Does this work?

Yes.

I've been looking to see what the time constant of the ring heater is. The attached plot shows the voltage measured by the photodiode in response to the heater turning on and off with a period of 30 minutes.

The time constant looks to be on the order of 600s.

I just replaced the brass Hartmann plate with the Invar one. The camera was off during the process but has been turned on again. The camera is now warming up again. I've manually set the temperature in the EPICS channels by looking at the on-board temperature via the serial communications.

 I also made sure the front plate was secured tightly.

 Here's a plot of the 15-day output of the SLED.

Currently there is an 980nm FC/APC fiber-optic patch-cord attached to the SLED. It occurred to me this morning that even though the patch cord is angle-cleaved, there may be some back-reflection than desired because the SLED output is 830nm (or thereabouts) while the patch cord is rated for 980nm.

 I'm going to turn off the SLED until I get an 830nm patch-cord and try it then. 

Correction: I removed the fiber-optic connector and put the plastic cap back on the SLED output. The mode over-lap (in terms of area) from the reflection off the cap with the output from the fiber is about 1 part in 1000. So even with 100% reflection, there is less than the 0.3% danger level coupled back into the fiber. The SLED is on again.

I've assembled the box Mindy ordered from Newport that will house the Hartmann sensor. It's mainly to reduce ambient light, air currents and to keep the table cleaner than it would otherwise be.

We need to add a few more holes to allow access for extra cables.

I'm in the process of aligning the cross-sampling experiment for the HWS. I've put the 1" PBS cube into the beam from the fiber-coupled SLED and found that the split between s- and p-polarizations is not 50-50. In fact, it looks more like 80% reflected and 20% transmitted. This will, probably, be due to the polarization-maintaining patch-cord that connects to the SLED. I'll try switching it out with a non-PM maintaining fiber.

Later ...

That worked.

I've set up a crude alignment of the cross-sampling system (optical layout to come). This was just a sanity check to make sure that the beam could successfully get to the Hartmann sensor. The next step is to replace the crappy beam-splitter with one that is actually 50/50.

Attached is an image from the Hartmann sensor.

I've been setting up the cross-sampling test of the Hartmann sensor, Right now I'm waiting on a 50/50 BS so I'm improvising with a BS for 1064nm.

The output from the SLED (green-beam @ 980nm) is around 420uW (the beam completely falls on the power meter.) There are a couple of irises shortly afterwards that cut out a lot of the power - apparently down to 77uW (but the beam is larger than the detection area of the power meter at this point - by ~50%). The BS is not very efficient on reflection and cuts down the power to 27uW (overfilled power meter). The measurement of 39uW is near a focus and the power meter captures the whole beam. There is a PBS cube that is splitting the beam unequally between s- and p-polarizations (I think this is due to uneven reflections for s- and p-polarizations from the 1064nm BS). The beam is retro-reflected back to the HWS where about 0.95uW makes it to the detector.

There is a 1mW 633nm laser diode that is used to align the optical axis. There are two irises that are used to match the optical axis of the laser diode and the SLED output.

I've set up the HWS with the probe beam sampling two optics in a Michelson configuration (source = SLED, beamsplitter = PBS cube). The return beams from the Michelson interferometer are incident on the HWS. I misaligned the reflected beam from the transmitted beam to create two Hartmann patterns, as shown below.

The next step is to show that the centroiding is a linear superposition of these two wavefronts.

The SLED in the cross-sampling experiment produces unpolarized light at 980nm. So I added a PBS after the output and then a HWP (for 1064nm sadly) after that. In this way I produced linearly p-polarized light from the PBS. Then I could rotate it to any angle by rotating the HWP. The only drawback was that the HWP was only close to half a wave of retardation at 980nm. As a result, the output from this plate became slightly elliptically polarized.

The beam then went into another PBS which split it into two beams in a Michelson-type configuration (REFL and TRANS beams) - see attached image. By rotating the HWP I could vary the relative amount of power in the two arms of the Michelson. The two beams were retro-reflected and we then incident onto a HWS.

I measured the power in the REFL beam relative to the total power as a function of the HWP angle. The results are shown in the attached plot.

I got the LTG CO2 laser to deliver 50.02W as measured by the Thorlabs 200W power head today. This required running the Glassman HV supply at full power (30.0kV, 31.1mA), tweaking the end grating and output coupler alignments, and cleaning the ZnSe Brewster windows on the laser tubes, and it only lasted a few seconds before dropping back to ~48W, but the laser delivered the specified power. In the factory it delivered 55W at the 10.6 micron line I am using now- I checked it with the CO2 laser spectrum analyzer- so there is more work to do.

Cheryl Vorvick, Chris Guido, Phil Willems

Attached is a PDF with some initial noise testing. There are 5 spectrum plots (not including the PreAmp spectrum) of the laser. The first two are with V_DC around 100 mV, and the other three are with V_DC around 200 mV. (As measured with the 100X gain preamplifier, so ideally 1 and 2 mV actual) We did one spectrum (at each power level)  with no attempt of noise reduction and one spectrum with the lights off and a make shift tent to reduce air flow. The 5th plot is at 200mv with the tent and the PZT on. (The other 4 have the PZT off).

The second plot is just the spectrums divided by their respectives V_DC to get an idea of the RIN.

I've set up a quick experiment to modulate the angle of the Hartmann sensor probe beam at 10mHz and to monitor the measured prism. The beam from the SLED is collimated by a lens and this is incident on a galvo mirror. The reflection travels around 19" and is incident on the HWS. When the galvo mirror is sent a 1.1Vpp sine wave, then beam moves around +/- 0.5" on the surface of the Hartmann sensor, giving around 50mrad per Vpp.

The galvo is currently being sent a 0.02Vpp sine wave at 10mHz.

I changed the drive amplitude on the function generator to 0.05Vpp and have measured the angle of deflection by bouncing a laser off the laser mirror and projecting it 5.23m onto the wall. The total displacement of the spot was ~3.3mm +/- 0.4mm, so the amplitude of the angular signal is 1.6mm/5.23m ~ 3.1E-4 radians. The Hartmann Sensor should measure a prism of corresponding magnitude.

The frequency is still 10mHz.

I've set up an experiment to test the HWS intensity distribution displacement measurement code. Basically the beam from a SLED is just reflecting off a galvo mirror onto the HWS. The mirror is being fed a 0.02Vpp *10 gain, 10mHz sinewave from the function generator.

The experimental setup is shown below.

I hacked the HWS code to export the Gaussian X and Y centers to Seidel Alpha and Beta channels in EPICS (C4:TCS-HWSX_PSC_ALPHA, C4:TCS-HWSX_PSC_BETA)

 I've had the output from a fiber projected about 400mm onto the Hartmann sensor for around 5 days now. (The divergence angle from the fiber is around 86 mrad).

I played around with the temperature of the lab to induce some defocus changes in the Hartmann sensor. The system is mostly linear, but there are relatively frequent jumps in the defocus of the order of 1E-4 m^-1. This may be due to a number of things - the Hartmann plate may be moving, the fiber holder may be shifting back and forth, there may be some issue with the source wavelength shifting.

• A change in defocus, dS, of around 1E-4 m^-1 from a point source at 400mm from the Hartmann plate (dS/dx = -1/x^2), corresponds to a change in the end position of the fiber of around 16 microns. Seems a little big ... unless it's not secured properly ...
• Also the defocus vs temperature slope is different from what James measured last year. There is an additional -4E-5 m^-1 K^-1 due to the expansion of the stainless steel table moving the point source further or closer to the Hartmann plate. That leaves about -3E-4 m^-1 K^-1 for the Hartmann sensor. This is roughly twice what James measured last year. 

Sun 30th May 2011 - 11:40AM - the z-axis control on the NewFocus 9091 fiber coupling mount was not tightened. I tightened that to secure the control.

 I ran through the procedure to calibrate the lever arm of the Hartmann sensor. The beam from a 632.8nm HeNe laser was expanded to approximately 12mm diameter and injected into a Michelson interferometer. The Hartmann sensor was placed at the output port of the Michelson.

1. I tilted one of the mirrors of the interferometer to induce a prism between the two beams at the output. This created about 135 vertical fringes on the CCD.
2. With the Hartmann plate removed, I recorded the interference pattern and took its 2D FFT. There was a peak in the Fourier transform about 134 pixels from the DC level. 
3. This next part is questionable ...  I centroided the frequencies around the peak in the FFT to try to determine the spatial frequency of the fringes to better than the bandwidth of 1/1024 pixels^-1 (yes, they're strange units). This is, probably acceptable at improving the accuracy of the frequency measurement if it is known that the signal is a generated by a pure sine wave in the spatial domain - this is not an unreasonable assumption for the output of an interferometer. Anyway, the peak fluctuated around 133.9 units from DC by around +/- 0.1 units.
4. The prism between the two beams is the measured spatial frequency (measured as 133.9 oscillations across the CCD) multiplied by the wavelength and divided by the width of the CCD (= 1024 x 12um). In other words, the prism is the ratio of the wavefront change across the CCD divided by the diameter of the CCD (= 6.895 +/- 0.005 mrad)
5. Next, I inserted the Hartmann plate, blocked one of the beams and recorded the spot pattern. I then blocked the other beam and unblocked the first and recorded another spot pattern. 
6. The mean displacement between the spot patterns was calculated. Due to a fairly noisy intensity distribution (the 2" mirrors were AR coated for 700-1000nm and hence there were some stray beams), the mean displacement was relatively noisy - about 5.60 pixels with a standard deviation of around 0.3 pixels and a standard error of around 0.01 pixels ( = 67.2 um)
7. The lever arm is equal to the mean displacement of the spots divided by the prism. In this case, 9.75 +/- 0.02 mm
8. I removed the Hartmann plate and confirmed that the FFT of the fringes from the IFO still had a peak at 133.9 +/- 0.1 units. It did.

 The 50W Access Laser is now in the lab. We need to wire up the interlock to the laser, plumb the chiller lines to the power supply and to the laser head and also wire up all the electrical and electronics cables. Additionally, we will need to plumb the flow meter and attach a circuit to it that triggers the interlock if the flow falls too low.

The data from the long-term measurement of the HWS is presented here. The beam envelope moves by, at most, about 0.3 pixels, or around 3.6 microns. The fiber-launcher is about 5" away from the HWS. Therefore, the motion corresponds to around 30 micro-radians (if it is a tilt). The beam displacement is around 4 microns.

The optical properties change very little over the full 38 days (about 2 micro-radians for tilt and around 2 micro-diopters for spherical power).

The glitches are from when the SLED drivers were turned off temporarily for other use (with the 2004nm laser).

There were known to be huge (65%) heating beam power losses on the SRM AWC table, somewhere between the CO2 laser and the test optic. Today I profiled the setup with a power meter, looking for the dominant source of losses. It turned out to be a 10" focusing lens which had the incorrect coating for 10.2 microns. I swapped this lens with a known ZnSe 10" FL lens (Laser Research Optics LX-15A0-Z-ET6.0) and confirmed the power transmittance to be >99%, as spec'd. There is now ~310 mW maximum reaching the test optic, meaning that the table losses are now only 10%.

Using a single-axis micrometer stage I also made an occlusion measurement of the heating beam radius just in front of the test optic. I moved the 10" focusing lens back three inches away from the test optic to slightly enlarge the beam size. In this position, I measure a beam radius of 3.5+/-0.25 mm at 1.5" in front of the test optic (the closest I can place the power meter). The test optic is approximately 20" from the 10" FL lens, so the beam has gone through its waist and is again expanding approaching the test optic. I believe that at the test optic, the beam is very close to 4 mm.

For archive purposes, attached is a write-up of all the HWS measurements I've made to date for the SRM CO2 projector mock-up.

The 400 mW CO2 laser on the Hartmann table is currently configured for a measurement of its relative intensity noise. It is aligned to a TCS CO2P photodetector powered by a dual DC power supply beside the light enclosure. I got some data last night with the laser current dialed back for low output power (0.5-10 mW incident), but still need to analyze it. In the meantime please don't remove parts from the setup, as I may need to repeat the measurement with better power control.

Attached for reference is the RIN measurement from the initial data.

I did a beam size/beam propagation measurement of the low power CO2 laser (Access Laser L3, SN:154507-154935)

 [Aidan, Marie]

We tested the output of the fiber launcher D1800125-v3. We were using a 6mm spacer in the SM1 lens tube and 11mm spacer in the SM05 lens tube and the 50 micron core fiber.

The output of the fiber launcher was projected directly onto the CCD. Images of these are attached (coordinates are in pixels where 100 pixels = 1.2mm)

There is a lot of high-spatial frequency light on the output. It looks like there is core and cladding modes in addition to a more uniform background. There was an indication that we could clear up these annular modes with an iris immediately after the fiber launcher but I didn't get any images. We're going to test this next week when we get an SM1 mountable iris.

And here's the output of the fiber launcher when I fixed it at 313mm from the camera, attached an iris to the front and slowly reduced the aperture of the iris.

The titles reflect the calculated second moment of the intensity profiles (an estimate of the equivalent Gaussian beam radius). The iris is successful in spatially filtering the central annular mode at first and then the outer annular mode. 

We'll need to determine the optimum diameter to get good transmission spatially without sacrificing too much power.

Here is the output from D1800125-v5_SN01.

Title was wrong - this is actually config [12,2,4,125]

I'm considering the 86-711 2" 532nm PBS from Edmund Optics for the ETM HWS at the sites.

https://www.edmundoptics.com/optics/polarization/linear-polarizers/532nm-50mm-diameter-high-energy-laser-line-polarizer/

The effect on the transmission through the system, compared to the THorlabs PBS, is shown in the attached plot.

Conclusion: it looks almost as effective as the Thorlabs PBS with the added benefit of being 2" in diameter.

Went down to the lab and showed Rana the setup. He's fine with me being down there as long as I let someone know. He also recommended using an adjustable mount  (three screws) for the test mirror instead of the mount with top bolt and two nubs on the bottom - he thinks the one with three screws as constraints for the silica will be easier to model (and be more symmetric constraints)

Mounted the f=8" lens (used a 2" pedestal) and placed it on the table so the image fit well on the CCD and so a sharp object in front of the lens resulted in a sharp image. The beam was clipping the f=4" lens (between gold mirror and test mirror) so I spent time moving that gold mirror and the f=4" lens around. I'll still need to finish up that setup.

The beam reflecting off the test mirror was clipping the lens between gold mirror and test mirror, so I reconfigured some of the optics, unfortunately resulting in a larger angle of incidence.

From the test mirror, the beam size increases much too rapidly to fit onto the 2-inch diameter lens with f=8 that was meant to resize the beam for the CCD of the HWS. It seems that the f=8 lens can go about 6 inches from the test mirror, and an f ~ 2.3 (60 mm) lens can go about 2 inches in front of the CCD to give the appropriate beam size. However, the image doesn't seem very sharp.

The beam is also not hitting the CCD currently because of the increase in angle of incidence on the test mirror and limitations of the box. I'd like to move the HWS closer to the SLED (and will then have to move the SLED as well).

The table is set up. The HWS and SLED were moved slightly, and a minimal angle between the test mirror and HWS was achieved.

There are two possible locations for the f=60mm lens that will achieve appropriate magnification onto the HWS: 64cm or 50 cm from the f=200mm lens. 

At 64cm away, approximately 79000 saturated pixels and 1054 average value.

At 50cm away, approximately 22010 saturated pixels and 1076 average value.

Currently the setup is at 64cm. Could afford to be more magnified, so might want to move the f=60mm lens around. Also, if we're going to need to be able to access the HWS (i.e. to screw on the array) we might want to move to the 50cm location.

With Jon's help, I changed the setup to include a mode-matching telescope built from the f=60mm (1 inch diameter) lens and the f=100mm lens. These lenses are located after the last gold mirror and before the test optic. The height of the beam was also adjusted so that it is more centered on these lenses. Note: these two lenses cannot be much further apart from each other than they currently are, or the beam will be too large for the f=100mm lens.

We considered different possible mounts to use for the test optic, and decided to move it to a mount where there is less contact. The test optic was also moved closer to the HWS to achieve appropriate beamsize on the optic coming from the mode-matching telescope.

The f=200 lens is now approximately 2/3 of the distane from the test optic to the HWS, resulting in an appropriately sized beam at the HWS.

Current was also turned down to achieve 0 saturated pixels.

Attached the grid array of the HWS.

Applied voltage (5V, 7V, 9.9V, 14V) to the heater pad and took measurements of T and spherical power (aka defocus).

The adhesive of the temperature sensor isn't very sticky. The first time I did it it peeled off. (Second time partially peeled off). We want to put it on the side of Al if possible.

Bonded a mirror (thickness ~6 mm) to aluminum disk (thickness ~5 mm) and it's still curing.

To the best of my ability, calculated the magnification of the plane of the test optic relative to the HWS (2.3) and input this value.

Increased the temperature slightly and saved data points of defocus to txt files when temperature leveled out. This was a slow process, as it takes a while for things to level out. I only got up to about 28.5C, and will need to continue this process.

I also plotted the best-fit defocus for each temperature from COMSOL (Temperature vs. Defocus), and looking at values from HWS it seems that we're off by a normalization factor of approx. 4.

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.

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)

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)

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.

 For Wednesday, June 16:

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

 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:

128 images, spot search point (100,100), threshold level 129

 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):

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:

1000 microseconds:

1500 microseconds:

2000 microseconds:

3000 microseconds:

4000 microseconds:

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

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:

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):

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:

Set to 1Hz:

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:

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.

Nice work!

 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:

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:

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

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:

After:

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

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):

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.