I just want to catch up on my conclusion that a single seismometer cannot be used to do the filtering of horizontal NN at the surface. The reason is that there is 90° phase delay of NN compared to ground displacement at the test mass. The first reaction to this shoulb be, "Why the hack phase delay? Wouldn't gravity perturbations become important before the seismic field reaches the TM?". The answer is surprising, but it is "No". The way NN builds up from plane waves does not show anything like phase advance. Then you may say that whatever is true for plane waves must be true for any other field since you can always expand your field into plane waves. This however is not true for reasons I am going to explain in a later post. All right, but to say that seismic dispalcement is 90° ahead of NN really depends on which directoin of NN you look at. The interferometer arm has a direcion e_x. Now the plane seismic wave is propagating along e_k. Now depending on e_k, you may get an additional "-" sign between seismic dispalcement and NN in the direction of e_x. This is the real show killer. If there was a universal 90° between seismic displacement and NN, then we could use a single seismometer to subtract NN. We would just take its data from 90° into the past. But now the problem is that we would need to look either 90° into the past or future depending on propagation direction of the seismic wave. And here two plots of a single-wave simulation. The first plots with -pi/2<angle(e_x,e_k)<pi/2, the second with pi/2<angle(e_x,e_k)<3*pi/2:

The hall effect sensor is quite noisy, and I am trying to find where the noise comes from. The first I tried today is to measure the power spectrum and coherence among three hall effect sensors (in the vertical direction). Here is the result:

(the unit for the power spectrum density is in digital volt per root hertz.)

I do not quite understand why there is almost no coherence (apart from the 60Hz power line), even though the power spectra are almost identical among these sensors.

Can someone shed some light where the issue is? Is the noise non-stationary or what?

--------Another measurement with fewer average---------------------

It seems that when the number of average is small, the coherence is large, an indication of non-stationary?

This is the pressure trend when I close off the valve between the pump line and the cryostat. I am not totally sure how to interpret this, but the fact that the pressure didn't go much lower (like the 10^-6 region) when the pump is only pumping the line makes me think that there may be a leak in my line. Something to investigate.

Having assembled the full Michelson, attempts are being made to lock it. 

Attached are two pictures: the first is the Michelson without servo/feedback loop on. The second is the resulting waveform of the settings that got closest to a lock. Still playing with it....suspect that perhaps the solenoid of the magnetic actuator isn't able to handle as much power as needed. Might need to replace it with one that has more turns?

I put the pump back on the CQ tank. The pressure had only risen to 4 uTorr over a day of being sealed off, so I spooled up the Hi-Cube, opened the valve and then reengaged the large turbo.

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.

I have completed curve-fitting to get what I consider to be a reasonable estimate of the quality (Q) factor for the 'Remus' cantilever blade spring.

Sample MATLAB code is included below for the first data set of the 'Remus' blade.

I created two new functions, 'dampedsine.m' and 'chinew.m' to make the code 'findQ.m' work. Parameters in 'chinew.m' had to be changed for each new set of data. For each set of data there were 2 independent sets per cantilever blade spring so that we can compare them; see if they are similar...this is hopefully the indicator that the code is working as it should, not that the same errors per produced twice. In addition to having two separate data sets for each cantilever blade spring, I am including two plots: one with the whole range of data, one zoomed version so the level of accuracy can be understood visually.

If the formula for the curve fitting is  function=A+B*e^(-t/tau)*cos(w*t+phi)

If the formula for the quality (Q) factor is Q=pi*(w/(2*pi))*tau

And in the MATLAB code, the matrix 'xout' contains the respective values of the variables

then....

REM2:---------------------------

>> xout

xout =

    0.8934

    0.1779

  436.3865

   13.0989

    0.3746

>> QREM2

QREM2 =

   2.8581e+03

REM3:---------------------------

>> xout

xout =

    0.8884

    0.4516

  424.6310

   13.0978

    2.4434

>> QREM3

QREM3 =

   2.7809e+03

The only problem occurs when we consider the 'Romulus' cantilever blade spring. This is evident not only in the graph (we can see that the green line that represents the curve fitted line is oscillating but not damping), but also in the solution for the variables of the curve fitting and the calculated Q value, which is 3 orders of magnitude higher than those for the 'Remus' cantilever blade spring.

 ROM2:---------------------------

>> xout

xout =

   1.0e+05 *

    0.0000

    0.0000

    1.5785

    0.0001

   -0.0000

>> QROM2

QROM2 =

   1.0404e+06

Here are the last of the calculations for the quality (Q) factor of the cantilever blade springs: Romulus. I was having difficulties last time simply because I wasn't playing with the initial x conditions enough...

As before, I have collected two sets of data for the cantilever blade spring (called Q3, Q4 in the plot names). For each set, I have two plots: the first is a view of the full data curve with the curve fitting curve, and a second one that is just zoomed in to show how close the two are, visually. As you can see from the zoomed in view, the second set of oscillation data for the Romulus blade had many imperfections, which could explains why the difference in calculated Q's for the Romulus data set was larger than the difference in Q for the Remus cantilever blade.

I used the a version of the same code as for the Remus cantilever blade calculations, so I will not be redundant and post them here again.

ROM2, second go:---------------------------

>> xout

xout =

    0.8754

    0.7198

  408.3907

   13.1822

    5.2313

>> QROM2

QROM2 =

   2.6917e+03

ROM3:---------------------------

>> xout

xout =

    0.8813

    0.5866

  352.7866

   13.1829

   -0.0238

>> QROM3

QROM3 =

   2.3254e+03

On Monday, tested a 1998 (Rev. 0) RFPD originally found in Crackle (serial #010). Looks like it was first resonant at 24.493 MHz, but was later tuned for 14.75 MHz. I used the AG4395A network analyzer in CTN following the procedure in the previous ELOG post, splitting R output into the test input of the RFPD. Driving at up to -10dBm, couldn't see any resonant feature in the TF below 150 MHz. Tuning the inductor L1 made no difference. The regulator (U3 and U4 near bottom right in picture below) outputs were nominal.

I borrowed a flat response (DC to 125 MHz) PD from CTN lab (New Focus 1811) along with its power supply for short term use.

Below are some photos of the aformentioned RFPD. I added some kapton to keep dust off the PD.

There was some issue with the pumps apparently. Giordon will detail this in the elog very soon.

This evening, around 7:30, I restarted the turbo. The coarse gauge was bottomed out at 1 mTorr.

I turned on the laser and the HV. Then re-aligned the laser and the input and output optics and rebalanced the detectors.

Several of the mounts were loose: single screw, joints not tight, pointless use of a flipper mirror. All very sloppy - should be fixed Monday morning.

I have restarted a sweep from 20 - 22 kHz with 1 kV DC and 0.5 kVpk sine.

Wondering why we don't see any signal. Is the stress induced polarization modulation too small? Seems unlikely since we're almost shot noise limited in the readout. Perhaps the ESD force pattern is too weak or perhaps the ESD is broken (open rather than short) ?

Discussing with Calum and Alastair during Friday donuts, we thought we could possibly use the laser vibrometer.

Triggered by that, I wondered if we could just make a Michelson with the disk making the reflection for one arm.

Then this evening, I noticed that the reflection from the disk already has a fringing pattern in it; my guess is that this is from the two surfaces. Maybe this fringe signal already has the mode vibration in it?

The issue with the pumps was basically my fault. I misinterpreted what was meant by turning on the pump and had forgotten to turn on the backing pump first before the UHV pump. Alastair went ahead and fixed this and reset the error as well (thanks!)

I'll be making a few mechanical adjustments to the set-up today and making it less sloppy. The sweep that Rana did from 20-22 kHz doesn't reveal any modes:

As a reminder - we predict a mode around 21kHz and allowed for up to 5% error in frequency (5% of 21kHz is roughly 1kHz).

Edit: currently have a sweep going 1kHz span centered at 21.4kHz.

Do you mean short rather than open?

We were considering the interferometric readout from the start, but the feeling was that we would just get killed by the CoM motion (pendulum, torsion, tilt, etc.). That was supposed to be one advantage of a transmission measurement.

I agree that the fringe we see is probably from the parallel disk surfaces. I'm having a hard time seeing how we could use this to our advantage, though. Judging by your COMSOL stuff, I wouldn't think there is a first-order displacement of the disk surfaces relative to each other for these modes. Also, if there was, we would have to be very careful about the yawing of the disk, and we'd also be sort of at the whim of the system in terms of whether the fringe is dark or bright or whatever without any stress.

 There is, indeed, a giant resistor inside of that cast aluminum box which converts the output of the HV driver into a SHV connector.

Its a thick film, Ohmite, MOX-1125-23E. Which Google tells me may be somewhere from 1-1000000 kOhm. Need a Ohm-meter to measure it, but there's not one in the lab.

However, it could be that this is why we can't ring up any modes.

Pictures are in our Picasa account.

Our HV driver is a Matsusas AMT-5B20 (http://www.matsusada.com/high-voltage/ams/AMS.pdf). According to the data sheet (attached) it has these specs:

Vdc = -5000 to + 5000 V

Imax = 20 mA

Slew = 360 V/uS

-3 dB BW = 20 kHz (full scale) or 40 kHz (10% scale)

So its not bad; we should still be able to ring up the modes up to 100 kHz, although we just drive a little harder.

(Also, remember to electrically isolate the PDs from the table)

I measured the resistance of the resistor: ~10 MOhms.

The cable capacitance (measured from the driver side of the SHV cable) is 200 pF. This must include the cable capacitance + the ESD capacitance. I leave it to Giordon to calculate these to see if the measurement makes sense.

Then I took a transfer function from the input (Vcon-in) to the output SHV connector. To make sure it was safe, I first used a DVM to measure the SHV connector and dialed the front panel knob to minimize this voltage. Then I set the spectrum analyzer to have a source output of 2 mVpk and connected it to the HV driver input.

The transfer function shows a rolloff above ~1 kHz. However, I don't think its steep enough to be a big issue for us. I have saved this data on the box as data registers D3 & D4 for Giordon to download and plot.

Finally, I have started a wide sweep with everything back on. It looks like there are some resonances around 4 kHz. Need to do some careful pickup hunting to see if these are real or electronics. Hopefully Giordon will come into the lab and download this data to check. So far it has been repeatable twice so I think its not a fluke of the noise.

[Rana, Giordon]

Plots from Rana's sweeps (transfer function of the input (Vcon-in) to the output SHV connector; wide sweep showing resonances).

 re-aligned optics for new position, balanced PDs, turned on HV, started a new sweep for 3.5 kHz

nothing visible, restarted sweep around 6 kHz and started up the Turbo at 13:58.

I also noticed that whoever is setting up the 'Remote' data taking is changing the input configuration of the channels of the SR785 into something non-sensical. Check your settings.

 Nothing visible in the 6.07-6.17kHz range either. I'm starting one around the 10.6kHz range

To: Eric, Rana, Giordon

Why are we doing 100-Hz sweeps again? I thought we decided to focus on narrower sweeps about the frequencies that Rana & Alastair measured with the "screwdriver method". 800 pts over 100 Hz near 6 kHz is not enough resolution to see the modes we want.

I asked Eric about this - and I'm not sure I was convinced. The explanation was something like "even if we don't see the total width of the peak, we'll still see some sharp peak somewhere". I even explained that the line width (gamma) of the peaks are around 0.03 and 300-800 points over 100Hz only gives a resolution of 0.3ish (we're still an order of magnitude off).

Appears to be fixed now - issue was the channel 1 input was set to be a differential "A-B" later on in the remote script - I removed that line and fixed it.

If you were just measuring the power in some wide band (e.g., measuring a PSD with a bandwidth that is wider than the resonance), then I think what you're saying is true. That is, you'd see some frequency bin with a higher signal than its neighbors', and you could then choose to make a finer sweep around it.

Since you are measuring a transfer function, that is not true. You are trying to excite a narrow resonance with too coarse a sweep. Since the excitation signal is only being stepped in frequency by the same intervals as your resolution, the best you can hope for is that by some chance it happens to choose a point near the resonance for that one drive cycle. The odds of this are quite small.

Use finer resolution and look for the peaks Rana saw.

Motivated in part by the conclusions below, improved estimated mode matching efficiency from a poor 13% at the beginning of day to 48% (estimated using the reflection signal levels from the rfpd). What helped was walking the beam with the last two mirrors, and then scanning the cavity output coupler around to center the resonant mode which at this point seems optimal. This process was tedious, but effective apparently.

The distance between the two mirrors is ~ 45 mm which slightly undershoots the planned 47.5 mm which could limit the achievable 100% in simulation-land, but I'm moving on for now, hoping the lock will bump it up enough for the OPO threshold to be within our pump power range.

 Hey Larisa, could you post the original data from the SR780, if you haven't already?  Thanks.

Also, can you just take the absolute value of the y-data, so you only take the real values and can plot on a log-log scale?

SCRN0030.TXT: 7-22-2011, magnitude data (40 data points)

SCRN0031.TXT: 7-22-2011, phase data (40 data points)

SCRN0032.TXT: 7-25-2011, magnitude data (100 data points)

SCRN0033.TXT: 7-25-2011, phase data (100 data points)

SCRN0034.TXT: 7-25-2011, magnitude data (100 data points)

SCRN0035.TXT: 7-25-2011, phase data (100 data points)

I have just posted the plots, both magnitude and phase in log-linear form. We do not want to take the absolute value of the y-axis to solve the log-log problem as you suggest because this would make the plot confusing and unusable to the reader.

So far, the test mass noise was white noise such that SNR = NN/noise was about 10. Now the simulation generates more realistic TM noise with the following spectrum:

The time series look like:

So the TM displacement is completely dominated by the low-frequency noise (which I cut off below 3Hz to avoid divergent noise). None of the TM noise is correlated with NN. Now this should be true for aLIGO since it is suspension-thermal and radiation-pressure noise limited at lowest frequencies, but who knows. If it was really limited by seismic noise, then we would also deal with the problem that NN and TM noise are correlated.

Anyway, changing to this more realistic TM noise means that nothing works anymore. The linear estimator tries to subtract the dominant low-frequency noise instead of NN. You cannot solve this problem simply by high-pass filtering the data. The NN subtraction problem becomes genuinely frequency-dependent. So what I will start to do now is to program a frequency-dependent linear estimator. I am really curious how well this is going to work. I also need to change my figures of merit. A simple plot of standard-deviation subtraction residuals will always look bad. This is because you cannot subtract any of the NN at lowest frequencies (since TM noise is so strong there). So I need to plot spectra of subtraction noise and make sure that the residuals lie below or at least close to the TM noise spectrum.

ETA: Dang it, I was trying to resubmit this as a new entry so it wouldn't overwrite your old entry, sorry....

I reorganized the presentation outline a bit  - tell me what you think.

I'm still not sure where to stick the noise budget, since most of that discussion is math, not very good for a 25 minute talk, but it's seems important...  Maybe it should come before the chopping simulation discussion, because it makes sense that "since the crackling signal will probably be below all of this noise (point to noise budget) we need to use this chopping technique..."

Here is a presentation (the LIGO one at LLO in ~10 days) outline of what I hashed out with Vanessa this morning.

We will be presenting together as one report rather than two separate, consecutive reports. According to Ken Libbrecht, each individual presentation was to be 15 minutes, with 5 minutes for questions. We were thinking a single 25 minute composite talk, with the 5 minute question round afterwards. We tentatively assigned the person who would be talking about each topic...

Let red=Vanessa, blue=Larisa. Keep in mind, this is tentative and we haven't assigned everything yet!

Intro:

• What is crackling noise? -- analogies, hysteresis, nonlinear energy upconversions, pictures
• Why should be care about it? -- blade springs and LIGO

Experiment (this makes up the body of our talk):

• What do we expect the signal to look like? How will we measure it? -- Basic Michelson explanation (using PZT setup as a simple initial model) and Chopping Simulation (crackling coefficients)
• Characterizing the blade springs -- Measuring Q and resonant frequency (rough estimate and final measurements)
• Initial Setup (Problems) -- Mirror-mass attachment design
• Magnetic actuator design - math (optional), design/build -- compare to PZT use, why we switched
  • Transfer function measurement, feedback loop
• Noise Budget -- electronics, shot, thermal, intensity, seismic noise

Where Are We Now? (And What's Next?)

• Final Setup pictures
• Summary of "Results"
  • Crackling predictions (crackling coefficients), noise budget
  • Spring characteristics -- Q, Transfer function
  • Ready for data collection!
• Designing an experimental setup with even lower noise -- seismic isolation stack and vacuum chamber, ... a better laser
• (optional) Adding to Noise Budget -- frequency noise, vacuum noise, (how noise will decrease with addition of chopping?)

Hit the "reply" button instead of the "edit" button next time... that way we can see earlier drafts of this.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Let red=Vanessa, blue=Larisa. Keep in mind, this is tentative and we haven't assigned everything yet!

Intro:

• What is crackling noise? -- analogies, hysteresis, nonlinear energy upconversions, pictures
• Why should we care about it? -- blade springs and LIGO

Experiment (this makes up the body of our talk):

• Intro to PZT-Michelson version
• Noise Budget using PZT setup info to make rough estimates. Maybe we could show just these by themselves, not all other things
• Initial Setup (Problems) -- Mirror-mass attachment design
• Measuring Q and resonant frequency (rough estimate and final measurements)
• Magnetic actuator design - math (optional: just flick a screen of equations at them?), design/build -- compare to PZT use, why we switched
• Transfer function measurement, feedback loop
• Chopping Simulation (crackling coefficients, how noise will decrease with addition of chopping?) -- I put this here because the chopping circuit come physically after the PD in our Michelson, and it hasn't come up at any other time

Current status and Summary:

• Final setup pictures
• Final Noise Budget -- electronics, shot, thermal, intensity, seismic noise, frequency noise, vacuum noise
• Crackling predictions (crackling coefficients) ----is this based on measurements we might do in the future ~2 weeks?
• Designing an experimental setup with even lower noise -- seismic isolation stack and vacuum chamber, solid state laser

Comments: I moved some stuff around. Also changed some stuff because it seemed redundant (see changes to summary sub-bullets) or unnecessary (why would we talk about the seismic stack or the vacuum tank separately? What is there to say about it, other than, at most, one sentence?) Additionally, I just wanted to use this outline to list topics, you were going on ahead and sorting them. Slow down.

Hmm, I see too much red.

• Quote:

  ETA: Dang it, I was trying to resubmit this as a new entry so it wouldn't overwrite your old entry, sorry.... I reorganized the presentation outline a bit  - tell me what you think. I'm still not sure where to stick the noise budget, since most of that discussion is math, not very good for a 25 minute talk, but it's seems important...  Maybe it should come before the chopping simulation discussion, because it makes sense that "since the crackling signal will probably be below all of this noise (point to noise budget) we need to use this chopping technique..."   Here is a presentation (the LIGO one at LLO in ~10 days) outline of what I hashed out with Vanessa this morning. We will be presenting together as one report rather than two separate, consecutive reports. According to Ken Libbrecht, each individual presentation was to be 15 minutes, with 5 minutes for questions. We were thinking a single 25 minute composite talk, with the 5 minute question round afterwards. We tentatively assigned the person who would be talking about each topic... Let red=Vanessa, blue=Larisa. Keep in mind, this is tentative and we haven't assigned everything yet!   Intro: What is crackling noise? -- analogies, hysteresis, nonlinear energy upconversions, pictures Why should be care about it? -- blade springs and LIGO Experiment (this makes up the body of our talk): What do we expect the signal to look like? How will we measure it? -- Basic Michelson explanation (using PZT setup as a simple initial model) and Chopping Simulation (crackling coefficients) Characterizing the blade springs -- Measuring Q and resonant frequency (rough estimate and final measurements) Initial Setup (Problems) -- Mirror-mass attachment design Magnetic actuator design - math (optional), design/build -- compare to PZT use, why we switched Transfer function measurement, feedback loop Noise Budget -- electronics, shot, thermal, intensity, seismic noise Where Are We Now? (And What's Next?) Final Setup pictures Summary of "Results" Crackling predictions (crackling coefficients), noise budget Spring characteristics -- Q, Transfer function Ready for data collection! Designing an experimental setup with even lower noise -- seismic isolation stack and vacuum chamber, ... a better laser (optional) Adding to Noise Budget -- frequency noise, vacuum noise, (how noise will decrease with addition of chopping?)

Intro:

• What is crackling noise? -- nonlinear energy upconversion, Barkhausen Noise (not just hysteresis), earthquakes, pictures
• Why should we care about it? -- blade springs and LIGO

Experiment (this makes up the body of our talk):

• How will we measure it? Intro to Michelson: PZT version as simple analogy
  • (the PZT noise budget is essentially useless, we should probably just drop it unless we have excess time)
• Switching to Springs
  • Characterizing the springs: Measuring Q and resonant frequency (rough estimate (optional) and final measurements)
• Initial Setup with springs (Problems) 
  • Mirror-mass attachment design
  • Magnetic actuator design - math (optional: just flick a screen of equations at them?), design/build -- compare to PZT use, why we switched
    • Transfer function measurement, feedback loop (since the transfer function we are measuring is of the motion of the spring over the motion of the magnetic actuator)
• How will we measure it (part II)?
  • Noise Budget -- electronics, shot, thermal, intensity, seismic noise -- (I don't have frequency noise or vacuum noise yet, those are under future things to do.  And Noise Budget should come before Chopping because the whole point of Chopping is to extract a signal below the noise floor.)
  • Chopping Simulation (how do we expect the signal to look, how will we extract it from beneath the noise floor, crackling coefficients, [how noise will decrease with addition of chopping? - I don't know the answer to this, actually])

Current status and Summary and Future Work:

• Final setup pictures - on seismic stacks, with mirror attachment and magnetic actuator, and vacuum chamber
• Crackling predictions (crackling coefficients) -- These crackling predictions are a necessary part to design the chopping technique, since they tell us what signal to demodulate by; they should not be in the summary.
• Designing an experimental setup with even lower noise -- seismic isolation stack and vacuum chamber, solid state laser

I moved the noise budget back into the main body, since it should come before chopping.  Also it seems like poor presentation conduct not to have at least a very very brief summary of the main points - I assume we'll summarize a bit while we show them final setup pictures.  We have to sort the topics eventually anyway, I'm not sure why you would un-sort them...  It's easier to design the powerpoint this way, and it's important to know the logical connections between each topic and the motivation behind speaking about them.

Since two of my items are optional, there's actually more blue than red...  If you want, you can also discuss the mirror-attachment design, since you did that nice model?  However if you do that you'll basically be talking for the entire first half of the presentation.

The reason I split up the seismic isolation and the vacuum chamber was because I figured (1) we need to split up the summary/future work anyway and (2) I did a (very tentative) look at how the seismic isolation stack would decrease the noise on the noise budget and how we would measure that more accurately in the future, so I figured I should talk about that when it comes up.

Your rough estimate of the Q measurement could be a good thing to talk about; I think it's good to show an initial estimate before going into the final measurement...it lends more credence to the final measurement if the numbers are quite close.

What we do with the mirror-mass design doesn't matter much. EIther of us could do it; but yes, showing the 3D model would be good. I just wish there were some way of making maybe a short video clip so we (the viewer) could go and see the object from all sides.

The final noise budget and chopping at the end of the body of the talk will be all yours, and I imagine that will take up a good chunk of time itself. If that's the order we will be doing it in, maybe I should do some of the bit that comes after it (in the conclusion). Maybe not necessarily for the pictures of the final setup...we could just flick through those and show them... but I could do the cackling coefficient stuff, then when we move on to improvements, you could do the seismic isolation and I'd do the vacuum tank:

Current status and Summary and Future Work:

• Final setup pictures - on seismic stacks, with mirror attachment and magnetic actuator, and vacuum chamber --just show them without much talking
• Crackling predictions (crackling coefficients) -- These crackling predictions are a necessary part to design the chopping technique, since they tell us what signal to demodulate by; they should not be in the summary.
• Designing an experimental setup with even lower noise -- seismic isolation stack and vacuum chamber, solid state laser

I saw that you've started working on the Powerpoint this morning. I am working on the transfer function bit (I will have to consult with Seiji a bit before this is completely done), and will send you the material to incorporate. What else should I be doing? Everything that is currently blue?

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...

 I know it's not LaTeX-y, but I figure it would be a good idea to leave a copy of what got sent in.

In order to study the current setup better to improve the design of the 2nd version experiment, I did some seismic coupling analysis. The plan is to shake the optical table with a white noise (5V, pre-amplified with a bandwidth 10-1k Hz, input 0.5A, 2V) mini-shaker (B&K type 4810), while the motion of the table is monitored by a 3-axis accelerometer. A full description of the seismic noise picture should include analysis of the coupling from table motion to Mich signal, bench (damped by rubbers) inside the chamber to Mich signal, and we also want to characterize different coupling from bench to different optical elements.

The first and easiest thing I tried is to characterize the transfer function between table vibration and Mich signal. The table was shaken in x, y, and z directions separately, with hopefully three linearly independent measurements of a_x, a_y, and a_z measured for each 1hr shaking. In this way we built matrix [a_xx, a_xy, a_xz; a_yx, a_yy, a_yz; a_zx, a_zy, a_zz] where the additional index indicates the shaking direction. With [e_x, e_y, e_z] for each shaking measured by servo, simply solve [a_xx, a_xy, a_xz; a_yx, a_yy, a_yz; a_zx, a_zy, a_zz][T_x, T_y, T_z] = [e_x, e_y, e_z] will give us the transfer function along x, y and z. 

The picture is plotted with coherence between a_ii (where i is the driving direction) and mich signal is larger than 0.8. the result seems to agree with our expectation that the seismic noise transfer function follows the power law trend. 

However, the coherence is very bad. I tried increasing the noise power by limiting bandwidth to 10 - 300 Hz and inputing 0.8A 3.0V to the shaker). From the result of the z-drive result, the coherence in low frequency range is improved a lot, so I am going to finish the three-axial analysis. While the last trial of data is fit by 1/f^2, the later trial is better fit by 1/f^3, but this kind of fit is tricky. There are many resonances and it is difficult to judge which fit is the best. 

I tried superimposing the two and they are similar where both of them have good coherence.

I also did analysis (keep data with coherence > 0.8) for the coupling from directly the bench motion to optical elements. I mounted another mini-accelerometer on the newport mirror mount and clamp it to the table like what we did inside the chamber.

x has a generally higher level because the accelerometer is mounted along x-direction on the mirror mount. It seems that the transfer function is much smaller than one, which probably indicates a difference in calibration between the two signals. I will at some point mount the accelerometer one next to the other and measure the relative calibration, which should be simply a flat transfer function. 

Another problem here is that I got very bad coherence at low frequency. I have no good explanation why there seems to be a high-pass cutoff around 30 Hz, but we definitely need to push the measurement down to 10 Hz. 

During last few days, I designed the signal conditioning circuit for the hall effect sensors maglev. It mainly contains two parts:

1. The constant gain part.

2. The dewhitening part. It contains two types of high pass filters: one has a zero at 0.5 Hz and pole at 5 Hz, the other one has zero at 5Hz and pole at 50Hz. Due to the uncertainty in the shape of the signal (the floating plate motion), I put them in series (add one additional place holder) and also add jumpers to bypass the intermediate stage if necessary for possible modifications.

The schematics is shown in the attached pdf file: [signal_conditioning_hall_effect_sensor_2channels.pdf].

The Altium file for the schematics and pcb layout is also attached [signal_conditioning_hall_effect_sensor.zip], which uses the multiple channel design idea.

A spiral shape is a very good choice for array configurations to measure spatial spectra. It produces small aliasing. How important is array configuration for NN subtraction? Again: plane waves, wave speeds {100,200,600}m/s, 2D, SNR~10. The array response looks like Stonehenge:

A spiral array is doing a fairly good job to measure spatial spectra:

The injected waves are now represented by dots with radii proportional to the wave amplitudes (there is always a total of 12 waves, so some dots are not large enough to be seen). The spatial spectra are calculated from covariance matrices, so theory goes that spatial spectra get better using matched-filtering methods (another thing to look at next week...).

Now the comparison between NN subtraction using 20 seismometers, 19 of which randomly placed, one at the origin, and NN subtraction using 20 seismometers in a spiral:

A little surprising to me is that the NN subtraction performance is not substantially better using a spiral configuration of seismometers. The subtraction results show less variation, but this could simply be because the random configuration is changing between simulation runs. So the result is that we don't need to worry much about array configuration. At least when all waves have the same frequency. We need to look at this again when we start injecting wavelets with more complicated spectra. Then it is more challenging to ensure that we obtain information at all wavelengths. The next question is how much NN subtracion depends on the number of seismometers.

We are trying to chopping the signal today.

   The low noise amplifier can be used as bandpass filters for 10-100 HZ.

   We are trying to figure out the signal squaring. The mixers in the lab only work for high frequency (> 500 KHZ).

   Frank recommends us to use AD734 4-Quadrant multiplier. 

   We checked the electronics lab in Downs and 40 m and couldn't find it. We plan to order some AD734.

 I ordered 5 of AD734 and thinking about how to make a circuit for squaring the signal.

    The "chopping" signal readout technique requires that we square the signals.  Basically we need to (as rana suggested):

(1) square the signal from PD, (after 10-100Hz bandpass) to convert it to power, and band pass it again.

(2) square the driving signal (might be varied from 0.1- 1Hz.) This is illustrated in the diagram as doubling the frequency ("2 x freq" box.)  The driving signal for PZT is offset. So the signal is  V drive = A + B xsin (2pi fdrive t) with A > B. This ensures that the voltage on one end of the PZT is always higher than another end. We might need to high pass this signal first, to get a signal with only 2 fdrive frequency after we square it.      

(3) multiply signal from (1) and (2) to demodulate the signal.

Basically, 3 multipliers are needed.

The first one is for (1), so the input frequency is ~ 10 -100Hz, and the output is 20-200 Hz.

The second multiplier is for (2), the signal is ~ 0.1 - 1 Hz, but this one might have large DC term after we square it.

The third one is for (3), this one has to multiply 2 low f signals together which is quite similar to (2), so the design can be the same.

I'll consult Frank and/or Koji again before finalize the multiplier circuit.

In the mean time, we might try this mixer to multiply the signal. I'll order one.

koji, mingyuan, tara: We designed the circuit for multiplying/ squaring signals with AD734. 

    The details for each signal are discussed here. 

    The "general multiplying circuit" box in the diagram shows how each AD734 will be powered/ fed input signal.

     For the signal from the PD, we need to bandpass(10-100Hz) it first. We plan to use a SR560. To split the signal to x and y input, we will use a T connector. Then square the signal and band pass it again at 0.1 - 100Hz bandwidth.

     For the signal from the function generator which drives the PZT. We will high pass it, by either SR560 or a high pass circuit. We might need a buffer here if the output impedance of the function generator is not high. Split the signal with a T again, and square it.

    After both signals are squared, we multiply them together. Send one to X1 input, another signal goes to Y1 input. Then we FFT the output signal from W.

 I tested the mixer, the demodulated signal from input at 10 - 100 Hz might be too small and too distorted to get reliable data.

  As we want to square/demodulate  signal in 10 - 100 Hz BW. a low frequency mixer might be a good tool. I asked Alastair to buy this mixer for me, and it arrived today.

  The lowest acceptable frequency in the design is 500 Hz, but I don't know how well it works at 10 - 100 Hz so I tested it.

   ==Setup and result==

   I used  SR785 to generate sine wave, then split it with a T and connected the output to LO and RF of the mixer. 

   I tested that the mixer works fine at the designed frequency.  The plot below shows the result from  1kHz signal input.

Next, I changed the frequency to 10 Hz, 50Hz, and 100Hz.

  The demodulated signal is then observed in frequency domain (left column of the plot) and in time domain ( right column of the plot)

I think the peaks at driving frequencies (10Hz, 50Hz, 100Hz and their harmonics) appear because of the offset of the sine input signal.

The results for low frequency  seem to be too distorted. We will test the AD734 chips tomorrow. I got the package this afternoon.

 We tested AD734 on the diagnostic bread board, the result is good.

     We want to square/multiply signals between 10 to 100 Hz, so we use AD734 chip to do the work. The circuit is connected as described here

We try to square the signal. the test signals are sine waves at 10 Hz, 50Hz. The output are nice sine waves, but the gain is high (72dB). The chip rails as the input exceeds 0.5 Vpkpk. We will have to check the signal from the PD in the setup to see if it is higher than 0.5 Vpkpk or not. If so we can change the gain of the chip. Otherwise we can go ahead and use it.

The spectrum of the output, for 10Hz input, there's a peak at 20Hz output. For 50Hz input, there's a peak at 100Hz. The response is flat between this bandwidth.

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.
• 

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.

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.

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.

    ==setup==

    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.

   ==result==

       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.

 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.

[Giordon, Zach]

NB: The vacuum system was back at 10^-7 Torr when we started work on Friday. 

We began using the lock in to monitor demodulated time series while driving modes and then allowing them to ring down. We used two different driving methods:

1. Narrowband white noise. Using either the Agilent analyzer or FG as the broadband source, and then filtering to a 1-2kHz bandwidth with an SR650 filter.
2. Swept sine using the Agilent FG. Set the center frequency to the mode frequency as seen on the spectrum analyzer, and then used a ~10-Hz span with a sweep time of ~0.1-1 second to drive the mode.

Both used a DC bias of 3 kV. For the readout, we set the internal SR830 lock in reference signal to ~10-100 Hz offset from the measured mode peak, and the time constant such that there was a clear signal at these beat frequencies without excess high-frequency fuzz. The lock in input was of course the differential PD signal, with the difference taken by an SR560. It was basically like an SRS/Agilent product demo down there.

The noise method was obviously just not strong enough somehow. Looking at the AC drive signal, we increased the power until there was a rough peak-to-peak level of ~2 kV, above which I did not dare go. Looking at the readout, there was basically no difference at all with the noise drive on or off.

The coherent drive seemed to do something, but as expected it both excited and damped the mode as an unpredictable function of the mode drift and the sine sweep. That said, when it excited the mode, there was a notable increase in the signal. When the drive was turned off while the output was at relatively high amplitude, the signal immediately went down to its unexcited level. The timescale was well under a second.

There are at least two possibilities:

1. The excited signal seen while using the sinusoidal drive is actually a spurious EM coupling. This seems unlikely because of the low-frequency amplitude fluctuations seen while driving, which are suggestive of alternating excitation and damping.
2. The mode Q is just that low. The ~2 Hz linewidth (Q ~ 10⁴) I measured using the spectrum analyzer would correspond to decay times under 1 second. In all fairness, we don't know what it should be for this random sample a priori anyway.

It seems odd that we have a hard time ringing the mode up substantially, since the DC bias visibly excites the pendulum mode upon turn-on (so the electrostatic force is high enough to do something). It could be that the vibrational modes' admittance is just much lower than that of the pendulum, or that there is a great deal of cancellation from the particular symmetry. Another thing is that the sample might be getting subtly tapped by the ESD assembly every once in a while, and this destroys the coherence of the measurement.

We might consider slightly adjusting the arrangement (e.g. by translating it) to see if there is any improvement.

I got a chance to talk with Norna about the strain range we are in for our maraging steel blades:

We typically load the blades to a stress level of 800 MPa to 1000MPa. The upper value there is approx. 55% of the yield stress which is ~1.9 GPa. The Young’s modulus E = 186 GPa.

—> strain rate = d/dt [ (F sin(wt) + F0) / E ] = (wF/E) cos(wt) —> maximum rate = wF/E = (2 pi 0.125 Hz) (800 counts ~ 1um deflection) / 186 GPa

400 MPa ~ 1mm deflection

4 kPa ~ 1um deflection

—> max rate = 1.689e-08 /second

Also, the triangular shape gives equal stress along the length of the blade when loaded.

In addition, as [1996 Dahmen] "Hysteresis, avalanches, and disorder-induced critical scaling: A renormalization-group approach" shows a relationship between hysteresis and crackle, on page 14 878 they show how a model scaling hysteresis loop area with r, where r is associated with the average avalanche size: A_sing ~ r^(2-alpha) (MFT :alpha =0), I am thinking maybe materials with larger hysteresis loop area would generate crackling noise more “easily”. If this is the case, a good candidate would be the AISI 1085, which is also called music wire; it’s a high carbon steel. 

Reference: [1998 Beccaria] "The creep problem in the VIRGO suspensions: a possible solution using maraging steel"

A folder on the 40m svn server has been created to store crackle related files

The location is: /trunk/crackle

This currently includes the latest poster, a MATLAB subdirectory which holds all of the code from my last elog, a Lit subdirectory with a couple of papers in it, and an ExpChar directory which houses the bulk of the measurements I've made regarding the experiment.

Specifically listing what is in each sub-dir

/trunk/crackle/ExpChar/:

• Blades: transfer functions and ringdowns of the blades via shadow sensor
• Laser RIN: measurements of RIN in different configurations (fiber, no fiber, dark noise, etc.)
• Loop: Measurements of the Loop TF
• Mich: spectra of the Michelson error signal
• Servo: LISO files of the servo circuit, and transfer functions (liso and measured)
• ShadowSensor: Circuit of the shadow sensors and TF of the damping
• circuit.graffle: OmniGraffle drawing of the crackle NIM box circuitry