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ID Date Author Type Category Subjectup
  1502   Tue Apr 19 17:33:17 2016 GabrieleDailyProgressCrackleBeam steering installed

I installed the beam steering mirror on the laser board. Unfortunately, the only place where I could easily fit it in is before the telescope. Therefore I'm not compeltely sure of the actuation range. Morevoer, since I moved the mirrors before the telescope, the beam size at the photodiodes might have changed slighlty. It would be good to measure it again and tune the telescope if necessary. I realigned the beam on all mirrors and lenses on the laser board. In any case the Michelson alignment was lost after the installation of the QPD.

  1514   Mon Apr 25 15:44:24 2016 GabrieleDailyProgressCrackleBeam steering servo progress

Following the design reported in 1513, I built two circuits, using a test breadboard. I also measured the transfer functions which turned out to be very close to the desired one. Some component values have changed (70k -> 68l, 2u -> 2.2u, 800 -> 820, 5p -> 4.7p).

After Xiaoyue re-aligned the beam into the QPD, I tested the servo and it worked at the first attempt. The QPD signal goes to zero quickly when the servo is closed. The loop seems quite robust: one can kick the table without loosing control. Here is a comparison of the QPD signal with loop open and closed. There is a lot of gain peaking at ~100 Hz. Probably the phase margin is not optimal there.

According to my measurment, for the Y loop the controller gain should be larger by about a factor 2, since there is less actuation gain. The gain peaking is consistent with low Y gain. This can be easily accomplished by hchanging the 100 ohm resistor with a 50 ohm resistor in the first stage.

  1462   Wed Apr 6 01:16:40 2016 XiaoyueDailyProgressCrackleBeing more careful about seismic and acoustic coupling

I did a long time acoustic noise injection today GPS time 1143923760 - 1143928875 in order to do multicoherence anlaysis to project the total noise contributed by acoustic noise and seismic noise, due to the fact that we see high coupling between acoustic and seismic noise in high frequency range. The result is shown below. Compared to the former separate seismic noise and acoustic noise projection, my conclusion that acoustic noise dominates the high frequency part stays unchanged. Another thing to note is that the acoustic noise is also coupled relatively strongly to Mich in frequency range 10 ~ 40 Hz, there appears a small bump. This was not observed before we float the laser board and might be an aftermath of the improperly mounted laser board cover that's working like a microphone itself.

Attachment 1: noise_project.pdf
  1011   Wed Jun 24 16:30:29 2015 GabrieleDailyProgressCrackleBell jar in position

[Xiaoyue, Gabriele]

Even though we can't pump down since we're still missing the 6"3/4 blanks and feed-throughs, we put the bell jar on top of the collar, routing the cables through a slit on one of the 6"3/4 caps. The bell jar was in position at about 3:30pm LT.

After this the Michelson interferometer got very much misaligned. So we need to install picomotors on one of the Michelson folding mirrors. Tomorrrow we'll retrofit the Crackle1 picomotors on a new mount and install them in Crackle2.

Meanwhile, we were able to lock the Michelson, even though the visibility is very bad: we estimated that the optical gain is about 8 times smaller.

In the plot below, top panel: green is the lock error signal without the bell jar; purple with the bell jar installed (we didn't multiply it by 8 to compensate for the different gain); red with bell jar in position and all damping loops off.

  521   Sat May 5 15:13:15 2012 ZachDailyProgressCoating QBevel added, mode at ~37.16 kHz now in COMSOL


By intersecting the cylinder with a torus, I was able to get something very close to a flat bevelled edge. I adjusted the size of the bevel until the 37 kHz mode matched roughly what we have empirically. I have updated the 3D COMSOL file

Interestingly, it still doesn't show the 2.6-kHz mode.

Screen_Shot_2012-05-05_at_3.06.41_PM.png Screen_Shot_2012-05-05_at_3.07.18_PM.png

Edit by Giordon:

It seems to predict the 64.448kHz mode that we saw though (centered the frequency around 64khz in COMSOL)


  1694   Mon May 1 02:54:10 2017 XiaoyueDailyProgressCrackleBinning analysis on Exp and Sim crackle data

In Elog 1690 I summarized the driving frequency demodulation analysis of the highC and the new maraging steel blades data, with driving frequency basis of 0.19 Hz. The results from the new maraging steel blades are very promising as it's showing a positive 1F in-phase modulated noise component, and there seems to be a frequency dependency of this +1FI noise. In order to investigate the time profile of the Michelson signal, we devised a binning averaging method to analyze the band-passed data. To facilitate the process, I used [20, 55] Hz single band-passed data. The band-passed mich data (after seismic subtraction) are downsampled to a sampling rate of 16 Hz, squared, and then folded in time to one driving period. The driving period is divided into 30 bins. We take averages and std of squared MICH signal in each bin for driving ON and OFF segments separately: b1 = <mich^2_ON> and b0 = <mich^2_OFF>.

In below figures, I plot the difference between ON and OFF average mich^2: b1-b0. Left figure averages data in selected segments with the low-frequency integrated noise threshold criteria (i.e. exclude driving segment with integrated mich spectrum power in low frequency regime ( [20, 40] Hz ) that exceeds 3std threshold). This selection has also been applied to all Elog 1690 demodulation analysis. Right figure averages data in selected segments without applying the spectrum integral rule, but only pick bad segments according to UGF monitor values (the UGF criteria are applied all the time for all analysis) and in-phase calibration channel std (which contributes only negligible difference to the results in the end).


The results are very different. The one with spectrum integral selection (Left) gives mainly a negative 2F quadrature (-2FQ) behavior, which is consistent with the former demodulation analysis. On top of the major -2FQ noise, we can barely see a positive 1F in-phase (+1FI) component superimposed. I think a promising next step is to fit and subtract the first order 2F behavior and visualize the left 1F and other components. The one without spectrum integral selection (Right) gives a huge +1FI behavior for driving frequency f = 0.0475 Hz and f = 0.38 Hz tests. The comparison between the two cases indicates that the segments exhibiting large low-frequency noise are likely carrying a huge +1FI noise component. Are they crackling noise that is occasionally becoming enormous?

We think the strongest evidence to convince people whether these demodulated noises are crackling noise or not is the +1FI modulation plus driving frequency dependency. In my former micromechanical study of pre-yield crackling noise (shown as in the left figure below), we found through a direct crackle experiment simulation that the microplastic noise are modulated in +1FI fashion, and the dynamic mechanical analysis work indicates a driving rate dependency on the dissipation feature. Besides this predicted micromechanical noise due to dislocation dynamical response to external stress, all the other possible sources of modulated noise in our Michelson setup listed in Elog 1692 cannot be +1FI modulated and driving frequency dependent at the same time. 

Following this logic I investigated the driving frequency dependency in the micromechanical crackling experiment simulation -- I prescribed stress oscillation ON/OFF segments (100 seconds/segment * 60 segments) in sequence on top of a 50% yielding quasi-static stress. I tested 5 different driving frequency [1, 2, 4, 8, 16] rad/s. For each single-frequency driving test, the same load function is applied onto 16 random system generated from the same simulation parameter (based on the single-crystalline copper system for now). I used a "bootstrap" method to make most from my simulation results: I statistically analyzed the strain rate response difference taken between all pair combinations of the 16 independent samples. In this way, from 16 samples I can have C16^2 = 120 crackling simulations.

The binning analysis results on the crackle simulations are shown in the figure below on the right, which clearly indicates a frequency dependency of the +1FI modulated noise. It seems that:

1. the noise peak amplitude becomes higher with faster driving

2. the noise peak with faster driving lags more behind in time.

It's interesting to note that the slowest (0.045 Hz) and fastest (0.38 Hz) driving results (w/o spectrum selection) agrees more or less with the simulation results, but we don't see consistency if taking the other two intermediate driving frequency cases into consideration. It's hard to conclude anything at this step. I would like to first try looking at (hopefully) only the 1F components of the analysis results with spectrum selection, and then apply the binning analysis on the 0.1267 Hz series tests for further investigations.


Attachment 4: diff_dispr2.pdf
  406   Wed Feb 8 13:45:44 2012 Giordon StarkDailyProgressCoating QBirefringence, Stress-Optic Coefficients

  This eLog will serve as a compendium of numbers I've found for helping with the calculation.

We're dealing with birefringence here, which means that our light splits into two rays, each of which experiences an index of refraction. The overall outcome we expect is that the net rotation involved is linearly dependent on the amount of birefringence / stress induced in the mirror.

We know from the stress-optic law (Copied the image from wikipedia)

R = Ct( \sigma_{11} - \sigma_{22})\

  • R - retardation (we denote it as delta)
  • C - stress-optic coefficient
  • t - thickness
  • σ is the first (σ11) and second (σ22) principal stresses

 Note: C is measured in Brewsters, retardation is defined as a difference in indices of refractions divided by the thickness. Cite (http://goo.gl/X6sae).

 From conversations with Zach, our calculations comes in two parts.

  1.  Determine how much stress exists when exciting the fused silica and use these principal stresses (unknown) in a calculation for retardation
  2. For a given level of retardation, figure out the amount of rotation involved

Here are numbers we've found. I've attached PDFs where relevant and otherwise linked to websites.

  • An IEEExplore paper cites Wikipedia (http://en.wikipedia.org/wiki/Fused_quartz#Physical_properties) for these numbers
  • From the PDF (Dispersion of Stress Optic Coefficient in Glasses)
  •  From the PDF (17 Optical Materials)
  • In the PDF (Birefringence Dispersion), there is another formula for determining - the stress optic coefficient for the material (in nm/cm/MPa) as  R = no3/2 * (q11 – q12) [Equation 3].
  • Results show a value of 35 +/- 1 at a wavelength of 633nm (our wavelength!)
  • This result is good because from (http://goo.gl/X6sae ;; slide 20) - we also have a relationship between stress-optic coefficient R and retardation (delta) as σ = delta/t*C.
  • From the PDF (The Stress-Optic Effect)


Attachment 1: Dispersion_of_the_stress-optic_coefficient_in_glasses.pdf
Dispersion_of_the_stress-optic_coefficient_in_glasses.pdf Dispersion_of_the_stress-optic_coefficient_in_glasses.pdf Dispersion_of_the_stress-optic_coefficient_in_glasses.pdf Dispersion_of_the_stress-optic_coefficient_in_glasses.pdf Dispersion_of_the_stress-optic_coefficient_in_glasses.pdf Dispersion_of_the_stress-optic_coefficient_in_glasses.pdf
Attachment 2: 17_optical_materials.pdf
17_optical_materials.pdf 17_optical_materials.pdf 17_optical_materials.pdf 17_optical_materials.pdf 17_optical_materials.pdf 17_optical_materials.pdf 17_optical_materials.pdf 17_optical_materials.pdf
Attachment 3: Birefringence_dispersion_in_fused_silica_for_DUV_lithography.pdf
Birefringence_dispersion_in_fused_silica_for_DUV_lithography.pdf Birefringence_dispersion_in_fused_silica_for_DUV_lithography.pdf Birefringence_dispersion_in_fused_silica_for_DUV_lithography.pdf Birefringence_dispersion_in_fused_silica_for_DUV_lithography.pdf Birefringence_dispersion_in_fused_silica_for_DUV_lithography.pdf Birefringence_dispersion_in_fused_silica_for_DUV_lithography.pdf
Attachment 4: The_Stress-Optic_Effect_in_Optical_Fibers.pdf
The_Stress-Optic_Effect_in_Optical_Fibers.pdf The_Stress-Optic_Effect_in_Optical_Fibers.pdf The_Stress-Optic_Effect_in_Optical_Fibers.pdf The_Stress-Optic_Effect_in_Optical_Fibers.pdf The_Stress-Optic_Effect_in_Optical_Fibers.pdf The_Stress-Optic_Effect_in_Optical_Fibers.pdf
  548   Fri Jul 20 11:44:42 2012 igalDailyProgressCrackleBlade Spring Eigenfrequencies (Damping On/Off)

 We investigated the eigenfrequencies and damping of the two blade springs we are using in our experiment using shadow sensors with LED lights:


We recorded the signals from the shadow sensors with the DAQ software for each of the two springs with and without the damping circuit. For Spring 1 (frequency = 2.08 Hz), we produced the following plots:

Blade1_DampOff.png  Blade1_DampOn_CloseUp.png

And the plot for Spring 2 (frequency  = 1.93 Hz):


We were only able to produce one plot for the second spring due to an error in the damping circuit which caused the spring to oscillate at a specific frequency, regardless of the damping gain.

It was expected to see that the springs are underdamped, especially when the damping circuit was off. In each case, we also plotted an exponential fit with the form Y = A*exp(-t / tau). For each of the three cases above, we attained the following values:

Spring 1, Damp off:  tau = 90s;

Spring 1, Damp on:  tau = 0.7s;

Spring 2, Damp off:  tau = 33s.

These values make sense. Although we used springs of similar spring constants, Spring 1 is attached to a lighter mass than Spring 2, thus yielding a lower tau value when the damping circuit was off.

  558   Wed Aug 15 23:25:47 2012 igalDailyProgressCrackleBlade displacement from drive signal

 Last week, Eric and I recalibrated the shadow sensors:

  • Shadow sensor A calibration factor: 3.71 V/mm
  • Shadow sensor B calibration factor: 4.04 V/mm.

We also measured the noise of the 0.1Hz low frequency sinusoidal drive from the function generator after being passed through the crackle circuit at various amplitudes:


Then, using an SR785, we obtained the transfer functions for each coil (shadow sensor signal / actuator signal):


Notice that there are two resonant peaks in each transfer function. This is because the oscillations of the two mass-spring systems are coupled by the seismic isolation stacks, which also oscillate. Consider the transfer functions of each blade when the motion of the seismic isolation stacks was suppressed:


For this reason, Koji proposed at our crackle meeting to suspend both masses from the same blade holder and to incorporate more and heavier seismic isolation stacks to decrease the stacks' resonant frequencies.

Nonetheless, I then used the data from the first four plots and the shadow sensor calibration factors to produce a plot of the displacement noise of each blade caused by the low frequency drive:


Ideally, we would have conducted all of these measurements with the system under vacuum. Unfortunately, after replacing the viton ring of the polycarbonate window and the optical fiber, the chamber pressure only goes as low as about 130Torr. It was concluded at the crackle meeting that we should replace the polycarbonate window with a metal flange.

  780   Thu Mar 20 23:32:41 2014 ericqSummaryCrackleBlade excitation leaking into Calibration

I've been getting distracted by all the things going on with the design of the new setup, and not taking enough data on the current one!

As we saw in an earlier layout, driving the blades too hard couples misalignment into the calibration line signal at harmonics of the drive frequency, which masquerades as a crackle section. When we changed the layout to be more symmetric, this alleviated the effect in large part, allowing us to drive the blades harder. 

However, I've been negligent in systematically determining just how hard we can reliably drive in the current setup without inducing big systematics. So, I set up an ever increasing amplitude, and looked at the fourier components of the calibration line height signal at harmonics of the drive frequency, and did it twice. 


Takeaway: the drive itself always shows up directly, whereas the 2F signal (which is where we traditionally look for force-proportional crackle) is fine until ~2k counts or so. The 4F seems fine throughout. 

However, what strikes me now, is that when we switch to the non-maraging steel blades, they are less stiff, meaning this amount of force leads to more displacement and more misalignment, so if I want to make a truly apples to apples comparison, maybe I need to stick to lower amplitudes?

Or, what I think I'll actually do: Use at least three low amplitudes that will work for the softer blades, but also do the highest amplitudes I can in the maraging blades to get the best upper limit I can. 

  781   Fri Mar 21 13:49:30 2014 GabrieleSummaryCrackleBlade excitation leaking into Calibration


Or, what I think I'll actually do: Use at least three low amplitudes that will work for the softer blades, but also do the highest amplitudes I can in the maraging blades to get the best upper limit I can. 

 Yes, this seems the right thing to do.

  222   Tue Jun 21 16:06:51 2011 Larisa ThorneDailyProgressCrackleBlade plots and Q/b calculation thoughts

I figured out how to plot the graphs given data points gathered by the oscilloscope.Results have been published below.... 

NOTE: there are two blades ("Romulus" and "Remus"). There are two plots per blade: the one with the noticeable sinusoidal shape will be used for Q calculation (see here), whereas the one which looks like a compressed version thereof helps us see how the amplitude of the oscillations decreases over time, exhibiting the "damped" motion, from which we will somehow calculation b.


I had an idea for calculating T1/2: if Amplitude( T1/2)/ Amplitude(t@0) = 1/2 . is true, then I just need to find a maximum in the y values (in the voltage data for the graph, since it is not a smooth function), find the closest minimum, then take the difference. This would give me some point near where the amplitude is at "zero". Then all that would have to be done is to find the corresponding x values (time, in seconds) to this maximum and middle "zero" point, and subtract these time values to get the T1/2 value. It's pretty tricky to implement in MATLAB.

Somehow that doesn't seem right though. If one tried to visualize that, wouldn't it seem like we were just measuring the time interval it takes to get through 1/4 of the wave's period? I don't think I understand what is meant by T1/2....

Attachment 1: Qspring3plot2.pdf
Attachment 2: Qspring3plot1.pdf
Attachment 3: Qspring3plot3.pdf
Attachment 4: Qspring3plot4.pdf
  870   Thu Dec 18 14:37:58 2014 GabrieleSummaryCrackleBlade properties

I checked the elastic deformation of the blades we have for the crackle2 suspension. I measured the deflection close to the blade tip when applying the same (unknown) load.

We have three different kind of blades with the same dimensions. The two blackened ones are marked A and B. We then have a v2 blade, and several v3 blades with serial number. Here are the deflection:

Deflection [mm]
A 57
B 58
v2 36
001 40
002 40
003 39
004 38
006 39
008 40
010 39
011 39
012 40

All the v3 blades show the same deflection within error, except maybe for SN 004.

  757   Wed Dec 4 18:36:02 2013 GabrieleDailyProgressCrackleBlade resonance measurements

 [Gabriele, Xiaoyue]

We took some time to measure the mechanical response of the two blades around the resonance frequency. We injected some common noise between 0.5 and 10 Hz and looked at the shadow sensor outputs.

We clearly see the first mode of both blades at about 2 Hz, and the second coupled one at 5 Hz. 


A quick fit gives the following poles and zeros (in Hz):


0.0083102 +     3.8822i
-0.045248 +     6.1484i
-0.002453 +     1.8849i
-0.013101 +     5.0392i
-0.054801 +     5.9915i


-0.01952 +     4.0533i
-0.078004 +     5.8236i
-0.017985 +     1.8791i
-0.018052 +     5.0409i
-0.14897 +     5.9551i

The resonance frequencies are pretty close.

  248   Wed Jul 20 11:42:52 2011 Larisa ThorneDailyProgressCrackleBlade spring waveform plots, set-up pictures

 As promised, the plots and set-up pictures are attached.


***Note: I have tampered with the plots. In the original data from the oscilloscope the domain (time axis) would have time= 0 seconds at the center of the plot, with negative times to the left and positive to the right. I changed it so that instead of starting with large negative values on the left, the plots begin at zero. This in no way affected the actual time values and intervals. 

***Note: I've also attached the original data, in the form of .xls files (they were .csv before). The numbers TEK00074-79 correspond with the plots I have attached in the order they appear.




--I will try to come back later and consolidate the plots as subplots on a single plot so this post won't be so long.

--Still working on curve fitting.


Attachment 1: IMG_2012.jpg
Attachment 2: IMG_2013withlaser.jpg
Attachment 3: TEK00074.xls
Attachment 4: TEK00075.xls
Attachment 5: TEK00076.xls
Attachment 6: TEK00077.xls
Attachment 7: TEK00078.xls
Attachment 8: TEK00079.xls
Attachment 9: Qwaveform1REM.pdf
Attachment 10: Qwaveform2REM.pdf
Attachment 11: Qwaveform3REM.pdf
Attachment 12: Qwaveform1ROM.pdf
Attachment 13: Qwaveform2ROM.pdf
Attachment 14: Qwaveform3ROM.pdf
  601   Thu Nov 1 17:20:16 2012 ericqDailyProgressCrackleBlade system characterization and more

I remeasured various blade characteristics, to be sure that the models I build of their transfer functions are accurate, and to balance them well. I also remeasured the shadow sensor calibration, since I use them in various ways.

  • Shadow sensors were calibrated with a blade and micrometer stage. Fit the data to an erf curve, linearize around half maximum. 
  • Resonant frequencies and Qs measured via shadow sensor ring down. Fit to damped oscillation.
  • Spring constants measured by adding known mass, observing change in shadow sensor signal. 
  • Actuator strength measured by applying constant voltage, observing change in shadow sensor signal. 

Blade A System


  • Shadow sensor calibration: 4.07 V/mm
  • Blade resonant frequency: 1.907 Hz
  • Blade Q: 62.6
  • Blade spring constant k: 473 N/m
  • DC blade response: 4.96 um/Vcoil


Blade B System


  • Shadow sensor calibration: 4.41 V/mm
  • Blade resonant frequency: 1.766 Hz
  • Blade Q: 55.6
  • Blade spring constant k: 548 N/m
  • DC blade response: 3.79 um/Vcoil 


Combining these measurements, I increased the final gain stage for blade B's actuator to 1.31x, compared to 1.0x for blade A. I then drove the blades with a .125Hz signal. Their oscillations were indeed of the same magnitude.

Upon locking and driving at the same amplitude as last week, the peak in the error signal noise spectrum at the drive frequency had gone down by a factor of ten. This is not as good as I had hoped, but still improvement. Undriven, the lock does not seem much different. However, I didn't spend much time looking at it, because I want to look at it under low pressure. 

Right now, the chamber is pumping down, as I hope that some of the noise last week was due to acoustics that the vacuum will minimize. However, so far it looks like pumping down screws up my alignment. Hopefully it will recover when I turn the pump off. 

Speaking to Rana last Friday, I learned more about how to properly filter the collected data, namely using a model of my loop (in terms of poles and zeros), rather than noisy data that I measured. Modeling the blades as harmonic oscillators is straightforward, as the poles are determined by the resonant frequencies and Qs. 

However, I am unsure how to model my servo in this way. By placing poles and zeros at the corner frequencies, I am able to reproduce the general shape of the transfer function, but not the right gains. I am sure there is a systematic way to do this, but I have not been able to find it yet. Basically, how does one translate a filter circuit into s-plane poles and zeros?

I've also taken some measurements of the laser's intensity noise as different spots. The fiber is definitely introducing a fair bit of noise. I want to examine it further, but since I have the chamber pumping down right now, I'll have to wait until after my next measurements. A while back, Dmass suggested that the way we're feeding through the fiber may be putting it under a lot of stress, and coupling it strongly to vibrations in the flange/chamber. 





  602   Fri Nov 2 07:15:04 2012 ericqDailyProgressCrackleBlade system characterization and more


Right now, the chamber is pumping down, as I hope that some of the noise last week was due to acoustics that the vacuum will minimize. However, so far it looks like pumping down screws up my alignment. Hopefully it will recover when I turn the pump off.  

The pressure got down to ~120 mTorr and I turned off the pump. The alignment stayed terrible (tiny fringe-to-fringe voltage). 

Not able to make any measurements, I brought it back to atmosphere, and it got even worse (no fringing).

  1196   Fri Aug 28 14:29:08 2015 GabrieleDailyProgressCrackleBlock 2 touching?

I continued my investigations to understand the glitches reported by Xiaoyue and investigated this morning.

In brief, I think one of the lateral magnets of block 2 is intermittently touching the OSEM, and this is causing the glitches.

You don't have to read below, but for educational purposes, here is the deduction flow that brought me to this conclusion.

First of all a premise, I first checked that all suspension shadow sensor signals were ok, but I didn't look carefully at the block shadow sensor signals. Maybe looking since the beginning at the block signal would have given some hints.

However, I looked at a spectrogram of the MICH error signal, and saw that the glitches were kind of irregularly spaced:

So I computed the band-limited RMS of this signal between 10 and 100 Hz, which seems a good region to identify the glitches. Looking at the time series of the BLRMS didn't tell me much. So i decided to identify the glitch times by selecting all samples of the BLRMS above a given threshold (kind of arbitrary since I didn't really calibrate the BLRMS). Then I checked for correlations between the glitch times and all suspension and block signals, in a way similar to what I did in the past, 1122. I couldn't find much.

So I made an histogram of the time interval between subsequent glitches. Excluding the single sample difference, which is an artefact of my analysis, I found something interesting:

Glitches are peaked at an interval of about 125 ms, which pointed me back to better check if this was related to any motion in the system.

Looking more carefully at the OSEM signals, I found that Y2 was suspiciously more noisy than Y1, and it seemed to have glitches at quite the same time. Here is a rough superposition of the spectrograms:

So I computed the BLRMS of Y1 and Y2 between 10 and 50 seconds, and confirmed that Y2 is much noisier than Y1 and non stationary:

Comparing the Y2 and MICH error signal BLRMS, one can see a very close resemblance:

At least quiet and noisy periods are conicident. Since I don't see this behavior in Y1, I tend to conclude that this coincidence is not due to the lock polluting the Y motion, but rather the Y2 signal witnessing something rubbing or touching in block 2, and then polluting the MICH signal. It's a very small effect, since we are able to lock the Michelson. 

Finally, to further convince myself, here is a comparison of Y1 and Y2 spectra. They are quite different:

  1398   Thu Feb 25 12:05:16 2016 GabrieleDailyProgressCrackleBlock coils (now) working

The correspondence of DAC channels and coils that I wired into the model turned out to be wrong. So I tracked down each DAC channel to the correspondind driven coil. I modified, compiled and installed the new model.

In the process I found that Z2 coil driver was not working. After a bit of work I found out that the output BUF634 was broken. This is likely due to a wrong connection of the Z1/Z2 connector going from the coil driver board to the mother board. This likely shorted the Z2 output and burnt the BUF634.

  997   Wed Jun 17 09:00:54 2015 GabrieleDailyProgressCrackleBlock z actuation

[Xiaoyue, Gabriele]

Yesterday we swapped the 270 ohm resistor in the coil driver output with a 51 ohm, to increase the dynamic range of the actuation for Z1 and Z2. We rescaled the uN to V calibration of both coil filtr banks and the damping was working again with the same gain.

Then we set down to measure the Z actuation transfer function, from force to displacement read with the OSEM. The result for one of the two blocks is shown in the picture below:

We expected a simple pendulum like resonance. However, we see a structure at about 0.6 Hz with produce a large phase rotation. Moreover, the slope at high frequency is closer to f^-4 than f^-2 and the phase shows a large rotation. If this is the true actuator response, it's not surprising that we couldn't lock.

We tried to understand the origin of this strange shape. The first thing we realized is that the blocks are 2.2 kg and they are actuated against the suspended breadboard which is about 20 kg, so the recoil is not neglegible. Indeed, when we drive the blocks, we see motion in all breadboard OSEMs. However, we don't understant yet how this can give us a f^-4.

We checked that the strange slope is not due to a direct electronic coupling of coil corretion to shadow sensor, as was happening in crackle1. The following plot shows in red what happens when we switch off the shadow sensor LED. In this case, at least, there is no signficant electronic crosstalk. We should check what happens when the magnet is blocked or when the magnet is completely out of the OSEM.


s suggested by Eric Q, we direclty connected the coil driver output to the shadow sensor board input (we bypassed the PD bias supply using the test points just before the whitening). In this way we could check that the loop response is flat as expected, and the total delay is of the order of 280 us.

Finally, here is a better measurement of the Z1 transfer function, using white noise an going to higher frequencies. The zero at 20 Hz and the transfer function flattening are very suspicious, since they're very similar to what we saw in crackle1 due to electronic cross talk.

At the end of the day, we had no conclusion. Moreover, the Z2 shadow sensor electronic board (which we never touched) stopped working. We replaced a burned OP27, that got very hot during operations, and a burned AD587. We tested the board on the bench and it seemed to be working. However, after putting it back in the box, it was not working and the OP27 got hot again. When the PD cable is connected, it seems that the board fails and drives all the other board signals to bad values. More investigations today.

  998   Wed Jun 17 10:54:17 2015 GabrieleDailyProgressCrackleBlock z transfer functions - more

The transfer function we measured yesterday and claimed was falling like f^-4 was taken between the COIL_OUT and the SENS_OUT. But the COIL_OUT is not calibrated in uN, since it's after the digital whitening and before the analog de-whietening. So basically to get the real transfer function we have to multiply with the digital whitening. This makes the slope less steep.

Indeed, the second measurement, up to higher frequency) was taken between COIL_IN2 and SENS_OUT, thus including all the right compensations of whitening. This transfer function can be quite well fitted with a simple second order system: the double pole gives us the resonance peak, and the double zero is used for the notch at 20 Hz. 

So I guess there is no mistery anymore in the actuation TF, since the high frequency flattening should be due to the direct electronic crosstalk from coil to shadow sensor. We should try to measure it by blocking the blade.

  1553   Tue Jun 7 15:41:04 2016 XiaoyueDailyProgressCrackleBlock2 damping oscillation

Y2 OSEM control seems to output large actuation and excite small, low frequency osillation. Z2 coil outputs are saturated. I don't see why this is happening... 


  1554   Wed Jun 8 15:08:35 2016 GabrieleDailyProgressCrackleBlock2 damping oscillation

Z2 coils are saturated because of a loop instability: the damping gain was too high. I reduced it from 1 to 0.2, and now damping works just fine. A gain of 0.5 is good too. It's not surprising that the damping gain is too large: we have the same coil/magnets, but the block mass is much smaller. Probably Z1 is marginal too.

The Y2 problem is related to the torsional mode of the block suspension, which I measured to be at 195 mHz. It looks like the damping is exciting this mode. Adding a 195 mHz notch in the damping filter bank solve the problem. My guess is that the Y1 magnet is not very well centered with respect to the block. Or maybe the suspension wire is not well centered with respect to the block. In both cases the result is a large coupling of Y force to Z torque.


Y2 OSEM control seems to output large actuation and excite small, low frequency osillation. Z2 coil outputs are saturated. I don't see why this is happening... 



  1555   Fri Jun 10 00:51:33 2016 XiaoyueDailyProgressCrackleBlock2 damping oscillation

Indeed Y1 magnet is seriously tilted and caused the 195 mHz oscillation problem. After centering this torsional mode went away -- we no longer need the 195 mHz notch for Y2 damping. I double checked other magnet positions, and recentered the board OSEMs carefully. The board balance changed slightly afterwards, but was easily counter weighted.


Z2 coils are saturated because of a loop instability: the damping gain was too high. I reduced it from 1 to 0.2, and now damping works just fine. A gain of 0.5 is good too. It's not surprising that the damping gain is too large: we have the same coil/magnets, but the block mass is much smaller. Probably Z1 is marginal too.

The Y2 problem is related to the torsional mode of the block suspension, which I measured to be at 195 mHz. It looks like the damping is exciting this mode. Adding a 195 mHz notch in the damping filter bank solve the problem. My guess is that the Y1 magnet is not very well centered with respect to the block. Or maybe the suspension wire is not well centered with respect to the block. In both cases the result is a large coupling of Y force to Z torque.


Y2 OSEM control seems to output large actuation and excite small, low frequency osillation. Z2 coil outputs are saturated. I don't see why this is happening... 




  881   Mon Jan 12 14:10:03 2015 GabrieleDailyProgressCrackleBlocks and beam aligned on Crackle2

This morning I finished the alignment of the second block of the Crackle2 system, using the positioner already mentioned by Xiaoyue. It consists of a translation stage with three degrees of freedom (to properly align the wire to the clamp and to adjust the vertical position of the block) and of a rotational stage (to adjust the wire rotation and the block yaw position).

Now both blocks are suspended and free. I also aligned the input laser beam to the two iris I installed previously, and proceeded with the alignment of the Michelson interferometer. Now the beam is hitting both suspended mirrors, and both the symmetric and antisymmetric beams are extracted and sent to the photodiodes. I didn't fine tune the alignment of the beams on the photodiodes. The reflections from the two arms are roughly overlapped.

  1203   Tue Sep 1 11:39:41 2015 GabrieleDailyProgressCrackleBlocks and suspension recentering

After I glued the X2 magnet back in the right position, block 2 looks good. So the message to take home is:

The magnet positions are important! The small change in the center of mass position due to a misplaced magnet is enough to counteract the recall force of the wire torsion, and make the block rotation around Z unstable.

Now all suspension OSEMs are centered. Instead of moving them to the center of the linear range, I purposely set them on a position giving a larger value: I'm trying to counteract (at least partially) the drift we saw during the last pump downs. If this drift is consistent, we should end up (after pump down) with better centered suspension signals.

I recentered the X2, Y2 and Z2 OSEMs, and as far as I can tell they are in good positions. No intervention on X1, Y1 or Z1.

I'm leaving the system undamped starting from 11:40 LT, to check if everything is free to move.

Looking at data from 12:10am to 1:10pm, I computed the attached spectra. All suspension signals and block signals look good:

  • the suspension signals show a whole bunch of undamped resonances, as expected
  • the block signals show similar resonances, and in particular there is no significant difference in the pairs of signals: X1 vs X2, Y1 vs Y2 or Z1 vs Z2
Attachment 1: block_signals.png
Attachment 2: suspension_signals.png
  1372   Fri Feb 5 18:02:01 2016 GabrieleDailyProgressCrackleBlocks suspended and OSEM installed and cabled

Today I suspended the two blocks and aligned them. It was much easier than in the past, thanks to the new blade clamps and the rotating block clamps. I also installed the OSEMs. Again, centering the magnets was easy, since now I can move them up and down without having to reglue them. Finally I installed the breakout board on the back of the breadboard and cabled all the OSEMs. Some wires were too long, and it was easy to shorten them. Some were too short, and with a bit more of effort I soldered some extensions. 

Attachment 4: 2016-02-05_17.49.06.jpg
  970   Fri May 8 17:50:14 2015 GabrieleDailyProgressCrackleBoard again sensed and damped

This afternoon I re-centered and re-aligned all the breadboard OSEMs and the block OSEMs. The board and the blocks seem free, there is no evident sign of anything touching anywhere. I could close all damping loops (both breadboard and blocks) without problems. I'm leaving all damping loops on.

I also re-installed the two folding/alignment mirrors on the laser breadboard and added a new mirror to send the beam into the suspended optical setup. For the moment being, the beam is just hitting the first mirror on the breadboard, roughly on the center. I didn't align it carefully into the Michelson yet.

  968   Mon May 4 18:31:38 2015 xiaoyueDailyProgressCrackleBoard sagging down

[Gabriele, Xiaoyue]

The fringes were becoming faster and the former lock scheme no longer works. Using the good part of single blade transfer function I measured, we fitted for the differential blade model, in unit of um/uN. Optical gain is calculated to be 5.61 mW/um using peak to peak SERV_IN1 reading of 0.95 mW. Using plant model -- multiplication of differential blade model and optical gain, in unit of mW/uN -- we designed in sisotool the new compensator. However using this lock filter we are still not able to lock the interferometer.

We start to question if there's anything really wrong with the alignment. By comparing the shadow sensor signals (blue curve damped, red undamped) with the locked ones (green) we clearly see a difference. Then we noticed the board is badly sagged probably due to creep, and is definitely touching down. We are going to re-adjust the OSEM positions to try solving this problem.

Attachment 2: blade_tf_vecfit.png
Attachment 5: compose.png
  1893   Fri Jan 15 10:57:39 2021 PacoLab InfrastructureEquipmentLoanBorrow AG4395A and EOM Driver TF re-tune

See equipment borrowing note here.

Attempting TF measurement for resonant EOM driver, but not having luck reproducing the measurements done recently (Dec-03), so I started debugging the circuit. Both power supply connections (+- 18 VDC) seem nominal. The MAX2470 buffer regulated input is nominal at 5VDC. Looking at MMBT5551 HF transistor, base-emitter voltage is -0.60 VDC (nominal wrt -0.66 V). Using a scope, I feed a single tone (36 MHz, 190 mVpp) and look at the RFmon output and it looks ok (gain ~ 1). I changed the RFmon SMA cable and that seemed to do the trick... Bad cable (now in trash) stole my morning.

Tune EOM driver resonance to 35.993 MHz (shown below for reference).

Attachment 1: EOMDriver_TF_Inp_to_RFMon_CloseUp_15-01-2021_160402.pdf
Attachment 2: EOMDriver_TF_Inp_to_RFMon_Wide_15-01-2021_151039.pdf
  158   Mon Aug 23 22:07:39 2010 JenneThings to BuySeismometryBoxes for Seismometer Breakout Boxes

In an effort to (1) train Jan and Sanjit to use the elog and (2) actually write down some useful info, I'm going to put some highly useful info into the elog.  We'll see what happens after that....

The deal:  we have a Trillium, an STS-2, a GS-13 and the Ranger Seismometers, and we want to make nifty breakout boxes for each of them.  These aren't meant to be sophisticated, they'll just be converter boxes from the many-pin milspec connectors that each of the seismometers has to several BNCs so that we can read out the signals.  These will also give us the potential to add active control for things like the mass positioning at some later time.  For now however, the basics only.

I suggest buying several boxes which are like Pomona Boxes, but cheaper.  Digi-Key has them.  I don't know how to link to my search results, so I'll list off the filters I applied / searched for in the Digi-Key catalog:

Hammond Manufacturing, Boxes, Series=1550 (we don't have to go for this series of boxes, but it seems sensible and middle-of-the-line), unpainted, watertight.

Then we have a handy-dandy list of possible sizes of nice little boxes. 

The final criteria, which Sanjit is working on, is how big the boxes need to be.  Sanjit is taking a look at the pinouts for each seismometer and determining how many BNC connectors we could possibly need for each breakout box.  Jan's guess is 8, plus power.  So we need a box big enough to comfortably fit that many connectors. 

  962   Fri Apr 10 16:28:31 2015 GabrieleSummaryCrackleBreadboard OSEM naming

  957   Mon Apr 6 18:41:37 2015 GabrieleDailyProgressCrackleBreadboard magnets in place

Xiaoyue, Gabriele

We glued all the six magnets used to control the breadboard, in the foreseen position. To install the two magnets that will be used to control vertical and roll, we machined two triangular aluminum supports our of some scrap metal we had in the lab.

We checked that all OSEMs can be installed in position without interferences.

  1303   Tue Oct 6 14:49:57 2015 GabrieleMiscCrackleBreadboard picture as of October 6th 2015

  1376   Wed Feb 10 15:34:52 2016 GabrieleDailyProgressCrackleBreadboard suspended from the roll-decoupling stage

[Xiaoyue, EricQ, Gabriele]

We suspended the breadboard from the roll decoupling stage, and suspended the latter too. We're using two tall posts as a temporary frame, see pictures. With the blocks clamped, we could easily balance the whole things, making the breadboad vertical. For the roll balancing, we decided to add some counterweights, instead of fine tuning the position of the suspension point. For the pitch balancing, we adjusted the position of the breadboard on the central suspension beam.

The roll resonant frequency is about 350 mHz.

However, when we realease the blocks, the previous balancing is no more good, and we weren't able to find a new balanced position yet. We decided to stop and think about the problem, to see if there is something fundamental we're missing here.

  933   Wed Mar 4 03:29:30 2015 xiaoyueDailyProgressCrackleBreakout cables

I soldered the breakout PCBs according to Gabriele's design. In addition to cabling all the 2-pin connectors, I cut the translational stage cable and resolder it to the 4-pin connector.


I mounted the board to the back of the optical breadboard and connected it to another board on the table using the 26-pin ribbon cable. I tested that the translational stage is working properly. The damping loop are also working, except that Z1 is reading ~1700 (max) no matter how I change the position of OSEM. The LED's are all on so there must be something wrong with Z1 PD. I still need to cut and solder the power supply for the AP/SP PDs.



  954   Sun Apr 5 23:52:49 2015 xiaoyueDailyProgressCrackleBreakout cables 2

I finished connecting all OSEM input /output cables to the breakout cable. 

Attachment 1: IMG_3323.jpg
  714   Fri Aug 16 18:37:56 2013 GiorgosDailyProgressSUSBringing Sensors closer to Plate, Correcting Offset and Gain

Yesterday, we tried levitating for one degree of freedom; we failed. The plate would move back and forth the equilibrium, but not settle there for more than a second. Haixing suggested moving the sensors closer to the plate, so that our signal is larger. This way, we can be less sensitivity to noise. However, that entails that we recalibrate the HE offset, the cross coupling measurement and the gains of our feedback loop.

So, today we moved the AC1, AC2, AC3 sensors closer to the plate and removed the DC1, DC2, DC3 sensors from our setup, since they are of no use. We also replaced the 91 gain of the HE sensors with a gain of 11 (11k and 1k are the resistors we used).
Then, we measured the response of the HE sensors and found that the signal produced changes by about 120mV for each mm; that is about a factor of 6 better than before.

Since the sensors are now at a different location, they have a different voltage offset; this should be larger since they are now closer to the levitated plate. To measure the new offset, we moved the motors such that the equilibrium would lie between the top and bottom motors. Then, we measured the offset reading of the sensors when the plate was stuck at the top and at the bottom and averaged the two. We used our measurements and, by taking into account the offset we had already applied in the first place, we replaced the resistors in our circuit such that the offset of the AC1-3 sensors would be no greater than 50mV. For AC1: R1=6.2K, R2=5.1K, for AC2: R1=13K, R2=11K, for AC3: R1=20K, R2=16K.

  1495   Thu Apr 14 18:04:14 2016 GabrieleDailyProgressCrackleBug in auxiliary control loop medm screen

I just realized that the order of the block OSEMs in the AUX control screen is wrong. 

The screen says X1 X2 Y1 Y2 Z1 Z2 but instead it is X1 Y1 Z1 X2 Y2 Z2

This might explain why the common mode damping wasn't working very well.


  830   Sat Aug 16 17:16:05 2014 xiaoyueDailyProgressCrackleCOMSOL simulation

I used COMSOL to compute the stress distribution on our blades. I set fixed constraint and a boundary load on the block clamp surfaces as demonstrated in the figure. In simulation I used extremely fine free tetrahedral mesh. The first principle stress contour is plotted. We see that we have large amount of blade areas that are bearing stress over 80% of the micro mechanical yielding (~250 MPa).


  1180   Wed Aug 26 09:37:21 2015 GabrieleDailyProgressCrackleCPU overload

That was likely a syncronization problem. I checked the BIOS settings, and they are still ok.

I applied the standard procedure in computer science: power down the cymac and boot it again, and there has been no CPU overload in 5 minutes.


 I found the excitations come and go. I checked the GDS and found the CPU overloaded now and then. I don't have clue how to solve the overloading problem...


Attachment 1: 44.png
  666   Sat Jul 13 18:31:30 2013 ericqDailyProgressCrackleCYMAC Lock achieved

The Crackle IFO has been locked with a CYMAC digital loop 

UGF is a little under 100Hz. This can and will be improved tomorrow. Damping was fairly straightforward to get working nicely. Getting the right TF for michelson locking took some fiddling. Now that I can mess around with arbitrary filters, the 38Hz wiggle that annoyed me before was easy to deal with. With some integrators, the RMS of the error signal is much, much, smaller than ever seen with the analog loop. 

There's still this odd feature around 150-200Hz that I think is the current culprit for instability as I try to up the gain (last seen in ELOG 636), and I plan on tackling it head on tomorrow. 

In the meantime, I took a spectrum to compare with results from June, as a sanity check. It shows some excess noise under 100Hz, but corresponds well after that. 


Once I get the UGF to a few hundred Hz, it's full steam ahead, driving the blades in common mode and hunting for crackle!


  668   Mon Jul 15 21:45:17 2013 ericqDailyProgressCrackleCYMAC Lock achieved

Some further details; here's what lock acquisition looks like on the error signal. Just before t=10, the main servo is switched on. At t ~ 12, the low frequency boost is engaged to squash the ~6Hz motion. At t ~ 14 I turn off the shadow sensor damping, which takes out some broadband-ish noise above 100Hz. 


My model of the Loop TF doesn't correspond too well right now. Foton has some rolloff in the phase of the servo in the hundreds of Hz regime, which MATLAB doesn't show with the same arguments. I'm presuming this is due to RCG limitations, and figure this is the reason for the phase discrepancy above ~200Hz. However, I'm not really sure about the pretty big disagreement at 50Hz. I'll check it out tomorrow. 


  1086   Thu Jul 23 15:44:17 2015 GabrieleMiscCrackleCable reference

[Xiaoyue, Eric, Gabriele]

Presently we have four cables coming out of the chamber.

  • Cable 1 (26 pins) comes from the suspended breadboard and carries the six block OSEM connections (LED, PD and coils), the AP/SP photodiodes power supplies and signals, and the M4 translation stage connections. All wires are used
  • Cable 2 (26 pins) comes from the breakout board on the chamber floor and carries the six suspension OSEM connections (LED, PD and coils). Only the first 16 wires are used
  • Cable 3 (4 pins) comes from the suspended breadboard and carries the signals for the M3 picomotor

The pinout of the 26 pins cables are the following

Pin 1 coil common ground
Pins 2-7 coil signals
Pins 8-9 LED power supplies
Pin 10 OSEM PD common ground
Pin 11-16 OSEM signals
Pin 17-19 Thorlabs photodiodes power supplies
Pin 20 Thorlabs photodiodes common ground
Pin 21-22 Thorlabs photodiode signals (21 AP, 22 SP)
Pin 23-26 Translation stage

We are going to redistribute this on the three DB25 connectors in the feedthough and on one DB9:

DB25_1: Cable 1 pins 1-16 (blocks OSEMs)
DB25_2: Cable 2 pins 1-16 (suspension OSEMs)
DB25_3: Cable 1 pins 23-26 (translation stage) and Cable 3 (picomotors)
DB9_1: Cable 1 pins 17-22 (photodiodes)

  1215   Wed Sep 9 22:26:35 2015 XiaoyueDailyProgressCrackleCables cleanup

Today I shortened all the OSEMs, translational stage, and picomotor wires to the right lengths to clean up the back of the optical board:

I built new connectors using the magical cable insertion tool introduced by Federico, which saved me from soldering in the chamber!

Before we have individual flat cable for picometer. Now I am trying to integrate the 4 wires to the breakout PCB as we have pin 17 ~ 22 available. I labeled the two white, two black cables as 1, 2, 3, 4, and they are going to be connected to 19, 17, 20, 18 to keep the connection, with 18 ~ 20 going to the feedthrough as the 4-wire flat cable before, and 18 would work as the red reference wire.

The next step is to wire up the PD power supply and output to a flat cable that can be clamped through the stages.

  1210   Thu Sep 3 08:21:09 2015 XiaoyueDailyProgressCrackleCabling for new PD installation

We are going to use the 6 cables for the Thorlabs PDs for new PDs wiring. I plotted a schematics to show how the diodes are going be connected from board to the electronic box:

  1389   Thu Feb 18 17:25:29 2016 GabrieleSummaryCrackleCabling on bread board back

Here is how the OSEMs are cable to the breakout board on the back of the suspended breadboard:

D1/C1 = Z1 (left looking at the front of the bread board)

D2/C2 = Z2 (right looking at the front of the bread board)

D3/C3 = X1

D4/C4 = X2

D5/C5 = Y1

D6/C6 = Y2

  1387   Wed Feb 17 17:00:54 2016 GabrieleDailyProgressCrackleCabling work

This morning I made and pulled the power supply cable, from the Cymac rack to the optical table.

I also prepared the four 25' long STP (shielded twisted pair) cables and connected three of them to the ADC board on one side. More to come tomorrow.

  389   Mon Jan 30 04:38:14 2012 Giordon StarkDailyProgressCoating QCalculated Noise Measurements of Photodiodes, Preamp Setup

Attached a lot of things - the PDF contains an updated list of parts with links to part specifications. We're still missing information (or would like more information) about the following parts that we currently have:

  • vacuum
  • polarizing beam splitter
  • QWP and HWP

The PDF also describes the calculated noise shown in ComparisonOfNoise.png. We found that the noise expected from each photodiode is 7.6e-8 -- coming out of the preamp would have a noise of 7.6e-8 * sqrt(2) [factor from the combination of the input photodiode signals]. Everything seems to be on the up and up - but I will talk with Zach (and Rana if he's around) about what we've got here.

Talked with Zach after everything on Friday - here's a brief discussion of what we talked about on the whiteboard using markers that contained all the colors of the rainbow.

  • Step 1: Once we get the ESD and the sample, we're going to look at the output and compare it with the drive frequency so that we expect to see oscillations
  • Step 2: Then, we'll excite the sample and then let it decay and observe a decaying sinusoidal on the oscilloscope
  • Step 3: Then, we'll add in the lock-in amplifier and tune it so that we effectively chop off most of the signal (in a perfect case, we see no more sinusoidals, and simply just a decay curve)
  • Step 4: ???
  • Step 5: Win a senior thesis


Attachment 1: NFLR.png
Attachment 2: NOLSR.png
Attachment 3: PDA36A.png
Attachment 4: LaserNoiseComparison.png
Attachment 5: LaserNoiseResiduals.png
Attachment 6: ComparisonOfNoise.png
Attachment 7: ExperimentalSetup.pdf
ExperimentalSetup.pdf ExperimentalSetup.pdf ExperimentalSetup.pdf ExperimentalSetup.pdf ExperimentalSetup.pdf
Attachment 8: ExperimentalSetup.png
  640   Wed Jun 19 11:42:51 2013 ericqHowToCrackleCalculating Frequency Noise

I want to include laser frequency noise in my noise budget, so we discussed making a very asymmetric Michelson in yesterday's meeting, to try and make a measurement of the laser I'm using. I sat down to do the calculation of relating the PD voltage PSD to frequency noise, but tripped up a bit. Looked for references, and couldn't find anything that didn't dive straight into optical cavities, etc. I realized that a Michelson is essentially a delay line, and found an old HP doc called "Phase Noise Characterization of Microwave Oscillators" which talks about delay lines.

The key difference was that I was initially modeling frequency noise as f(t)=f0 + df(t), whereas using a field that oscillates as sin(2 pi f t + d phi (t)) is much more fruitful. 

I translated the math into things I'm used to thinking about and wrote a quick note which I'm attaching here. Once we get the lab cleaned up after the hold drilling, I'm going to set up a measurement to quantify the frequency noise of my laser. 



Attachment 1: freqnoise.pdf
freqnoise.pdf freqnoise.pdf
ELOG V3.1.3-