images 18 and 32.

 

An experiment was then done which had the exact same procedure except that it was done at a stabilized lab temperature and with the SLED turned off, such that only the background appears in each image. A logarithmic plot of the absolute value of the difference in intensity at each pixel for each image can be seen at: http://www.youtube.com/watch?v=Y66wL5usN18

Other work was being done in the lab throughout the day, so the lights were on for every image but one. I made a point of turning off the lights while the 38th image was being taken. The framerate of the linked video is unfortunately a little too fast to really see what goes on (I adjusted the framerate while viewing it in MATLAB but forgot to do so for the AVI), but you can clearly see a major change in the image during the 38th image, and during that image only (it looks like a red 'flash' at the 38th frame, near the very end). The only thing that was changed while taking this specific image was the ambient light level, so this major difference must be due to ambient light. A plot of the difference between images 38 and 1 is shown below:

72210b_ambient.png

Note that the maximum difference between the images is 1107 levels, which for the 200 images in each summed image corresponds to an average shift of ~5.5 levels. This is of a very similar magnitude to the shift that can be seen in the histogram of the previous experiment. This suggests that changes in ambient light levels are perhaps somehow responsible for the noisy regions of the image. Note also the non-uniformity of the ambient light; such a non-uniform change could certainly shift the centroid positions.

One question is how, exactly, this change might have propagated into the analysis. The shape of the background level change appears to be very different from the shape of the noisy regions seen for this plate configuration. This is something which I need to examine further; this, combined with the fact that the changes in the noise appear to occur one image after the actual change in intensities, suggests to me that there could perhaps be some subtle things going on with my data analysis procedures which I don't currently fully understand.

Still, I highly suspect that ambient light is the root cause of the noisy regions. It would be a remarkable coincidence if the centroid displacement shift was not ultimately due to the observed intensity shift, or if the intensity shift was not due to a change in ambient light (since the intensity shift in the histogram analysis and ambient light change in the background analysis are observed to correspond to roughly the same magnitude of intensity change). I had initially suspected that effects from ambient light would be negligible since, while taking test images while setting up each experiment, the image did not appear to change based upon whether I had the lights on or off. I checked this a few times, but did not examine the images closely enough to be able to detect such a small non-uniform change in the intensity of each image.

If ambient light was responsible, this could also perhaps explain why the location of the noise appeared to depend on the orientation of the plate. The Hartmann plate would be in the optical path of any ambient light leaking in, so a change in the orientation of the plate could perhaps change the way that the ambient light was propagating onto the sensor (especially since the Hartmann plates are slightly warped and not perfectly planar). That's all purely speculation at this point, but it's something that I intend to investigate further.

I tried analyzing some previous data by subtracting part of the background, but was unsuccessful at reducing the noise in the results. I attempted to reduce the background in previous data by setting all values below a certain threshold equal to zero (before inputting the image into the centroiding function). However, the maximum threshold which I could use before getting an error message was ~130. If I set the threshold to, say, 135, I received an error from the centroiding function that the image was 'too dissimilar to the hex grid'. I did analysis of the images with a threshold of 130, but this still left random patches of background spaced between the spots in each image. The presence of only patches of background as opposed to the complete background actually increased the level of noise in the results by about a factor of 3. I would need to come up with a better method of subtracting the background level if I wanted to actually reduce the noise in this data.

The next step in this work, I think, will perhaps be to better enclose the system from ambient light to where I'm confident that it could have little or no effect. If noisy regions were not seen to appear after this was done, that would more or less confirm that ambient light was the cause of all this trouble. Hopefully, if ambient light is indeed the cause of the noise, reducing it will enable an accurate and reliable measurement of thermally induced defocus within the Hartmann sensor.

  78   Mon Jul 26 18:47:12 2010 James KMiscHartmann sensorHex Grid Analysis Errors and Thermal Defocus Noise

My previous eLog details how the noise in Hartmann Sensor defocus measurements appears to vary with ambient light. New troubleshooting analysis reveals that the rapid shifts in the noise were still related to the ambient light, sort of, but that ambient light is not the real issue. Rather, the noise was the result of some trouble with the centroiding algorithm.

The centroiding functions I have been using can be found on the SVN under /users/aidan/cit_centroid_code. When finding centroids for non-uniform intensity distributions, it is desirable to avoid simply using a single threshold level to isolate individual spots, as dimmer spots may be below this threshold and would therefore not be "seen" by the algorithm. The centroiding functions used here get around this issue by initially setting a relatively high threshold to find the centroids of the brighter spots, and then fitting a hexagonal close-packed array to these spots so as to be able to infer where the rest of the spots are located. Centroiding is then done within small boxes around each estimated centroid location (as determined by the hexagonal array). The functions "find_hex_grid.m" and "flesh_out_hex_grid.m" serve the purpose of finding this hexagonal grid. However, there appear to be bugs in these functions which compromise the ability of the functions to accurately locate spots and their centroids.

The centroiding error can be clearly seen in the following plot of calculated centroids plotted against the raw image from which they were calculated:

centerror.PNG

At the bottom of the image, it can be seen that the functions fail at estimating the location of the spots. Because of this, centroiding is actually being done on a small box surrounding each point which consists only of the background of the image. This can explain why these centroids were calculated to have much larger displacements and shifted dramatically with small changes in ambient light levels. The centroiding algorithm was being applied to the background surrounding each of these points, so it's very reasonable to believe that a non-uniform background fluctuation could cause a large shift in the calculated centroid of each of these regions.

It was determined that this error arose during the application of the hex grid by going through the centroiding functions step-by-step to narrow down where specifically the results appeared to be incorrect. The function's initial estimate for the centroids right before the application of the hex grid  is shown plotted against the original image:

centinit.png

The centroids in this image appear to correspond well to the location of each spot, so it does not appear that the error arises before this point in the function. However, when flesh_out_hex_grid and its subfunction find_hex_grid were called, they produced the following hexagonal grid:

hexgrid.png

It can be seen in this image that the estimated "spot locations" (the intersections of the grid) near the bottom of the image differ from the actual spot locations. The centroiding algorithm is applied to small regions around each of these intersections, which explains why the calculated "spot centroids" appear at incorrect locations.

It will be necessary to fix the hexagonal grid fitting so as to allow for accurate centroiding over non-uniform intensity distributions. However, recent experiments in measuring thermally induced defocus produce images with a fairly uniform distribution. It should therefore be possible to find the centroids of the images from these experiments to decent accuracy by simply temporarily bypassing the hexagonal-grid fitting functions. To demonstrate this, I analyzed some data from last week (experiment 72010a). Without bypassing the hex-grid functions, analysis yielded the following results:

72010a.png

However, when hexagonal grid fitting was bypassed, analysis yielded the following:

72010a_nohex.PNG

The level of noise in the centroid displacement vs. centroid location plot, though still not ideal, is seen to decrease by nearly two orders of magnitude. This indicates that bypassing or fixing the problems with the hexagonal grid fitting functions should enable a more accurate measurement of thermally induced defocus in future experiments.

  91   Tue Aug 17 22:34:14 2010 ranaMiscGeneralETM temperature after a 1W step

This attachment is a Shockwave Flash animation of the iLIGO ETM getting a 1 W beam with a 3.5 cm radius getting fully absorbed onto the surface at t = 0.

Attachment 1: etmt.swf
  112   Thu Feb 24 14:20:55 2011 AidanMiscRing HeateraLIGO H2 Ring Heater Pics

 Here are some pictures of the ring heater segments destined for the H2 Y-arm this year.

 These still need to be put onto ResourceSpace.

Attachment 1: aLIGO_Ring_Heaters.zip
  116   Tue Mar 1 10:47:18 2011 AidanMiscHartmann sensorElectron to Counts conversion efficiency

Using some of the old data from James (attached below), I calculated the CCD conversion efficiency (CE) from electrons to bits (Counts).

Number of electrons(Ne) = QE*Number of Photons(Np)

noiseE = sqrt(Ne);

Number of Counts (NCo)= CE*Ne

Noise in Counts (noiseCo)= CE*sqrt(Ne)

noiseCo = sqrt(CE * NCo)

log(CE) = 2*noiseCo - NCo

Therefore CE = 10.0^(2*noiseCo - NCo)

From James's data on the intensity noise in the CCD, CE = 0.0269

 

Quote:
 
Using this function, I did the same analysis of the upper-left 200x200 pixels over all 200 images:

(data from 200 images, over the upper-left 200x200 pixels)

 

  156   Tue Nov 29 09:13:49 2011 ranaMiscLIGO 3GSwitching from CO2 to shorter wavelength solid state laser

 Around a year ago, Phil and I discussed the possibility of using an OPO to possibly generate our own laser beam at ~2 microns for TCS. This was to avoid all of the usual hassle of the 10 micron CO2 laser.

As it turns out, the 1.5-3 micron range doesn't have enough absorption in fused silica: the absorption depth would be basically the whole thickness of the optics and this is not so useful when trying to correct surface heating.

During my recent trip to JILA, Jan Hall mentioned to me that it should be possible to operate instead at ~5 microns, where laser technology may be solid state and where we can use Si:As detectors instead of the inefficient HgCdTe ones which we use now.

JWST, in partnerships with industry, have developed some Si:As detectors:  http://www.jwst.nasa.gov/infrared.html   

Some internet searching shows that there are now several laser technologies for the mid-IR or MWIR range. Some are <1 W, but some are in the ~10 W range.

Of course, its possible that we'll switch to Silicon substrates, in which case we need to re-evaluate the goals and/or existence of TCS.

  157   Tue Jun 5 17:25:43 2012 Alex MauneyMiscaLIGO Modeling6/5/12 Daily Summary

- Had a meeting to talk about the basics of LIGO (esp. TCS) and discuss the project

- Created COMSOL model for the test mass with incident Gaussian beam.

- Added a ring heater to the previous file

- Set up SVN for the COMSOL repository

  158   Wed Jun 6 16:54:09 2012 Alex MauneyMiscaLIGO Modeling6/6/12 Daily Summary

- Got access to and started working with SIS on Rigel1

- Fixed SVN issues

- Refined COMSOL model parameters and worked on a better way to implement the heating ring to get the astigmatic heating pattern.

  159   Thu Jun 7 00:23:11 2012 Aditi MittalMiscLIGO 3GSummary June 5 and June 6, 2012

 June 5

-Discussed the actual project outline 

-Installed Comsol on the system

-Learned the basics of Comsol with the help of tutorials available on 40m wiki

and others.

 

June 6

-Made few simple models in Comsol 

-Studied LIGO GWADW slides for a better understanding of the project.

-Setup SVN to access remote repository.

 

 

 

  160   Thu Jun 7 16:50:16 2012 Alex MauneyMiscaLIGO Modeling6/7/12 Daily Summary

- Created a COMSOL model with thermal deformations

- Added non-symmetrical heating to cause astigmatism

- Worked on a method to compute the optical path length changes in COMSOL

  161   Thu Jun 7 23:24:56 2012 Aditi MittalMiscLIGO 3GSummary June 7, 2012

-Created a COMSOL model for variation of temperature in two mass system.

-Used the above model for cryogenic conditions.

-checked it analytically.

  162   Fri Jun 8 16:36:47 2012 Alex MauneyMiscaLIGO Modeling6/8/12 Daily Summary

- Tried to fix COMSOL error using the (ts) module, ended up emailing support as the issue is new in 4.3

- Managed to get a symmetric geometric distortion by fixing the x and y movements of the mirror to be zero (need to look for a better way to do this as this may be unphysical)

- Worked on getting the COMSOL data into SIS, need to look through the SIS specs to find out how we should be doing this (current method isn't working well)

 

  163   Fri Jun 8 23:51:13 2012 Aditi MittalMiscLIGO 3GSummary June 8, 2012

-Created a COMSOL model for cryogenically shielded test mass with compensation plate.

-Analyzed the behavior of the model in different size configurations.

  164   Mon Jun 11 17:11:01 2012 Alex MauneyMiscaLIGO Modeling6/11/12 Daily Summary

- Fixed the (ts) model, got strange results that indicate that the antisymmetric heating mode is much more prominent than previously thought

- Managed to get COMSOL data through matlab and into SIS

 

  165   Mon Jun 11 20:53:31 2012 Aditi MittalMiscLIGO 3GSummary June 11, 2012

 -Continued with the same cryogenic model created and varied the length of  outer shield and studied the temperature variation inside.

-Compared the temperature difference given by COMSOL with manually calculated one.

  166   Wed Jun 13 16:36:14 2012 Alex MauneyMiscaLIGO Modeling6/12 and 6/13 Daily Summary

- Realized that the strange deformations that we were seeing only occur on the face nearest the ring heater, and not on the face we are worried about (the HR face)

- Read papers by Morrison et al. and Kogelnik to get a better understanding of the mathematics and operations of the optical cavity modeled in SIS

- Read some of the SIS manual to better understand the program and the physics that it was using (COMSOL licenses were full)

  167   Thu Jun 14 05:37:30 2012 Aditi MittalMiscLIGO 3GSummary June 13, 2012

-Derived formula for manual calculation of temperature due to total influx.

-Compared the results by COMSOL and by the formula.

  168   Thu Jun 14 16:51:03 2012 Alex MauneyMiscaLIGO Modeling6/14/12 Daily Summary

- Plugged the output of the model with uniform heating into SIS using both modification of the radius of curvature, and direct importation of deflection data

- Generated a graph for asymmetric heating and did the same

- Aligned axes in model to better match with the axes in MATLAB and SIS so that the extrema in deflections lie along x and y (not yet implemented in the data below)

Attachment 1: SIS_Outputs.txt
Unchanged field:
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
   FP cavity modal analysis using cold optics parameters
 
ROC(ITM) = 1934, ROC(ETM) = 2245, Cavity lenggth = 3994.499999672, total Gouy = 2.7169491305278
Fval(ITM) = -4297.7777755379, OPL(ITM) = 0.13793083662307, Fval(ETM) = -4988.8888885557
waist size = 0.01203704073212, waist position from ITM = 1834.2198819617, Rayleigh range = 427.80682127602
 
Mode parameters of cavity fields
ETM AR (out base) : w = 0.0619634      R = 1548.276       z  = 1519.925       z0 = 207.583        w0 = 0.008384783   
... 138 more lines ...
Attachment 2: Assymetric_Heating_Line_Graph.png
Assymetric_Heating_Line_Graph.png
  169   Mon Jun 18 16:30:36 2012 Alex MauneyMiscaLIGO Modeling6/18/12 Daily Summary

- Verified that the SIS output does match satisfy the equations for Gaussian beam propagation

- Investigated how changing the amount of data points going into SIS changed the output, as well as how changes in the astigmatic heating effect the output

     + The results are very dependent on number of data points (similar order changes to changing the heating)

     + Holding the number of data points the same, more assymetric heating tends to lead to more power in the H(2,0) mode, and less in the H(0,2)

 

  170   Mon Jun 18 23:42:39 2012 Aditi MittalMiscLIGO 3GCryogenic Shielding

 -Read about blue team design for maximum power budget.

-Read third generation talks to get a better understanding of the work. 

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