Since I am still using the HiCube pump for the gyro, I figured it was a good idea to check the pressure level of the bell jar every now and then.

It is at ~160 mTorr right now, which I assume is OK to leave it at (?).

I removed the pump on 6/15, so it has taken ~8 days to get to this level.

Here is a recap of a phone conversation between Rana, Nic and me, which I am remembering from my mindbrain:

• I described the stalemate at which we had arrived:
  • We have used COMSOL to estimate ideal clamping losses assuming perfect contacts. Using these models, we have found ways to make the ideal clamping loss for a simple structure---steel clamping to a thick (~500 um) piece of Si, while a thinner portion (~50-100 um) of the Si juts out to become the resonator---nearly as low as the intrinsic loss of bulk Si. Clearly, this would be good enough to investigate any surface effects, but the clamp interface will never truly be ideal.
  • We began thinking about ways to further reduce the clamping loss by adding isolation/cancellation schemes. For example, we studied the butterfly resonators that have been able to achieve very low loss for particularly well isolated modes.
  • We then considered how we might construct something like this while also building a twin cavity setup. Initially, we thought of using a single Si wafer with two resonators, each of which would be situated as an end mirror in its own cavity. This concept emerged in two differing contexts: 1) Compactness and clamping desing (i.e., it seemed convenient to clamp a single wafer by the middle on each end of the cavities, and have each wafer serve both cavities) and 2) isolation/cancellation schemes, mostly since there is some superficial similarity between the butterfly-type resonator and a wafer with more than one cantilever on it.
  • We then wasted away trying to think of how we could model such a system while taking into account all the relevant figures of merit (clamping loss, resonator-to-resonator coupling, etc.)
• Rana then elucidated his theory that there are three things we have to consider here. From simplest to most complex:
  
  1. With a simple cantilever geometry, how do we design a clamp that least disturbs the measurement of thermal noise in the resonator? We think we have this one solved, using the varying thickness approach, but it relies on a good idea of the imperfections in the surface contacts. Likely, we will want an added layer of isolation/cancellation in addition to a good clamp, due to these imperfections.
  2. How can we isolate the resonator from the clamp so that extra clamp noise from non-idealities is suppressed? If we only care about a particular mode or set of modes, we can do something akin to the butterfly resonators, as these isolate particular modes very well from the motion of the clamp. However, we are also interested in broad off-resonance behavior. I believe this rules out something as simple as the balanced-oscillator approach of the butterfly resonators, and instead requires something closer to the cascaded passive isolation stages of our suspension systems.
  3. How do we integrate all this into two parallel cavities to make our beat-based measurement? If we work through (1) and (2) to make something that is good enough to allow us to measure surface effects with high accuracy, we may find that we have something that's not particularly suitable for integrating into a twin cavity setup. That said, we already have our cryostat, so we have to figure out how to put something useful into that space.
• With all that in mind, our plan was to do the following:
  • Immediately, we should buy some wafers that have the desired thickness ratios cut into them. It is important that the resonator sections are thinned symmetrically from both faces of the wafer (i.e., not etched down from one side so that one cantilever face is coplanar with one original wafer face). We can have these be several cantilevers distributed around one circular waver, or perhaps better is having a wafer cut to make several standalone cantilevers with a thick clamping section at one end. Ideally, several of these would be punched out of the original wafer structure as in the original ideal.
  • The above resonators will be tested with ringdowns in the smaller cryostat. Using different clamp ideas, we will see how close we get to the ideal clamp loss given by COMSOL. This will give us some idea of how much extra cleverness we will need to put in the real versions.
  • At the same time, we will begin building the optical setup with macroscopic mirrors.
  • The goal is that both the resonator prototyping and the optical setup are completed in parallel, and then the final clamp/resonator is installed in the main cryostat for immediate science.

Here is a screenshot of the axisymmetric COMSOL model used to get the ideal clamping losses from a thick/thin structure. Clearly, the strain energy in the ideal case is localized at the center, far from the steel/Si interface. This has been confirmed with a full 3D model of a more traditional cantilever.

[Nic, Zach]

Today, we unpacked the IR Labs cryostat that will be the centerpiece of the Cryo SUS experiment. 

Everything was more or less in order, except that the baseplate does not have any outward extensions with which to mount the cryostat to the table. Also, the holes for the screws holding the baseplate to the barrel are not countersunk. So, as of right now, the entire cryostat sits on these screws' caps, which is not ideal. We need to either a.) get a new baseplate made up with some wings on it and countersinking for the screws, or b.) work out another way to hold and mount the cryostat (for example, we might want some soft isolating material there anyway, though it will come at the expense of alignment drift).

I followed the instructions and removed the strange anodized heat shield bottom plate that comes with it during shipping, replacing it with the usual one and then resealing the chamber. As directed, I also pumped out the air again---the charcoal getter is not supposed to be exposed to atmosphere for long periods of time.

I returned the Gooch & Housego R26035-2-1.55-LTD AOM (SN 216939) from DOPO table

Received one Marconi 2023A (#539) from CTN and an SRS FS725 Rb clock. (See CTN/2605)

• Took a delay line box DB64 from QIL from the WOPO table. The box was marked Crackle on it.
• Took the compressed nitrogen cylinder for optics cleaning which was stored in Adaptive Optics lab.
• Took some lens from the cabinet in Adaptive optics lab.
• Took some other optics parts like pedestals, posts, lens mount etc.

QIL elog entry: QIL/2524

Here are some comments:

- The noise from Michelson ifo, that Dan posted yesterday, appeared to be just above the SR785 noise. But now Dan knows how to do the whitening to beat this noise down. The Michelson spectrum was not corrected for the loop gain. The voltage noise from Michelson was ~30nV/rtHz refered to the PD output at 100 Hz.  Today we measured the Thorlab PD100A dark noise to be around 15 nV/rtHz at 100 Hz (not bad for a cheap PD with ~10 V full range). We also tried to measure the laser intensity noise and found that we would expect it to be several times higher than the Michelson in-lock spectrum we got yesterday(?). The laser noise measurement was done by blocking one of the arms with a black glass dump. So the laser noise needs more investigation.

- Also for the reference the free swinging Michelson ifo p-p value was 60 mV. The DC value of the mid-fringe was also ~60 mV. So the contrast defect (Pmin/Pmax) was not great ~30%.

- Frank turned off the computer in the SUSlab for us as this computer was the largest audible source of noise. We expected to see the reduction of acoustic peaks in the spectrum around few hundred Hz but we are not able to lock the Michelson today for unknown reason. There were virtually no changes from yesterday configuration apart from some minor alignment due to replacement of the laser post. The p-p value is the same as yesterday. Anyway the chamber will be pumped eventually so the acoustic noise will not be a problem.

- We borrowed a SR650 from the CDS group to do the power demodulation measurement. We found that if the SR650 is setup to bandpass 80(hp)-100(lp) Hz then a 2 V p-p sine wave at 1 Hz is attenuated by the filter to 70 uV p-p value.

- Another option for the power demodulation is to record the time serieses of the Michelson output and the excitation signal using SR785 - it holds up 9 hours of data at 256 Hz - and then do the digital bandpassing, squaring, frequency doubling, and demodulation all in Matlab. 

- The up shot is that with the noise of 5e-14 m/rtHz above 100 Hz one can start doing the power demodulation to go below this noise by another factor of ~10 or more.

Attached is the initial proposed circuit design for the crackle michelson servos. First, a .07V offset is subtracted from the signal. (.07V is grabbed 
from a 15V regulator+voltage divider, not pictured)

A 300-3k bandpass, G=10, filter is added to a 1kHz, unity gain, filter. Next is a switchable gain stage, that provides a gain of 5 under .1 Hz. Once 
lock is achieved the switch can be disengaged, providing large gain at low frequencies, to counteract large low-frequency disturbances. The signal 
is then split and one leg inverted, and then the lockin amplifier signal added to both. The signal is then sent to the actuators through more 
amplifiers and a BUF634. 

Circuit made less bad with help from Koji!

Resistor values made more appropriate
Filtering portion *greatly* simplified
V_offset will be drawn from a regulator and a precision voltage reference, such as an AD584/587. 

Additionally, additional resistance may be necessary in series with the actuator coils, depending on their specific resistance. 

 After changing out the 1uF capacitor for a 220uF one, at Rana's advice, the filtering portion of the circuit was measured to have the attached frequency response. It corresponds to our expectations. 

 I have calculated the expected transfer function of the filtering portion of the servo circuit and compared it to the measured response. There is a low frequency discrepancy in the magnitude, and the phases look completely different. I suspect that my calculations are not perfect, so I will be revisiting that portion. 

 Fixed the phase measurement and recalculated using LISO, but now the magnitude has gone out of whack... Magnitude curves do have the right shape, qualitatively, however. It looks like a extra ~17db snuck in somewhere. I will investigate.

The phases are somewhat difference, but I am not sure how big of an issue this might be. 

Took some quick measurements of the laser noise with the laser (Uniphase 1103) and PD (Thorlabs PD100A). Not sure if we care about frequencies above 1.6kHz. The PD was set at 1500 V/A, and the PD has about .25 A/W at the laser's frequency (632nm). By Mingyuan's recommendation, the laser was turned on about 30min before this measurement. 

 Corrected the plot, now shows Relative Intensity Noise. (i.e. (dP/P) per rtHz).

 It turns out I was using a polarized capacitor, causing the mismatch between predictions and measurements for the circuit. 

The current schematic and Transfer Functions are attached.

 For the immediate future, the following tasks have been delegated to achieve a straightforward crackle measurement with the small blades. 

These items will ideally be completed before the 17th. Jan, Mingyuan and I will meet on Monday to create a concrete schedule. 

Eric

• Complete the active damping system (servo circuit debugging + shadow sensor selection/design)
• Design plexiglass disc with custom feedthroughs to seal chamber
• Find a roughing pump and gauge to get chamber down to 10mTorr (can have oil)

Mingyuan

• Acquire new O-ring for the top of the chamber
• With Eric G., work on using a fiber to get the HeNe laser light into the chamber, freeing up room

(For further improvements down the road)

• Material calculations for the plates, new plate drawings, quotes for plates
• Material property investigations of blade material

A picture of the whiteboard from the Nov 1st meeting is attached. 

 I wanted to change the servo circuit design to accomodate an adjustable offset, since at first pass at realigning the crackle michelson, a different DC value was seen at the PD than our previous efforts. 

I thought it would be straightforward to use a voltage divider with a adjustable resistor in series to set the offset, and then buffer it with an op amp. The output of the op amp corresponds to the voltage I expect. However, when testing the circuit that subtracts the offset from the pd signal, as built in the attached diagram, the output is on the order of -10 V when the PD input signal is .19V and the offset is at .05V. I'm not sure what I am doing wrong.

 Problem solved, circuit (minus damping) now looks like attached pdf.

Jan and I spent some time trying to lock the crackle interferometer with the servo circuit, rubber damping still in place.

While the circuit tested favorably with test input from a function generator, resulting in the expected actuator signal, it was hard to discern any affect on the PD signal in the crackle setup. Jan and I looked at the power spectrum of the PD with the circuit turned on and off, and it still looked ambiguous. 

At this point, we are unsure how to diagnose the interferometer, and the best way to determine if locking is taking place. 

 Put together the first shadow sensor for the active damping today. The circuit is pretty straightforward.

The signal ranges from ~ 0-1.5V over a few millimeters. 

Now, I just need to cook up another one, and add them to the control circuit, and we should be able to lock the michelson without the rubber blocks this week.

 Here's the latest schematic for the control circuit. There are some unspecified component values, mostly because I haven't decided on the frequency cutoff and gain of the shadow sensor signal. Also, I hope to have corrected some problems Koji pointed out with the way the signals are added before being sent to the actuators. 

 I was having reliability problems with the shadow sensors, which I think was caused by soldering too hot, damaging the LEDs. (Their datasheet indicates a max soldering temperature of 500 degrees, applied for 5 seconds max. I was definitely overstepping this.)

With an undamaged LED, I was able to get two PD ends of the sensor acting nicely, with a voltage range of about 3 volts. Jan has ordered more LEDs, and once these arrive, I will have two functional shadow sensors. I plan to take noise spectra with the LED on and off. Are there any other tests I should do before arranging them on the blades?

I'm working on the control circuit now. A slightly modified version of the schematic is attached, which takes Koji's feedback into account. 

 I have built the differentiating path for the shadow sensor signals. At first glance on a scope, it performs as expected, though the noise seems high. Attached are a schematic, oscilloscope traces showing the differentiating, and the theoretical transfer function of the circuit. 

I'm not sure that the transfer function is the one I really want, I think that a flat gain across lower frequencies would be better, and a capacitor across the feedback resistor could accomplish this. However, in that case I get a -180 degree phase shift instead of the -90 which I understand to be appropriate number for a differentiator. My understanding of all this is likely incomplete...

Tomorrow, I plan to measure what the shadow sensor sees when mounted on the (still passively damped) blades, to determine what frequencies are most important there. This should help me determine what transfer function I want, and then I can take power spectra / TFs of the whole affair. 

I mounted a shadow sensor near one of the suspended blades, from the structure that supports the actuator coil; made a makeshift flag, and aligned it such that the shadow sensor voltage was about half of when fully open. The shaking of the blade was visible on a scope, though quite small. 

I took a power spectrum of the voltage fluctuations, after passed through an SR560 (AC coupling, G=50), and got the following result. 

Note that the rubber blocks and eddy current magnets were still present on the setup when this was taken, since removal would require fairly invasive reconstruction, and the active damping is obviously not ready to replace them. I will eventually repeat the measurement without the external damping present. (In the meantime, I may try and see if I can do this measurement with a locked, passively damped system.) Also, I need to find a way to accurately measure the displacement range that the shadow sensors can detect, so I can convert the sensor's voltage noise into the blade's displacement noise. 

In any case, I think it will be important to design the active damping to handle the comparatively sizable oscillations at 40Hz and below.  

 Updates on active damping!

First, I performed a Voltage to Displacement calibration on the two shadow sensors, using a micrometer stage and a detector card to bring the sensor to half of its max voltage, and then measuring the voltage vs. micrometer displacement. The behavior was linear to within a few percent, so I feel confident in the conversion figure (different for each sensor, both both are close to 4V/mm)

This allowed me to turn the previously measured noise spectrum (incorrectly labeled PSD...) into displacement noise. Here's the plot:

Next, I adjusted some of the differentiator circuit values, to optimize for the relevant frequencies. Using liso, I calculated theoretical noise values and the circuit's transfer function. The noise should be well below the actual displacement noise, and I believe the TF looks good for actuating active damping. 

Finally, this morning, I've hooked the whole thing up, and gotten traces that show the differentiating happening.

However, when I connect the damping signal to the coil actuator, the ringdown time of the blade doesn't change. I think I don't have enough gain to drive the coils. I will insert a BUF634 and some gain to push more current this afternoon. Here's a trace of the blade ringing down, and the differentiator signal. 

 We started with the blades damped with rubber + magnets (6.2 sec 1/e time, blue trace is output of the shadow displacement sensor):

Then, I attached the shadow sensor and differentiating circuit, with a bit more gain than this morning (3.2sec):

Looks good, so I cranked the gain way up! (.54sec):

Even better! Next, I took out all of the passive damping. This was a giant pain, and it'll be awhile before the michelson is aligned again, because I really had to move things around. 

With no damping, the blade oscillations look like this:

Turning on the active damping circuit, and....

By eye, looks like about a 3 second 1/e time. So, already, the active damping is more effective than the passive damping. 

Next up: hard-wiring some permanent circuitry for all this. 

 Lately, I've been working on building a more permanent version of all the crackle circuitry into a NIM box. It seems that I really underestimated the time necessary to solder all of this together, so it's not quite done yet. I'm about 90% done with the board itself, and then have to enclose it in a box and hook up the appropriate switches, dials and BNC terminals. I expect to complete this Monday morning. Here's a picture of the board as it currently stands, though you probably can't infer much from it. 

Hopefully I haven't made too many amateur mistakes; time will tell. 

The board itself is done, now I have to hook it up to the requisite switches and potentiometers and box/wire it up in a NIM box. Will get started on that after class...

 What started out as attaching new, longer wires to the shadow sensors resulted in a few burnt out LEDs and much frustration in getting them working as before.

Anyways, here are the things I need to do to get data coming in:

• Recalibrate modified shadow sensors
• find/make a NIM faceplate with appropriate number of switches and BNC terminals, wire it up
• Second blade arm: Reattach loose actuation magnet and remove rubber and magnets
• Mount shadow sensors on both arms, position carefully
• Align michelson from scratch
• Turn on active damping, servo 
• Adjust gains until nice and locked
• Add "lockin" signal to actuation
• Read out PD signal into DAQ!
• Data!

I also need to start wiring up the vacuum feedthrough, among other things, for the improvements that will follow

 The crate is complete! 

Well, in theory anyways. Even when the active damping and servo are switched off, the output of the final op amps are railing at -15V. Here's an update schematic. It's little sloppy, sorry. 

In the situation I'm mentioning, the input of the 10k resistors on the final summing op amp all read 0V for the damping and servo paths, but there is a nonzero voltage on the lockin amplifier summing resistor. I put a 2.2 megaohm resistor between the lockin input and ground, for high input impedance, and so that the the op amps wouldn't have a floating input if the lockin wasn't connected. Am I making a mistake in doing this? Also, the problem persists when I take the BUF634 out of the feedback loop. 

Also, I would be highly surprised if I didn't make multiple amateur mistakes at this point. Any help is greatly appreciated!

 I found the problem with the circuit (misplaced a ground connection )

Anyways, the box now performs as expected, and is now hooked up in our NIM crate. I've reattached the loose actuator magnet, and removed all traces of passive damping from the setup. 

I've started the process of realigning the michelson, but it's very fussy, especially since the masses swing more now. Still, I should have it aligned by tomorrow, then it should be straightforward to damp and then lock it!

 Now that the electronics are working, I'm working towards setting up the chamber with active damping and a locked michelson to get some preliminary data. 

I recalibrated the shadow sensors, since I had modified them somewhat, and they are now powered by the crackle electronics box. 

I tried to align the michelson, but the masses swing like crazy with no damping present. Hence, I mounted the shadow sensors on the blade arms, positioned them to read about half of their maximum output, and turned on the damping.

However, it looks like I counted my polarities wrong, as I currently am producing anti-damping, making the masses swing around more. I think I'll switch the final gain of the shadow sensor path in the crackle box from noninverting to inverting to account for this.

Once this is done, I believe it will be possible to lock the michelson tomorrow!

 First off, I fixed the polarity of the active damping, and successfully damped both arms at once. The following oscilloscope trace shows the masses reacting to an impulse on the base plate first damped, then undamped. 

WIth damping in place, I then aligned the michelson the best I could. I eventually achieved modest alignment with contrast of +-.35V with a mean of about .9V.

The green trace shows the adjustable offset from the crackle box, which I positioned as shown. I then flipped on the servo circuit and...

Now, altogether, I'm not very knowledgable about interferometer locking, so I'm not sure if this is a good state to move forward with, if the alignment needs improvement, or anything else of a plethora of things that may not be ideal. I will poll wiser people at tomorrow's crackle meeting. 

Also, before tomorrow's meeting, I will take new displacement noise spectra of the shadow sensors, and spectra of the locked/unlocked PD signal. (Though I'm not sure what units are relevant for the PD signal. I will look into this.)

 Now that I've achieved lock, I compared the noise spectrum of the Michelson error signal now to the measurements Dan showed in his ELOG entry from Sep 07.

Old results on the left, new results on the right. NB: Neither of these measurements are corrected with the loop gain.

Noise in my locked signal appears to be higher. This is not a good sign, and I'm not sure why my spectrum has a different shape. Additionally, the shape of the laser intensity noise I measured has a qualitatively different shape than the old measurement, but is consistent with the measurement I made in late October. 

Given that the contrast in the old setup's aligned michelson signal was only 60-80mV, compared to .75-1V that I have achieved now, I'm surprised that the old noise is better. Today, I will try to measure the loop gain of the system to correct the noise spectrum.

Some results from this morning:

I achieved a really good alignment today, with a contrast ratio of around 90%. (~150mv-1.4V) However, I was not able to get as stable of a lock as I had previously. The lock was very sensitive to the servo gain, and the error signal oscillated with a frequency near the blade resonance (~4 Hz). I was not able to turn the damping off and stay locked; preventing me from taking a measurement of the loop gain. 

Nevertheless, I took a noise spectrum of the error signal in tenuous lock. Here it is:

This spectrum is much more similar to the one from September, though it does not fall to the laser intensity at high frequencies. It seems that I am limited by something else at high frequencies. Maybe it is the instability of the lock that causes this?

 Today was off to a good start. Jan has completed the analysis chain to produce visualizations of the time variation of the michelson's displacement noise, which will hopefully let us see the crackle noise synchronous with the drive. I was able to lock the michelson, and commonly drive the mirrors with a 1V, .1Hz signal. I took quick spectra of these configurations, to make sure our sensitivity was ok. 

At this point, I realized that the blades' motion due to the external drive had different amplitudes, due to the difference in blade strength and load mass. By a rough estimate, it seems that the crackle box + coils aren't able to move the blades very far at .1Hz, on the order of 100 microns. Thus, I fiddled around with the magnet/coil geometry, even stacking an extra magnet on the blade with the lower amplitude. By tuning the gain of the final summing op amps for each coil, I was able to get the same displacement from a .5V .1Hz signal on both blades.

Then, the problems began. Once the michelson was realigned, I was barely able to achieve any locking, and the error signal was *much* noisier than earlier in the day. I was no longer able to drive and/or disengage damping while maintaining lock.

I'm not entirely sure how to fix this. Did matching the blades' amplitudes at .1Hz actuation introduce an imbalance at frequencies that the servo actuates at? (Or would the negative feedback nature of the loop make this irrelevant?) Are my actuators generally too weak? Hopefully, I can regain undamped, driven, lock tomorrow so we can take data overnight.

Yesterday, I fixed my locking problems by changing the servo loop transfer function, to have gain at some frequencies that were very unstable. 

In the following screeshots, the yellow and cyan traces are my shadow sensor signals, the magenta is the PD signal, and the green is the the offset voltage that determines where on the fringe I try to lock.  

I took new noise spectra, and transfer function measurements, with these results. The data for the loop gain is attached as an ASCII file. As a quick check, the relative line width of the locked signal ~ 80mv/1.25V corresponds to ~20nm/317nm (half wavelength) fluctuation, which is about the value of the low frequency displacement noise.

The noise is now definitely lower than the measurements last year. 

With this in place, I started the .1Hz drive. This is about a 20 micron common mode displacement of the suspended masses.

The interferometer is stable in its locked state, so I left in running overnight, and Jan acquired a few hours of data. Results from this data is forthcoming and will go on my LVC meeting poster!

I've been working with crackle data, trying to get a solid result. 

Through simulating the crackle noise with the force dependent model (see simcrack.m), I found a relation between the coefficients that come out of the demodulation, and the displacement noise in the simulated michelson signal (alpha2noise.m, demod2noise.pdf).

It's a solid power law relation (quadratic, specifically), so I tried using this as a direct conversion for the demodulation output for the frequency range 45-55Hz (A minimum in the michelson sensitivity curve). However, when I apply the demodulation code and this conversion to displacement noise on the locked, undriven, data, the noise result is much higher than what is true, so I'm not sure where to go next (noisetrial.pdf).

Some reasons I may be doing things wrong:

-When simulating the crackle noise, I know the phase of the simulated drive, so the I and Q are properly defined. WIth the real data, since we did not record the drive signal, there is an ambiguity. I tried to mitigate this by using the magnitude (sqrt(I^2+Q^2)), which also scales with the noise seen in the simulated crackle signal. However, I feel like this may not be justified. 

-I have neglected the contribution of jerk-dependent crackling in this analysis. This could change the demodulation / noise relationship considerably. This is probably the next thing I will look in to. 

(I'm getting an error when trying to upload the plots. I'll try again later. In the meantime, links: demod2noise noisetrial ) 

 Zach was indeed very helpful. I moved the ESD over by one bolt hole, about 3/4" to the right (look though the input side through to the output side). We hope that this will let us excited new and interesting modes. 

Talking with Giordon today, I expressed that I am unsure about the ringdown data. I don't know if it is the noise that is high, or if the signal is low. Perhaps we are not exciting the mode properly, or the lockin is somehow not measuring optimally? While the shape of the data qualitatively makes sense in terms of reduced magnitude when the drive is turned off, the inability to fit might be explained by a low lockin signal while the drive is still engaged. I asked Giordon to see if he could estimate an anticipated lockin response from the height of the transfer function peak, to see if that sheds any light on the matter...

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

 Igal and I determined that the polarity on the damping signal was indeed wrong for one of the blades. We flipped the magnet, and damping works on both blades. Something weird is happening with the data acquisition system, so no plots at this moment, but successful damping is obvious on the scope. 

Right now, Igal is measuring the voltage vs. displacement curve for one of the shadow sensors which had it's LED/PD replaced. 

Some upcoming measurements include:

• Measuring the coil voltage to shadow sensor  voltage TF (which then will be converted into Coil Voltage to blade displacement TF)
• Taking the noise power spectrum of the drive signal
• Noise spectrum of the crackle electronics with the servo on (routing the offset voltage into the michelson input will produce noise solely due to the circuit)
• Overnight measurement of michelson signal and GS13 signal for coherence

We also want to come up with models for shot noise and seismic noise for our noise budget. (Jan suggests separate Day and Night seismic models).

 For quick comparison, here is the relative intensity noise from the pre-fiber setup. In general, it seems that using the fiber has introduced a fair amount of intensity noise into the setup, which may be problematic.

 The labels for the green and teal traces are a little misleading. These displacement noises are the result of the voltage noise from the .1Hz driving function generator multiplied by the coil voltage -> shadow sensor voltage transfer function and shadow sensor voltage->displacement calibration factor. The trace ends at ~100Hz since we don't believe the transfer function measurement at frequencies higher than that, due to the tiny signal amplitude from the shadow sensors. We will likely extrapolate the power law that the blade transfer functions show between 10-20Hz. Perhaps we should call this "drive noise," or something similar. In any case, it's disturbingly high.  

One suggestion Koji made last week was using a larger signal from the drive (which may have a higher SNR), and then attenuating to reach the desired drive level. 

 Modified the crackle control circuit to accept individual drive signals for each actuator, with the intention of being able to do blade transfer function measurements via michelson, instead of via shadow sensors. Updated schematic attached.

To test our analysis code, I recorded some data from a Wheatstone bridge. 

The .1Hz drive signal was fed to the terminals marked "IN", and the recorded signal was the difference of the terminals marked "OUT". All four resistors for the following plot were 1MOhm.

We see lines along the harmonics of the drive frequency in the double FFT, as expected. We'll look at this more to see how to extract a crackling noise amplitude from this. 

Referenced elog post is here: entry 270 

I set up the bridge with 5.1 kOhm resistors (though not wire wound, yet), a 100 ohm trim pot, and an AD620. With a drive frequency of 1.25 Hz, I adjusted the trim pot until the fundamental wasn't apparent on a oscilloscope trace. I was able to reproduce a similar spectral density plot, compared to the figure in the linked elog post above. 

I have also acquired ~30 minutes of data from this setup, to be analyzed later with forthcoming code.

On the simulation code front, however, things aren't so clean cut. With the attached MATLAB code, I create a time series of crackle noise + Johnson noise (and will add in the AD620 noise soon), and produced the following plots of the PSD and a "Double FFT", which is formed by looking at the FFT of individual PSD values at a given frequency.  The following plots were made with alpha=1e-6, where alpha sets the scale of the fluctuations in the resistance. (I.e. For a given resistor in the bridge R= R0( 1 + alpha*Vext*randn))

The time series looks as expected:

The PSD does not look like what is physically measured; instead the psd just sits on the Johnson noise throughout. I'm not sure why this is. Is there something fundamentally wrong with how I simulate the noise, or can it be chalked up to calculating the PSD incorrectly? 

Here, the double FFT does show evidence of the 2F component, however. However, no such line is observed at 1F. Why is this the case?

The upconversion of the crackle noise can be seen by comparing this line with the magnitude of the double FFT at frequencies unrelated to the drive. At the moment, we haven't worked out what the numerical values of the double fft mean, but here is a plot anyways. 

The code also includes demodulation calculations, which work out as expected. Specifically, a quadratic power law relates the Q demodulation result and "alpha" parameter (scale of crackling) above alpha=1e-8 or so. This is alternative to the double fft routine.

Next steps:

• Run collected time-series data through psd and double fft code, see what comes out. 
• Reconcile difference between simulation and measured data.
• Re-run with wire wound resistors
• Work out what double fft means quantitatively. 

 Through the demodulation analysis, I found that I observed crackling noise in a carbon film resistor, and no observable crackle noise in metal film resistors. 

Here is a plot comparing the Carbon-Film resistor's demodulation coefficient in time, both with the drive on and off:

 As expected from the simulation, the crackle effect shows up in the 2F Q signal. Unlike the simulation, however, the Q value is not very steady. I am not sure why this is the case (perhaps temperature effects?). 

The mean Q here is about -2e-11, which corresponds to a crackle coefficient of 2.5e-5. I need to compare this value with the literature (i.e. the section in Frank's Thesis that talks about resistor noise). This coefficient controls the fractional change in resistance like so: R=Rbase(1 + alpha * Vdrive*randn).

I also compare this result with the same setup, but with a metal-film resistor, which should exhibit no (or much less) observable crackle noise. This was indeed the case, as the mean of the metal-film's Q is on the order of the case with no drive, meaning that no crackling was observed. 

 Broke a few fibers recently, today I glued in our last one. 

Replacing the acrylic flange with a metal one, and getting a new L-shaped O-ring for the lid let us get down to 46 mTorr, by far our current best. 

However, we don't yet know how this affects our noise levels, since we cannot lock. My current suspicion is unwanted vibration modes in the blade+mass systems. When I engage the servo, I see oscillations at the scale of the fringe-to-fringe voltage at ~5Hz, in between the moments when it's swinging between fringes. This, along with the "cleft" at around the same frequency in the blade transfer function measurements made via shadow sensor, suggests non-vertical shenanigans that we can't actuate on / control. 

The steps I want to take to hopefully mitigate this will be:

• Adjusting the masses so that they are hanging as horizontally as possible during equilibrium (which is far from the case for one of the pair). 
• Adjusting the steering mirrors below the masses to ensure the laser beam is reflected vertically. (Dmass also suggested using a "corner cube" for this kind of thing, looks like these are three mirrors which are arranged to reflect a beam back to the source, insensitive to incoming angle to a certain degree)
• If I can find out specifically what the motion causing problems is, might it be possible to mechanically prohibit it? I've poked at the masses in various ways, but have yet to find a mode which looks like the right frequency, but my eyes are probably not the best tool for this...

Also, in the recent past, we have talked about redesigning the experiment slightly; namely mounting both blades on one single post. This would save room in our cramped little chamber and make it easier to align, as well as potentially reducing coupling of the masses (though not 100% sure about this).

Other things that are forthcoming:

• Finishing up the resistor bridge stuff (Need to compare to values in Frank's thesis, test other materials)
• Our noise budget needs a fair amount of work, part of which is working out the details of the Michelson's common mode rejection.