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ID Date Author Type Category Subject
  255   Mon Jul 25 15:07:56 2011 Larisa ThorneLab InfrastructureGenerallab 050

 The lab floor is being mopped tomorrow. Perhaps this would be a good time to clean/put stuff away? (I did start on this a little last week, but much can still be done)

  254   Mon Jul 25 12:33:58 2011 Larisa ThorneDailyProgressCracklediagram, with magnetic actuators

[Seiji, Larisa, Vanessa]


Attached is an update on the diagram for the blade crackling experiment. This includes the magnetic actuator (solenoid and Nd magnet configuration driven by a sinusoidal source), as well as a few SR560s and an SR780 which are used to modify (using filtering and gains) and test the signal produced by "shadow-blocking" the laser beam path by an oscillating mass attached a blade.

NOTE: we did not use the full Michelson set-up. This configuration uses shadow-blocking of a single mass oscillating.

Attachment 1: TRmagnetic2circuit.jpg
  253   Sun Jul 24 17:32:18 2011 Vanessa AconDailyProgressCrackleNoise Budget

 Another update on the crackling noise budget:

I've taken out the table-mirror vibration noise from the gyro lab data.  We thought a more accurate reading would come from the PZT setup's total noise plot, since that setup involved a beam splitter and two mirrors on the table.

The shot noise has been recalculated such that now instead being sqrt(2*h*f*P) where P is a constant, P is a cos(kx)^2 function, where x is the difference between the two beam path lengths, Ly-Lx.  Also, the conversion from power to meters is done by defining the signal-to-noise ratio as "gain (derivative of the power function dP/dx)" divided by "shot noise plus electronic noise," finding at what x value that ratio is optimized, then finding dP/dx at that value.  This did not change the value of the shot noise by much, however.  It only added sudden downward spikes because it is a square root of a cos(kx)^2 function on a log scale.  I think Rana said that it should be on the order of the seismic noise, so I'm not sure if it is correct as it is.

I have also changed the seismic noise such that instead of adding the noise from both springs in quadrature, I subtracted one from the other, since they should be somewhat correlated and because the path length difference is what matters in the end.  As an upper limit on the seismic noise, I still plotted the noise from one of the springs.

I have taken intensity data for the laser as well.  I shined the laser directly on the photodetector and recorded the power spectrum, and then took the DC voltage reading of the laser with the oscilloscope.  By dividing the power spectrum values by the DC Voltage, I got a relative intensity spectrum.  I then used the conversion factor from volts to meters (assuming we are at the steepest part of the Volts vs Ly-Lx plot, again) to get a spectrum in m/sqrt(Hz).

Also I changed the resonant frequency numbers a bit to match the data Larisa took, so now the resonant frequencies are 2.08 and 2.09 Hz.


Additionally, yesterday Seiji, Larisa, and I took readings from the magnetic actuator - blade spring setup to get a transfer function for the magnetic actuator, and setup a feedback loop to damp the system (more on this later).

Attachment 1: totalnoiseplot05.png
Attachment 2: totalnoiseplot.m
%%Total Crackling Noise Budget

% %%mirror vibration noise========================== =======================
% load gyro_mirror_noise.mat %note mirror (table) vibration noise is from gyro lab data (Alastair)
% f_mech_noise = gyro_single_arm_noise_calibrated(:,1); % frequency vector for plotting mechanical noise
% SA_x_noise = gyro_single_arm_noise_calibrated(:,2); % gyro single-arm noise calibrated to meters
% SA_x_noise2 = (SA_x_noise)*2*sqrt(2); %double mirror displacement to get noise in laser path length
% DA_x_noise = sqrt((SA_x_noise2).^2+(SA_x_noise2).^2+(SA_x_noise2).^2); %add noise from two mirrors in quadrature and beam splitter to get total incoherent noise in laser path system

... 164 more lines ...
  252   Sat Jul 23 17:22:01 2011 haixingDailyProgressSUSmatching the magnets

Yi Xie and Haixing,

We used the Gauss meter to measure the strength distribution of bought magnets, which follows a nice Gaussian distribution.
We pick out four pairs--four fixed magnets and four for the levitated plate that are matched in strength. The force difference is
anticipated to be within 0.2%, and we are going to measure the force as a function of distance to further confirm this.

In the coming week, we will measure various transfer functions in the path from the sensors to the coils (the actuator). The obtained
parameters will be put into our model to determine the control scheme. The model is currently written in mathematica which can
analyze the stability from open-loop transfer function.

  251   Fri Jul 22 12:47:54 2011 Larisa ThorneLab InfrastructureGenerallab equipment

I took the liberty of tidying up the Crackling table a bit.

The Cryo people left us a friendly reminder to "get our own shit": they had found many parts from their own experiment being used or lying around on our Crackling table. Parts belonging to the Cryo experiment are labeled with a dot of gold nail polish. I'm fairly sure I found, switched out and put away all these gold-dotted parts that were lying around on our Crackling table as I was cleaning up.

  250   Fri Jul 22 12:36:49 2011 Larisa ThorneDailyProgressCracklemagnetic actuator set-up notes

 Attached is the promised circuit diagram, describing what was done yesterday in terms of configuration. 

A few notes on the diagram:

  • The oscilloscope was hooked up in order to see the physical signal that was coming from the source and the signal that was seen by the photodetector (produced by the motion of the mass moving across the laser beam path)
  • The laser used in the experiment was one of the two HeNe lasers on the Crackling table (so lamda~633nm)
  • For those of you not familiar with what the SR780 is: a network signal analyser. This is an older machine taken from the (defunct?) LIGO lab in the High Energy Physics building, which Tara retrieved for the use of crackling experiments. It was used to measure the transfer function (of signal inputs B/A), using the Bode window type over the range of frequencies 1-10Hz.
  • Again, for those of you not familiar with the SR560: we used it to get rid of the DC offset in the signal. The SR560 contains a bandpass filter with corner frequencies 0.03-300Hz (well outside the frequency range of interest by a factor of 30 on each extreme), boosts the output signal by a gain of 10, and uses DC coupling.


New magnetic actuator configuration notes:

  • I soldered the wire ends of the solenoid to a couple of wires that had a BNC connector on the other end (see last image in this last post)
  • We calculated the resistance of the solenoid to be R=11.3 Ohms (11.7 total - 0.3 for the cables on the multimeter)
  • The inductance of the solenoid was found to be L=254uH

More to come later this afternoon...


Attachment 1: TFmagneticcircut.jpg
  249   Thu Jul 21 23:09:02 2011 Larisa ThorneDailyProgressCrackleUPDATE: experiment setup

 [Seiji, Larisa]

Seiji and I went down to the labroom to start working on the setup. What we put together obviously isn't the final version (see super sketchy pictures below), but it was enough to begin measuring the transfer function of a "one-armed Michelson configuration with the magnetic actuator driving the blade spring." We did not record any of the data gathered, as it was only a test/preliminary run. A final version will be run tomorrow afternoon, and I will publish the results thereof.


So for now, content yourselves with pictures of the experiment thus far.

Attachment 1: IMG_2014.JPG
Attachment 2: IMG_2016.JPG
Attachment 3: IMG_2017.jpg
Attachment 4: IMG_2019.JPG
Attachment 5: IMG_2015.JPG
Attachment 6: IMG_2020.JPG
  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
  247   Tue Jul 19 19:53:31 2011 Larisa ThorneDailyProgressCracklerepeat Q experiment

This is a repeat experiment of what was done here.

The difference this time was that instead of letting the HeNe laser path bounce off the bottom side of the hanging mass, I adjusted the path so that it would hit the corner of the clamp holding the hanging mass to the blade itself. The advantage to this is that there motion there is mostly "spring" motion, not "pendulum" motion with multiple modes that we do not want included. The disadvantage is that the motion will be much less (smaller), but this is negligible in light of the advantages. Also, the clamp is affixed slightly closer to the free end of each blade during the experiment.


I will attach the data, graphs and pictures of the setup at a later time. 

Once I have published these, I will continue to work on 'curve fitting' these to solve for the Q values of both blades. This involves guessing a similar curve function and comparing it to the data points, as well as the use of the 'fminsearch' function in MATLAB. More on this when I figure it out...all I have currently is a bunch of error messages...

  246   Tue Jul 19 15:56:07 2011 Larisa ThorneDailyProgressCracklelab 050

 Lab room phone: (626) 395-3877


Also, does anyone know the password for the lab room computer? It's the one that says "controls for dhcp-123-221.caltech.edu"

  245   Mon Jul 18 11:40:24 2011 Larisa ThorneDailyProgressCracklediagrams (for reference) and update on Q calculations

 Posted below is a better picture of the Romulus blade mass-mirror configuration, where one can clearly read the dimensions.


With respect to Q calculations: I spend much time trying to figure out how one would best do this. Rana lent me a book ("Data Reduction and Error Analysis for Physical Sciences"), and I also tried referencing a copy of "Numerical Recipes" from the 1980s. First, I tried searching for curve fitting methods, for which both the books agreed that some 'least squares' method would work. Then I realized that it wasn't the damped motion we wanted fitted: we wanted an equation to describe a line going through all the local maxima data points of the damped spring motion. That's when I got stuck and neither of the books proved helpful....much Internet research ensued...

I finally came across something called the "log decrement" method, which looked promising, and calculated my Q (~10^4). The only problem I have now is wondering whether the calculated result is reasonable; there are no tables or charts I could find that would tell me what range of Q values I should be expecting. The only useful information I could find said that tuning forks have a Q~10^3. The highest Q values I could find (in an attempt to get some idea of what the range of Q values are) was in high Q lasers and atomic clocks valued at Q~10^11. 


I would really appreciate some feedback, as I have been looking for Rana or Tara since this morning and can't find them.

Attachment 1: massmodel4-m1.jpg
Attachment 2: massmodel4-m2.jpg
Attachment 3: massmodel4-m4.jpg
  244   Fri Jul 15 14:04:27 2011 Vanessa AconDailyProgressCracklemagnetic actuator notes

 Fixed my calculations from my previous post.  Hopefully they are correct now.

Calculated the magnetic force on a small magnet at the end of a solenoid (approximating the magnet as a dipole with magnetic moment mu).

Attachment 1: magnet_calculations.pdf
magnet_calculations.pdf magnet_calculations.pdf
  243   Fri Jul 15 10:12:01 2011 Vanessa AconDailyProgressCracklemagnetic actuator notes

The magnet should be placed so that it is half out of the coil. At the mouth of the coil, you get a strong field gradient so you ought to calculate the force at that point. Then remember that the max current we can supply is 100 mA before the coil starts getting warm.

  242   Thu Jul 14 11:24:49 2011 Vanessa AconDailyProgressCrackleNoise Budget

 I've updated the thermal and seismic noise to reflect both blade springs, changed the thermal noise such that it uses the full fluctuation-dissipation theorem, and added some notes about where each piece of data came from.   

 The plot below is zoomed in from the previous one to 10Hz-100Hz.



Things we should think about:

Where our noise / sensistivity requirement is

How chopping / averaging will affect our sensitivity (it should improve it)

Recalculate / check our Q and w_0 values (these ones I found were approximate and from a different mass at a different distance along the blade spring, and Q differs very much from Tara's earlier measurements)







Attachment 1: totalnoiseplot04.png
Attachment 2: totalnoiseplot.m
%%Total Crackling Noise Budget

%%mirror vibration noise==========================
load gyro_mirror_noise.mat %note mirror (table) vibration noise is from gyro lab data (Alastair)
f_mech_noise = gyro_single_arm_noise_calibrated(:,1); % frequency vector for plotting mechanical noise
SA_x_noise = gyro_single_arm_noise_calibrated(:,2); % gyro single-arm noise calibrated to meters

SA_x_noise2 = (SA_x_noise)*2*sqrt(2); %double mirror displacement to get noise in laser path length
DA_x_noise = sqrt((SA_x_noise2).^2+(SA_x_noise2).^2+(SA_x_noise2).^2); %add noise from two mirrors in quadrature and beam splitter to get total incoherent noise in laser path system

... 108 more lines ...
  241   Wed Jul 13 18:51:45 2011 Vanessa AconDailyProgressCrackleNoise Budget

I added the noise spectra for thermal noise in the blade springs, shot noise, and seismic noise from the table affecting the blade spring (seismic noise is from Tara's data).  My code and plot are attached.

I will upload them to SVN once I figure out how to do so.


Tara: The seismic data was measured on the optical table in PSL lab.

The seismic noise is calculated from a simple model of a mass-spring system using f0 (resonant frequency) and Q from previous measurement.

You have to add seismic from both blades which have different f0 and Q.

DO NOT forget to mention that the noise measured in the plot are from different setup ( metal shim instead of steel blade).

Attachment 1: totalnoiseplot.m
%%Total Crackling Noise Budget

%%mirror vibration noise==========================
load gyro_mirror_noise.mat
f_mech_noise = gyro_single_arm_noise_calibrated(:,1); % frequency vector for plotting mechanical noise
SA_x_noise = gyro_single_arm_noise_calibrated(:,2); % gyro single-arm noise calibrated to meters

SA_x_noise2 = (SA_x_noise)*2*sqrt(2); %double mirror displacement to get noise in laser path length
DA_x_noise = sqrt((SA_x_noise2).^2+(SA_x_noise2).^2+(SA_x_noise2).^2); %add noise from two mirrors in quadrature and beam splitter to get total incoherent noise in laser path system

... 96 more lines ...
Attachment 2: totalnoiseplot03.png
  240   Wed Jul 13 13:05:30 2011 Vanessa AconDailyProgressCracklemagnetic actuator notes

 A quick calculation of the force from a solenoid on a small magnet (which we approximate as a dipole), from which we can find the dimensions and the number of coils for the solenoid we need (not sure if it is correct; will think more on it later).

Attachment 1: magnet_calculations.pdf
  239   Wed Jul 13 12:57:13 2011 Vanessa AconDailyProgressCrackleNoise Budget Update


 Using the approximate noise for vibration in the mirrors from Alastair's post, I have attached an updated noise plot with m/sqrt(Hz) on a log scale vs. Hz on a linear scale.

 Update: I've replotted the noise spectra, now with frequency on a log scale as well.

Attachment 1: totalnoiseplot02.png
  238   Wed Jul 13 12:08:20 2011 AlastairDailyProgressCrackleNoise Budget Update

loglog plots please.  Use the matlab loglog function instead of plot.



 Using the approximate noise for vibration in the mirrors from Alastair's post, I have attached an updated noise plot.


  237   Tue Jul 12 06:16:22 2011 Vanessa AconDailyProgressCrackleNoise Budget Update

 Using the approximate noise for vibration in the mirrors from Alastair's post, I have attached an updated noise plot with m/sqrt(Hz) on a log scale vs. Hz on a linear scale.

Attachment 1: totalnoiseplot01.png
Attachment 2: gyro_mirror_noise.m
load gyro_mirror_noise.mat
f_mech_noise = gyro_single_arm_noise_calibrated(:,1); % frequency vector for plotting mechanical noise
SA_x_noise = gyro_single_arm_noise_calibrated(:,2); % gyro single-arm noise calibrated to meters
SA_x_noise2 = (SA_x_noise)*2*sqrt(2); %double mirror displacement to get noise in laser path length
DA_x_noise = sqrt((SA_x_noise2).^2+(SA_x_noise2).^2+(SA_x_noise2).^2); %add noise from two mirrors in quadrature and beam splitter to get total incoherent noise in laser path system
semilogy(f_mech_noise,DA_x_noise); %plot seismic noise in mirrors on table in m/rHz vs Hz
%if we include beam splitter vibration
Attachment 3: mirror_vibration_noise.pdf
mirror_vibration_noise.pdf mirror_vibration_noise.pdf mirror_vibration_noise.pdf
  236   Mon Jul 11 16:27:16 2011 AlastairHowToCrackleMechanical noise in mirrors on bench

 This is some data measured in the ATF (by Zach) for 2 fixed mirrors on the bench, and gives some idea of what mechanical vibration noise you can expect.  You'll need to scale this for the number of mirrors in your own setup.  You can add this to your noise budget by including the following lines in your Matlab code:

load gyro_single-arm_noise_calibrated.txt;

f_mech_noise = gyro_single_arm_noise_calibrated(:,1); % frequency vector for plotting mechanical noise

SA_x_noise = gyro_single_arm_noise_calibrated(:,2); % gyro single-arm noise calibrated to meters

Attachment 1: gyro_single-arm_noise_calibrated.txt
   0.0000000e+00   2.0469258e-08
   7.8125000e-03   8.4330202e-08
   1.5625000e-02   2.8045726e-08
   2.3437500e-02   9.9272147e-09
   3.1250000e-02   8.0219609e-09
   3.9062500e-02   6.7856215e-09
   4.6875000e-02   6.7199016e-09
   5.4687500e-02   5.4151612e-09
   6.2500000e-02   4.6216977e-09
   7.0312500e-02   5.2115742e-09
... 999991 more lines ...
  235   Mon Jul 11 14:28:51 2011 JenneDailyProgressCrackleFinal draft: mass-mirror system design (Romulus blade)


 I am not very familiar with screw names/designations, and though I did estimate the diameters and lengths for my mass calculations, maybe someone who is can help me find/acquire longer ones?

NOTE: I realize the picture is crappy, but I included it just to give an idea of what I'm looking for...this one makes a hole 0.4cm in diameter, has a ~0.65cm diameter head, and currently has a 0.9cm long threaded end...whereas I'm looking for something that's perhaps >1.0cm, so that a nut can be used to secure it in place.

 Random guess based on the picture, but maybe that's a #4-40 x 1/2"?  All screws should be Imperial, not Metric.  I know it's dumb, but it's how we roll.

  234   Thu Jul 7 14:37:58 2011 Larisa ThorneDailyProgressCrackleFinal draft: mass-mirror system design (Romulus blade)

 This is a followup on previous post....


This is the final version of my design for the "Romulus" blade spring's mirror-mass system. 

I took into account the 'holes' in the masses that will be filled by screws (whose masses have a negligible effect on the system), and the total calculated mass of the system modeled in the attachment, plus the mirror mount+mirror, comes to ~1370.722794g, which is very close to the desired ballpark estimate of 1350g needed to bend the Romulus blade parallel to the plane of the optics table. The extra ~20g won't affect the configuration's effectiveness, because the mirror mount allows for many degrees of freedom, thus we can tilt it to compensate for the extra mass.


The only other thing to consider is the screws that will be used to affix the end mass cap to the aluminium strips, and the aluminium strips to the mirror mount. I found some in the lab room (see picture below), but found them too short to be really useful in the configuration designed... I am not very familiar with screw names/designations, and though I did estimate the diameters and lengths for my mass calculations, maybe someone who is can help me find/acquire longer ones?

NOTE: I realize the picture is crappy, but I included it just to give an idea of what I'm looking for...this one makes a hole 0.4cm in diameter, has a ~0.65cm diameter head, and currently has a 0.9cm long threaded end...whereas I'm looking for something that's perhaps >1.0cm, so that a nut can be used to secure it in place.

Attachment 1: massmodel3.jpg
Attachment 2: IMG_1987.JPG
  233   Wed Jul 6 14:29:19 2011 ranaMiscCrackleSimulation of Crackling Noise


I wanted to explore the difference between 2f and 4f demodulation and so I wrote my own crackle code (attached).

There are 2 crackle coefficients: the first one is proportional to the applied force. Since we are driving below the blades resonant frequency, the blade's nominal displacement is just directly proportional to the force.

The second coefficient is proportional to the derivative of the applied force and also the velocity of the blade.

The top-right plot shows the noise in the michelson: each of the crackle terms as well as shot noise.

Finally, the bottom left shows the output of the 2f and 4f demodulators. You can, yourself, change the stress and jerk coefficients in the code to see how it changes the demod outputs.

Attachment 2: cracklecode.zip
  232   Tue Jul 5 15:06:56 2011 Larisa ThorneDailyProgressCrackleMass-mirror system model

I've one-upped the schematic to a three-dimensional model, using some neat (free!) modeling software I just found called SketchUp, by Google (see link) This is a pretty versatile program, which is amazingly simple enough to pick up.

I used SketchUp to model my ("Romulus" blade spring) mass-mirror system. All the dimensions are included in the program file I wrote this to, which will yield approximately what is needed to bend the blade parallel to the optics table. I'll probably do some fine-tuning later.

EDIT: I seem to be having some troubles uploading the "massmodel2" programs I've saved, so I've attached a JPG of what can be seen in the SketchUp editor



***Note some minor adjustments to the plan: 

  1. The single metal strip connecting the mass end cap to the mirror mount will be made of aluminium NOT lead. Aluminium is much stronger (will not bend as easily), and the threaded holes for the screws will last longer than if it were made of lead
  2. There will be TWO of these aluminium strips, attached at orthogonal ends between mass end cap and mirror mount, for additional stability


Attachment 1: massmodel2.skp
Attachment 2: massmodel2.jpg
  231   Wed Jun 29 10:50:21 2011 Larisa Thorne and Vanessa AconDailyProgressCracklenew mass/mirror systems for ETMs...version2.0

[Tara, Larisa]

As calculations for mass and dimensions began for the previous design, I found it to be unnecessarily complex and set about trying to design something simpler that would fulfill our needs just as well. A few attempts later, together with Tara, we came up with a much better design---->see first attachment:

  • it utilizes parts we already have in the lab (i.e., the mirror mount, larger aluminum(?) base)
  • one can easily adjust the blade-bending mass
  • there are minimal calculations involved, mostly because there are a lot less screws/holes to account for
  • because we have the additional larger aluminum(?) base, we are not as constrained height dimension-wise ---->see second attachment


I've added a mock-up of the new design, with dimensions, and labeled the parts we do not already have in dark red.  The particular mass values I gave are for the blade spring Remus.

Note that it is not necessary to construct a new (rectangular prism) lead mass for the spring Remus, but doing so will allow a reduction of the lead mass's height (right now, the lead mass is about 5.4 cm tall).

I think aluminum or some other light metal will work best for the side plate, so we do not create too much asymmetry in the system.  The mass end cap (also metal) can be of a  heavier metal, such as steel.

Also, since the mirror frame is L-shaped, we could put in two side screws to attach the frame to the metal plate above, creating more stability for the attached mirror.

Attachment 1: IMG_1910.jpg
Attachment 2: IMG_1908.jpg
Attachment 3: mirror_mass_design3.png
  230   Mon Jun 27 14:02:46 2011 Larisa Thorne and Vanessa AconDailyProgressCracklenew mass/mirror systems for ETMs

 [Vanessa]: To try to combat the problem of the end of the spring (the part between the mass clamp and the mirror clamp) oscillating at its own independent frequency (even when the mass is not moving), we are designing a setup that places the mirror on the bottom of the mass.  Attached are some of our ideas for the design parameters involved and the proposed design.

Other design problems include the dimensions of the attached mass/mirror set-up, because the larger the moment of inertia, the more apparent the undesired (horizontal) modes of oscillation.  So even if the height of the set-up is altered so the masses lie above the 45 degree mirror, this problem still must be dealt with.

ETA: I have attached a very slightly altered version of the design Larisa put up, for my own clarification.

After this we need to design/construct the mechanism to move the spring, which will be a controlled magnetic field (consisting of a small solenoid with an AC power source suspended above the spring) with a magnet (attached to the top of the spring) inside.

[Larisa]: As mentioned in my last post, it was found that attaching mirrors to the bottoms of the ETMs was the most viable option. Attached below is the final diagram of the concept design....

This model has a few advantages:

  • One can easily adjust the mass load on the blade spring by adding extra masses between the "blade bend compensating mass" and "mass end cap"
  • As mentioned before, having the mirror at the bottom of the mass eliminates the need to have the mass be exactly what is needed to have the blade bend exactly parallel to the optics table surface
  • Screw-spring mechanism will allow the mirror to be tilted , again eliminating the need for perfect blade parallelism to optics table



After taking a few measurements on the current setup, it was found that the necessary dimensions of the ETM mass (HA, redundancy!) would be severely limited by the height of the base block holding up the blade and the 45 degree tilted mirror that guides the laser beam to the ETM.


The Romulus blade spring will probably only need about 1350g mass to make the blade sufficiently straight, but the Remus blade will need much more mass (see Vanessa's post for exact numbers)

One idea I had was perhaps to pick a material that would be heavier than the masses used...after some calculations, I found the density of one of the masses on the Remus blade (1801g) to be ~11.340g/cm3 , which corresponds most closely to lead (~11.389g/cm3). It would seem that this is one of the most cost efficient materials (compared to, say, gold) to make the room-temperature solid masses out of (lead density was the highest among those listed on this solid materials table: see here)

The other possibility is that we vertically displace the base that the blade springs are clamped to. This way we will not have to worry about the dimensions of the masses, and can just have bigger lead masses made. 

Attachment 1: Concept_art2.pdf
Attachment 2: Setup_with_springs_design_problems.pdf
Attachment 3: mirror_mass_design.png
Attachment 4: magnetic_coil_setup.png
  228   Fri Jun 24 15:44:23 2011 Larisa Thorne and Vanessa AconDailyProgressCrackleCrackling setup, with blades

Laser paths have been added in red (note: these are by no means all of the laser paths, only the ones that allow me to show the end test mass configuration)

Currently only one of the end test masses has a mirror attached...


The problem is that the mirrors attached to the blade springs are not on a plane that is parallel to the plane of the optics table, so the reflected beam does not follow the same path back. Rana mentioned at some point that perhaps it would be a better idea to affix the mirrors to the bottoms of the masses holding the blade springs down. I think that sounds like a more viable option.

ETA:  Added initial signal readouts from the photodiode with the mass moving, and with the mass stationary (zoomed in).  Notice that when the mass is moving there is some high frequency signal (300-500Hz) contained inside a larger wave packet (about 3.33Hz).  Possibly one signal is from the change in Lx and Ly in the Michelson setup, while the other is due to the slight changes in angle of the mirror on the spring, thus changing the level of overlap between the two recombining beams.  

However, even when holding the mass stationary we see the 300-500Hz signal.  Possibly some of that was from air currents / overhead lights / etc, because we were not yet able to put the plastic cover over the entire setup with the springs in the way.  More likely however is that the short amount of free spring that exists between the clamp for the mass and the clamp for the mirror is oscillating at its own frequency that is very difficult to damp, even when the mass is stationary.  We will try then to design a setup that positions the mirror on the bottom of the mass, rather than in a separate part of the blade spring.

Attachment 1: IMG_1885withlaser.pdf
Attachment 2: IMG_1886withlaser.pdf
Attachment 3: michelson_with_springs.png
Attachment 4: michelson_with_springs2.png
  227   Fri Jun 24 13:50:01 2011 Larisa ThorneDailyProgressCrackleDriven Noise curves

 Unlike in the earlier post, the configuration (specifically, the PZTs....we will switch tot the actual blade experiment soon) were driving the circuit.


Below are the resulting power spectrum density plots. Each represents the same basic configuration, but at different conditions (both driving frequency f and voltage amplitude Vamp could be adjusted).

Three conditions were tested:

  1. f=0.1Hz, Vamp=2V
  2. f=0.2Hz, Vamp=2V
  3. f=0.2Hz, Vamp=3V

For the first two plots, the same conversion factor to get from V/SQRT(Hz) to the desired units of meters/SQRT(Hz). Conversion=2.578199052E6 Volts/meter. Since the voltage amplitude was changed during the third test, the conversion factor had to be adjusted to conversion=3.892575039E6  Volts/meter. [If there is any confusion on how these were calculated, reference the post here]

The fourth plot superimposes all three previous plots.


Attachment 1: drivennoiseplot1.pdf
Attachment 2: drivennoiseplot2.pdf
Attachment 3: drivennoiseplot3.pdf
Attachment 4: drivennoiseplot4.pdf
  226   Thu Jun 23 12:59:46 2011 Larisa ThorneDailyProgressCrackleNoise budget curve, updated version

 I have made some adjustments to my noise curve from earlier.




The graphs have been consolidated into one, with appropriate scaling. You will notice the y axis has been adjusted by a conversion factor, as we want meters/SQRT(Hz), not Volts/SQRT(Hz).


Let deltaV=fringe amplitude from minimum to maximum, as seen on the oscilloscope when there is no driving force on the mirrors =638mV

Let deltaL=difference in Michelson X and Y arms =(wavelength of the He-Ne laser)/4

Let the conversion factor = [deltaV] / [deltaL]

Since most commercial He-Ne lasers produce a laser at wavelength of 633nm (Googled this), the conversion factor=4.031595577E6 in Volts/meter.


Attachment 1: noiseplot2.pdf
  225   Thu Jun 23 12:26:09 2011 Vanessa AconDailyProgressCrackleInitial Set-up: Noise Budget

Data taken June 22

We measured our initial set-up (with mirrors on PZTs, not masses on springs) noise and found a conversion factor from volts on the spectrum analyzer to meters (distance moved by the mirror).

Notes: I'm assuming that peak in the dark noise is from the lights, even though we have a plastic bin around the set-up.  Also, I used the most common wavelength value for HeNe lasers (from wikipedia).  I will confirm this value later.

ETA: Noise curves have been added for the PZT set-up.  Different curves are at different AC amplitudes and AC frequencies.  The curves do not change much in the 10-100Hz range, with varying low AC frequencies).

Attachment 1: 22_06_noise.pdf
Attachment 2: 2406_noise_budgets.png
  224   Thu Jun 23 12:18:15 2011 Vanessa AconDailyProgressCrackleMeasuring resonant frequency and Q factor of the blade springs

 Measurements taken on June 21.

Attachment 1: Q_and_res_freq.pdf
Q_and_res_freq.pdf Q_and_res_freq.pdf Q_and_res_freq.pdf
  223   Thu Jun 23 11:26:50 2011 Larisa ThorneDailyProgressCrackleA little noise budgeting

Today we started to set up the experiment which will eventually allow us to characterize the noise of the blade spring crackling. The configuration was an analog of the final configuration, where a controlled voltage over a PZT was used as the driving force on the ETMX only.


The first plot, labeled "Spectrum 1" represents the power spectral density plot of the all the noises prevalent in the configuration (i.e., seismic noise, shot noises, fluctuations due to air currents, etc).

"Spectrum 2" is similar, except that the only noise present is 'dark noise', which is the extra signal the PD gets when the laser beams are blocked from hitting it. This 'dark noise' can be thought of as some sort of background noise.


By observation, we can compare the orders of magnitude at which both the sum noise and dark noise curves exist.... Spectrum 1 is around the order of ~10-3 to 10-2  whereas Spectrum 2 is around the order of ~10-5. This confirms that the dark noise occurs within the range of values of the sum noise.


Attachment 1: Spectrum1loglinearbig.pdf
Attachment 2: Spectrum2loglinearbig.pdf
  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
  221   Tue Jun 21 14:53:29 2011 Vanessa AconDailyProgressCrackleMatlab simulation of Chopping

Our project is to set up a basic Michelson interferometer to measure and characterize the crackling in blade springs.  That crackling signal will likely be buried under other sources of noise and other parts of the signal, so we will use a chopping technique to extract the crackling signal.  We first set up a Matlab simulation of the chopping technique using a constructed "crackle" signal.  The code and explanation of that simulation are attached.

ETA: changed such that crackle = delta x(t), not delta x(t) - x(t).

Attachment 1: acon1.m
fs = 500;
ts = 1/fs;
tt = (0:ts:100); %time vector
k0 = 2; %ideal spring constant
fdrive = 0.1; %driving frequency
Amp = 1; %max amplitude
dist = Amp*sin(2*pi*fdrive*tt); %spring position
vel = 2*pi*fdrive*Amp*cos(2*pi*fdrive*tt); %spring velocity
noise_t = rand(1,50001)*2-1; %noise function
... 34 more lines ...
Attachment 2: matlab_explanation.pdf
matlab_explanation.pdf matlab_explanation.pdf
  220   Tue Jun 21 13:32:02 2011 Larisa ThorneDailyProgressCrackleQ and dampening measurements

 We went down to the SUS lab and ran some tests to get measurements we could use to calculate the Q and b (dampening factor/constant?) of the blade springs.


The setup was fairly simple (see attachment below): a laser beam was set up such that its path to a photo diode would be interrupted by the movement of a mass (which was attached to the spring blade). The resulting wave function as seen through an oscilloscope hooked up to the PD would give us the necessary data to calculate Q and b.

Given these sets of data, we can reference (this) to find that Q=4.53 f0 T1/2. Here T1/2 is the "decay by half life of amplitude", or the time it takes for the amplitude to be half of when it begins, and can be checked by plugging into the equation and seeing if the resulting expression is true: Amplitude( T1/2)/ Amplitude(t@0) = 1/2 .





TO DO list:



-- Take the oscilloscope data and figure out how to calculate  T1/2, so that Q can be calculated

-- Think about how to calculate b



Attachment 1: IMG_1842v2.pdf
  219   Mon Jun 20 17:26:37 2011 Larisa ThorneDailyProgressCrackleCrackling simulations

The rest of the chopping circuit has been designed (see first attachment). 

***NOTE: adjustments have been made to the crackling circuit, where the AC source signal is NO LONGER BEING SENT THROUGH THE SIGNAL SQUARER)


Because there are four "outputs", there will be four plots generated. There is a number at the "output" of each in the first diagram attached, which I associated with its corresponding plot number. Here is a sample of the MATLAB code I used for Circuit 1:

fs = 500;

ts = 1/fs;

t = (0:ts:100); %time vector

k0 = 2; %ideal spring constant

fdrive = 0.1; %driving frequency

Amp = 1; %max amplitude

dist = Amp*sin(2*pi*fdrive*t); %spring position

vel = 2*pi*fdrive*Amp*cos(2*pi*fdrive*t); %spring velocity

noise_t = rand(1,50001)*2-1; %noise function

Force = k0*dist; %ideal spring force

alpha = 0.5;

k = k0 + noise_t.*alpha.*k0.*(dist./Amp); % k = k0 + dk

dx = (k - k0).*dist/-k0;

crackle = dx/(alpha*Amp); % = noise*sin^2(2*pi*fdrive*tt)



[B1,A1] = butter(2,[10 100]/(fs/2));

y1 = filter(B1,A1,crackle);


%squared signal

ysq = y1.^2;



[B2,A2] = butter(2,[10 200]/(fs/2));

y2 = filter(B2,A2,ysq);












Vsin = sin(2*pi*fdrive*t);


%Doubled source

V1 = 2.*Vsin;



ymix1 = y2.*V1; 


%Low Pass Filter

[B3,A3] = butter(2,0.1); % error message when fc not within (0,1)

ylpf1 = filter(B3,A3,ymix1);


Attachment 1: crackle5circuitdiagram.pdf
Attachment 2: crackle5ylpf1.pdf
Attachment 3: crackle5ylpf2.pdf
Attachment 4: crackle5ylpf3.pdf
Attachment 5: crackle5ylpf4.pdf
  218   Mon Jun 20 12:11:49 2011 Larisa ThorneDailyProgressCrackleCrackling simulations

I should begin this ELOG with the warning that this is the first time I've ever used MATLAB...



First item on the agenda is to create a simulation which models the displacement due to the crackling noise on the blade spring. This can be done using MATLAB in just a few lines and generates a plot (see first attachment).

For this simulation, I picked random numbers for the constants, which is why it wil likely look a little funny. 

t =       1:0.1:100;  %time range

fdrive =  0.1   % driving frequency

MaxA =    2    %maximum amplitude

alpha =   1          %some constant

deltax =  MaxA.*sin(2.*pi.*fdrive.*t)

k0 =      1   % spring constant

Force =   k0.*deltax    %driving force

noise =   rand(1,1001); %some random noise function: our crackling noise?

k =       k0+noise.*alpha.*deltax;

dx =      Force./k

crackle = dx-deltax;  % crackling noise measured in terms of displacement



The next step is to attend to chopping. The second attachment is the circuit I drew to do this, but it differs a bit from what I've seen posted on this ELOG here. Which one is right??

From what I understand, the first simulation (above) results must be injected into the beginning of the top part of this circuit (coming from the PD). Then the signal needs to be bandpassed, squared, bandpassed again, the mixed with a source signal and time averaged to isolate the noise. On the subject of bandpassing: I've been reading up on trying to do this in MATLAB. There seem to be a few suggestions on the Internet, but none of them have worked for me...(then again, I'm probably doing it wrong). The crackling plot shows displacement at a range of frequencies, but I imagine that the chopping circuit will have more to do with voltages. How does this translate?



TO DO list:

-- Try to create a bandpass filter in MATLAB

-- Try to create a mixer in MATLAB



Attachment 1: crackleplot1.pdf
Attachment 2: cracklecircuit1.pdf
  217   Wed Jun 8 01:02:44 2011 mingyuan, taraMiscCracklePre setup for blade springs

We get all the part for blade spring holders, so we determine the setup and get the approximate minimum diameter of bell jar to be 18".

We decided to place the blade in the same direction, so that seismic in horizontal direction coupling into the blade will be common mode.

The masses that will pull the blades down have not been installed yet. We need longer 1/4-20 screws, probably ~2.5".




Note: I fixed the table legs so that 4 of them touch the floor. However, the steel chamber for reference cavity for cryo lab is left on our table. Its  presses on one end of the table and lifts one end completely off the rubber support, see the below picture to see the gap between the rubber and the table.

We want to remove the chamber first, so the table rests evenly on four legs before we measure the seismic noise on the table.




  216   Tue May 31 19:33:00 2011 taraDailyProgressCrackledata readout

By mingyuan, tara

We built a simple voltage summing circuit for adding DC level to the pzt. This circuit allows us to fine tune the inteferometer's differential arm length, so that we can operate at the fringe's maximum slope. Then we checked the peaks we observed from last time. It turned out to be harmonics from the common mode from driving.


The circuit schematic is shown below. The result Vout = Vin1 + Vin2. 



The adding circuit is used as shown in the schematic (highlighted in yellow.)


 *Later, we can use this summing circuit in a feedback control loop for locking the interferometer.

Then we used this circuit in the setup and repeat the measurement to check the peaks we observed last time. With the same setup, we observed the peaks again, but they probably are harmonics from 4Hz from common mode motion which was not perfectly cancelled.




     We repeated the measurement again with 0.7 Hz driving, and the peaks disappeared. The signal between driving and not driving the arms are very similar. The shape of the PSD changes slightly because of the lower amplitude of the driving signal, as we low pass the signal at 0.1 Hz.


We do need a seismic isolation and vacuum chamber. Right now, sound from people speaking in the lab can disturb the measurement.


 a few things we have to consider soon, before we use the maraging steel blades pulled down by a mass block in the experiment.

1) how should we push the blades?  capacitor plate? magnetic coil?

2) When can we move and get a better table, so that we can decide on seismic isolation stage.

3) We have to start looking for vacuum bell jar for the experiment.

4) lock the interferometer?

5) will we get an npro laser for the experiment?

  215   Tue May 31 17:49:47 2011 Mingyuan, TaraDailyProgressCreakdata readout



To have the ability of controlling the phase, we need adjust DC voltage of one of the PZTs independently.
We use the function generator to generate AC driving with a DC offset for one of the PZTs and use a OP270
chip to add the driving signal with another DC voltage for another PZT. By changing this DC voltage, we can
control the phase of interference signal. We adjust the voltage to put the PD intensity in the middle to have
the best sensitivity.
We did the same measurement as last time to check the peaks we observed. By use the same condition, we do see
a few extra peaks while the plates are being drovn at 2 Hz. We also changed the driving frequency to 0.7 Hz and
did the same measurement. The results looks different.
  Tara will upload the data later.

  214   Mon May 30 02:09:53 2011 Vladimir DergachevDailyProgressTiltmeterNoise spectrum after cleaning
First useful spectrum after cleaning. It appears to be at least as good as before. This plot uses pre-cleaning calibration - it should not have changed too much, I'll try doing another calibration after collecting more data.
Attachment 1: fine_combined_spectrum_zoomed_presentation.png
  213   Fri May 27 20:32:18 2011 taraDailyProgressCrackleData readout

By Mingyuan Tara

We measured the FFT of the demodulated signal from chopping technique. We did not see much. The background noise is still too high.

      With everything ready, we used chopping technique to measure crackling noise. We measure the PSD from the demodulated signal between a) the mirrors being driven at 2Hz, and b) background noise, when the system was at rest, no driving force applied to the mirrors. We did this to check if we can see any signal due to crackling noise/ rubbing noise/ pzt noise or any noise originated from the driving mechanism or not. The result is not quite clear, we see a few peaks from the driven system around 40 Hz, but we have yet to confirm and identify them.


        The setup is shown in the diagram below. For each bandpass through SR560, we added the gain to the signal as much as possible without railing the signal. Note that in this setup we did not bandpass the signal from PD after we square it , as shown in previous entries. Because Mingyuan did not understand why would we need to and I could not answer him properly, so I agreed to let him have it his way.



          When we measured the data from the driven system (red curve in the plot), the setup is as shown in the diagram. However, for background measurement (blue curve in the plot), we want to keep the DC supply provided by the function generator to the pzt so that the sensitivity of the signal remain the same. Hence, we used a second function generator to send in similar driving voltage to the squaring box, while the first function generator was set to the dc output voltage to supply the pzts, no sinusoidal output.   (We made a mistake by just unplugging the Vdrive to the pzt and to the squaring box, and the noise level dropped so much.) 



     The red and blue curve shows the psd of the demodulated signal when the blades were driven, and the static case respectively. The peak at 4 Hz that presents in both cases are from the square of the driving signal at 2Hz.

     There are a few  peaks around 36 - 40 Hz when the blades were driven. We could not see this in the SR785 monitor because the monitor was so faint. I just saw this after I plotted the data.  The peaks might come from some resonances in the setup. We expect crackling noise to be more broad band. We will confirm and identify the source of the peak to make sure that we can see some signal from the driving (it can be rubbing between metal, pzt noise, crackle.)

We will repeat the same measurement, and try changing driving frequency/ amplitude, to see if the signal changes or not.

  212   Fri May 27 17:00:28 2011 Mingyuan, TaraDailyProgressCrackleData readout



Today we measured the current system noise by the signal squaring and multiplier system we built.
The interferometer is quite stable now and the phase could be stable for more than half hour.
The plates are droven by 2 Hz 3 Vpp sinusoid signal with 4 V offset in common mode.
The signal From PD is band passed by SR560 with 200 gain and squared by AD 734 chip.
The driving signal is also band passed by S560 and squared by another AD 734 chip.
The two squared signal are multiplied by one AD 734 chip. The signal from multiplier is feed
to spectrum analyzer. We also measured the noise spectrum without driving plates. The results look the same.
The signal is very sensitive to talking and walking nearby the table. We suspect that the seismic noise dominates the noise.
The possible noise source:

  • shot noise
  • seismic noise
  • Thermal noise of the plates
  • Thermal noise of the mirror
  • PZT noise and rubbing
  • Air flowing
  • Laser power fluctuation
  • Laser frequency noise
  • noise from AD 734
  • noise from other electronics


Tara will upload the plots later.

  211   Thu May 26 19:39:48 2011 taraDailyProgressCrackleAD734 squaring circuit

By mingyuan, tara

We figured out the offset problem in AD734 chips, the box for squaring and multiplying signals is finished.


          The problem from the previous circuit was that the ground from the signal was grounded with the load ground. This time the load ground is separated from the signal ground, Z2 is grounded to load groundThese corrections fix the offset problem and the maximum allowed input ( was 0.6 V.) Now the input can be up to 10V. The output, Z, is (X1-X2)x(Y1-Y2)/10 as described in the datasheet. Now the chip are connected as shown below.




          We are thinking about not using the default denominator (/10) for a multiplying chip (we certainly need it for squaring chips, otherwise the output will rail), because after the signals (from PD and driving voltage) are squared, their dc levels are ~3 V. When the two are multiplied together, the voltage output drops to 3x3/10 = 0.9 V. So if we can have denominator = 1, the signal will be larger. However, we have to understand how the noise in the chip works first. See Mingyuan's entry about input referred noise of the chip ,it is roughly 3 mV/rtHz. If the SNR remains constant regardless of the denominator, we might not need to worry about it.

Attachment 1: ad734_crackle.pdf
ad734_crackle.pdf ad734_crackle.pdf
  210   Thu May 26 18:58:56 2011 Mingyuan, TaraDailyProgressCreakNoise from AD734






We figure out the offset issue of the chip AD 734. We measured the noise of chip AD 734 with 50 ohm input terminated.

The noise is shown below for two chips we are using and noise from spectrum analyzer is attached for reference.

The noise of AD 734 is about 1 uV/root(Hz) at around 50 Hz. The sensitivity of of the chip should be:

dV*dV/10 = 1 uV/root(Hz)  =>  dV ~ 3 mV/root(Hz)

We are not sure about that we understand the noise propagation through the chip correctly.  

Attachment 1: Noise_of_AD734_100_HZ.jpg
Attachment 2: Noise_of_AD734_800_HZ.jpg
  209   Wed May 25 20:04:28 2011 taraThings to BuyCracklepurchases

I ordered opto mechanical mounts for turning the beam vertically. See the details in psl log.

I also orderedspring lock washers and wave washers. There will be used when we clamp the guillotine things for putting the load on the tip of the blade.

The pressure from the clamp should not exceed the yield strength of the maraging steel blade. So the spring lock washer should give us some limits of pressure on the blade. There is no specification about how much pressure it would be, so I ordered two kinds of washer for testing.

  208   Tue May 24 19:47:16 2011 Mingyuan, TaraDailyProgressCracklestart crackling

 1) We removed the squaring circuit from the test board and built it on a board. The box for the circuit was prepared.

 2) We replaced the crappy beam splitter with a Thorlabs 20mm cube 400-700 nm beamsplitter. The beam power is evenly divided and has no multiple reflections. We measured the noise psd at the AS port.


      1) The circuit for squaring, multiplying signals was temporarily built on a plug-and-play test board which was neither sturdy nor compact. So We used a breadboard available in the EE lab to build the circuit.

The cartoon schematic is shown below.


      A) The signal from PD at AS port is band passed before squared (not shown here), then band passed again before.

      B) The driving voltage for PZT will be high pass to get rid of DC component (not shown here), then divided. We want a divider here because we might need to drive the pzts with higher voltage. The second divider might be unnecessary, but we have it just in case.

     C) Then we multiply  A and B and get the signal out for FFT.

     Currently, the chips have offset added to the output, ~ from -1 to -2 V. We tried adding the offset in Z2 let as suggested in the datasheet, but it killed the signal ??!!!. So we are planning to high pass signals that we care only their AC parts. Currently, we are not sure if we care about DC part of the V drive or not. We have to think about it.


     2) The beam splitter used in the original setup is not really for a beam splitter for Michelson IFO. It is not 50/50, and there are multiple reflections from the surfaces.

Thus, we ordered a cube beam splitter suitable the job and replaced it. It is mounted on a beam splitter mounted directly mounted on a 2" post, so we expect it to be more stable.




We measured the noise from AS port when the armed was not driven vs driven at 1 Hz. The result is shown below.

The calibration from V to differential arm length (Lx - Ly) is approximated from

dx ~ dV x  lambda/ 4 / (Vmax - Vmin)

At the maximum slope of the fringe, as we tap the table, the voltage will fluctuate between Vmax (from constructive interference)and Vmin (destructive interference.)  On the fringe, the differential arm length between maximum to minimum V output is lambda/4 (so the accumulated distance from round trip is lambda/2, a condition for changing from maximum Vout to minimum Vout). We can approximate the slope to be (Vmax - Vmin)/ (lambda/4).

Vmax - Vmin ~ 500 mV, lambda = 660 nm. so

dx = dV x 3x 10^ -7



The result is 5 - 6 orders of magnitude above the shot noise level (~ 1e-17 m/rtHz for this setup.) Noise characterization will be considered next, but from

a quick test of tapping, seismic is the dominating source.

  207   Fri May 20 23:19:36 2011 Mingyuan, TaraDailyProgressCracklestart crackling

We tried read out the signal from chopping technique.We could not see anything yet.

The signal when both IFO arms were driven were similar to the signal when there was no driving.


   After we made the necessary electronics for chopping technique, we tested if we could see the signal or not.


    We used a 4 mW HeNe laser as a source with a simple Michelson interferometer setup. We tried to operate at the maximum slope of the fringe. Each mirror was attached to a metal shim which could be pushed by a PZT behind it, see here . We drove the mirror with the same distance so that the common mode was canceled and only incoherent noise from crackle in each blade could be detected.


    The diagram omits the IFO part and the blades. The output beam from the IFO was incident on the PD. We operated at the maximum slope of the fringe. The driving voltage Vdrive was send to the PZTs pushing blades (with mirrors attached on them) at the end of both arms.

    The 1/2 and 1/10 dividers are used to reduce the signal down below 0.5 V. This number comes from the square testing. When the input signal to be squared is larger than 0.6, the output starts to rail. So we use 0.5V to be the upper limit for now.




       The PSD of the signal output when two arms are driven are similar to the background signal (arms are not driven). It might be that the gain setting are not optimized, the setup is too noisy, or problems from offset from the AD734 chip. We will figure that out next. We will also make a sturdy box for multiplying chip. Currently we just use temporary test board to operate the chips for the read out.

  206   Thu May 19 21:31:28 2011 Mingyuan, TaraDailyProgressCreakstart crackling


We used a big box to cover the optical loop. The interferometer is more stable now.

We build other two AD734 chip circuits for signal square and multiplier.

We already tested that we could square the driving signal and PD signal.

The square of the PD signal has a big offset from the AD 734 circuit. We need figure out how to take the offset out.

  205   Tue May 17 19:24:58 2011 mingyuan, taraDailyProgressCracklestart crackling

We brought the setup back. The interferometer is working and more stable. We will try extracting signal next.

    From this entry, we noticed the 180 degree phase shift in the signal when one arm was driven. The signal from PD followed the driving signal before drifted up and phase shifted by 180 with respect to the driving signal. We believed that this was the effect from the drift of the arm length. Suppose that we operate the IFO at the fringe's maximum slope. The drift in arm length will move the operating point on the fringe, and we might end up on the other side of the fringe which will show up in the 180 degree phase shift of the signal.

    The mirror was pushed by a piece of soft rubber which was glued to a pzt. Another end of the pzt was glued to a piece of plastic. This plastic piece was clamped on a translational stage. We thought that the soft rubber, the plastic and the translational stage caused the drift of the arm length.

So we tried to improved this by

  • replacing the rubber and plastic with two pieces of magnets. One was glued on the back of the mirror, another one was glued to the pzt. This did not work, the combination of the force, and the shim stiffness, had to be matched so the mirror position can be adjusted without letting the magnets touch each other. So we tried
  • replacing the rubber and plastic with stainless steel nuts, one nut is for clamping, another one is for pushing the mirror.
  • IMG_1580.JPG

we haven't got rid of the stage because we still need it for position adjustment purpose. We will use dc voltage offset on pzt to adjust the position later once we can add dc signal to the driving voltage.  Currently, we use a single function generator to drive both pzt simultaneously.


     With new pushing scheme, the drift becomes much less than before. The signal is in phase for more than a minute or two which should be enough for chopping technique later. The picture below shows the signal from driving voltage @ 2Hz(blue), and readout from PD at maximum slope (yellow).


     Once we made sure that the signal was quite stable, (that is, the operating point stays at the maximum slope most of the time), we measured the background noise. This is a readout from PD and maximum slope on the fringe without driving voltage applied on the pzt. Then we measured the signal when one arm was driven at 2 Hz. Finally, we drove two arms at 2Hz and adjust the voltage on the pzt so that the 2Hz common mode cancelled out.


 The plot shows the noise of the setup: 1) the background 2) when one arm was driven at 2 Hz. 3) Both arms are driven, with common mode at 2Hz minimized.

 We will try squaring the signal next. The read out from PD is ~ 200 mV. This value will determine if we need a divider for the signal or not.

ELOG V3.1.3-