I made a change to the c1ass model to normalize the PIT and YAW POP QPD outputs by the SUM channel. A saturation block is used to prevent divide-by-zero errors, I set the saturation limits to [1,1e5], since the SUM channel is being recorded as counts right now. Model change is shown in the attached screenshots. I compiled and installed the model. Ran the reboot script to reboot all the vertex FEs to avoid the issue of crashing c1lsc.

Attachment #1 - comparison of the POP QPD PIT and YAW output signal spectra with and without them being normalized by the SUM channel. I guess the shape is different between 30-100 Hz because we have subtracted out the correlated singal due to RIN?

This did not have the effect I desired - I was hoping that by normalizing the signals, I wouldn't need to change the gain of the ASC servo as the buildup in the PRC changed, but I found that the settings that worked well for PRMI locked with the carrier resonant (no arm cavities, see Attachment #2, buildup RIN reduced by a factor of ~4) did not work for the PRMI locked with the sideband resonant. Moreover, Koji raised the point that there will be some point in the transition from arms off resonance to on resonance where the dominant field in the PRC will change from being the circulating PRC carrier to the leaking arm carrier. So the response of the actuator (PRM) to correct for the misalignment may change sign. 

In conclusion, we decided that the best approach to improve the angular stability of the PRC will be to revive the PRC angualr feedforward, which in turn requires the characterization and repair of the apparently faulty vertex seismometer.

Summary:

I'd like to revive the PRC angular feedforward system. However, it looks like the coherence between the vertex seismometer channels and the PRC angular motion witness sensor (= POP QPD) is much lower than was found in the past, and hence, the stabilization potential by implementing feedforward seems limited, especially for the Pitch DoF.

Details:

I found that the old filters don't work at all - turning on the FF just increases the angular motion, I can see both the POP and REFL spots moving around a lot more on the CRT monitors.

I first thought I'd look at the frequency-domain weiner filter subtraction to get a lower bound on how much subtraction is possible. I collected ~25 minutes of data with the PRC locked with the carrier resonant (but no arm cavities). Attachment #1 shows the result of the frequency domain subtraction (the dashed lines in the top subplot are RMS). Signal processing details:

• Data was downloaded and downsampled to 64 Hz (from 2kHz for the POP QPD signals and from 128 Hz for the seismometer signals). The 'FIR' option of scipy decimate was used.
• FFT time used was 16 seconds for the multi-coherence calculations

The coherence between target signal (=POP QPD) and the witness channels (=seismometer channels) are much lower now than was found in the past. What could be going on here?

This afternoon, I kept the PRM locked for ~1hour and then measured transfer functions from the PRM angular actuators to the POP QPD spot motion for pitch and yaw between ~1pm and 4pm. After this work, the PRM was misaligned again. I will now work on the feedforward filter design.

Summary:
Using the data I collected yesterday, the POP angular FF filters have been trained. The offline time-domain performance looks (unbelievably) good, online performance will be verified at the next available opportunity(see update).

Details:

The sequence of steps followed is the same as that done for the MCL FF filters. The trace that is missing from Attachment #1 is the measured online subtraction. Some rough notes:

• The "target" channels for the subtraction are the POP QPD PIT/YAW signals, normalized by the QPD sum. For the time that the PRMI was locked yesterday, the QPD readouts suggested that the beam was well centered on the QPD, but the POP QPD (OT-301) doesn't give me access to individual quadrant signals so I couldn't actually verify this.
• I used 64s impulse time on the FIR filter for training. Maybe this is too long, but anyways, the calculation only takes a few seconds even with 64^2 taps.
• I found that the Levinson matrix algorithm sometimes failed for this particular dataset. I didn't bother looking too much into why this is happening, the brute force matrix inversion took ~4 times longer but still was only ~5 seconds to calculate the optimal filter for 20 mins of training data sampled at 64 Hz.
• The actuator TF was measured with >0.9 coherence between 0.3 Hz - 10 Hz and fitted, and the fit was used for subsequent analysis. Fit is shown in Attachment #2.
• FIR to IIR fitting took considerable tweaking, but I think I got good enough fits, see Attachments #3, #4. In fact, there may be some benifit to making the shape smoother outside the subtraction band but I couldn't get IIRrational to cooperate. Need to confirm that this isn't re-injecting noise.

Update Apr 5 1145pm:

• Attachment #1 has now been updated to show the online performance. The comparison between the "test" and "validation" datasets aren't really apple-to-apple because they were collected at different times, but I think there's enough evidence here to say that the feedforward is helping.
• Attachment #5 shows that the POP DC (= PRC intracavity buildup) RMS has been stabilized by more than x2. This signal wasn't part of the training process, and I guess it's good that the intracavity power is more stable with the feedforward on. Median averaging was used for the spectral densities, there were still some abrupt glitches during the time this dataset was collected.
• _{The next step is to do the PRFPMI locking with all of these recently retuned feedforward loops engaged and see if that helps things}.

that's pretty great performance. maybe you can also upload some code so that we can do it later too - or maybe in the 40m GIT

I wonder how much noise is getting injected into PRC length at 10-100 Hz due to this. Any change the PRC ERR?

I don't have a recent measurement of the optical gain of this config so I can't undo the loop, but in-loop performance doesn't suggest any excess in the 10-100 Hz band. Interestingly, there is considerable improvement below 10 Hz. Maybe some of this is reduced A2L noise because of the better angular stability, but there is also improvement at frequencies where the FF isn't doing anything, so could be some bilinear coupling. The two datasets were collected at approximately the same time in the evening, ~5pm, but on two different days.

Summary:

I've been thinking about the IMC WFS. I want to repeat the sort of analysis done at LLO where a Finesse model was built and some inferences could be made about, for example, the Gouy phase separation b/w the sensors by comparing the Finesse sensing matrix to a measured sensing matrix. Taking the currently implemented output matrix as a "measurement" (since the IMC WFS stabilize the IMC transmission), I don't get any agreement between it and my Finesse model. Could be that the model needs tweaking, but there are several known issues with the WFS themselves (e.g. imbalanced segment gains).

Building the finesse model:

• I pulled the WFS telescopes from Andres elogs/SURF report, which I think was the last time the WFS telescopes were modified.
• The in-vacuum propagation distances were estimated from CAD diagrams.
• According to my model, the Gouy phase separation between the two WFS heads is ~70 degrees, whereas Andres' a la mode simulations suggest more like 90 degrees. Presumably, some lengths/lenses are different between what I assume and what he used, but I continue the analysis anyway...
• The appropriate power attenuations were placed in each path - one thing I noticed is that the BS that splits light between WFS1 and WFS2 is a 30/70 BS and not a 50/50, I don't see any reason why this should be (presumably it was to do with component availability). see below for Rana's comments.

Simulations:

• The way the WFS servos are set up currently, the input matrix is diagonal while the output matrix encodes the sensing information.
• In finesse, I measured the input matrix (i.e. response sensed in each sensor when an optic is dithered in angle). The length is kept resonant for the carrier (but not using a locking signal), which should be valid for small angular disturbances, which is the regime in which the error signals will be linear anyways.
• Then I inverted the simulated sensing matrix so as to be able to compare with the CDS output matrix. Note that there is a relative gain scaling of 100 between the WFS paths and the MC2T QPD paths which I added to the simulation. I also normalized the columns of the matrix by the largest element in the column, in an attempt to account for the various other gains that are between the optical sensing and the digitizaiton (e.g. WFS demod boards, QPD transimpedance etc etc).
• Attachment #1 shows the comparison between simulation and measurement. The two aren't even qualitatively similar, needs more thought...

Some notes about the WFS heads:

• The transimpedance resistor is 1.5 kohms. With the gain stages, the transimpedance gain is nominally 37.5 kohms, and 3.75 kohms when the attenuation setting is engaged (as it is for 2/4 quadrants on each head).
• Assuming a modulation depth of 0.1, the Johnson noise of the transimpedance resistor dominates (with the MAX4106 current noise a close second), and these heads cannot be shot noise limited when operating at 1 W input power (though of course the situation will change if we have 25 W input).
• The heads are mounted at a ~45 deg angle, mixing PIT/YAW, but I assume we can just use the input matrix to rotate back to the natural PIT/YAW basis.

Update 215 pm 5/6: adding in some comments from Rana raised during the meeting:

1. The transimpedance is actually done by the RLC network (L6 and C38 for CH 3), and not 1.5 kohms. It just coincidentally happens that the reactance is ~1.5 kohms at 29.5 MHz. Note that my LTspice simulation using ideal inductors and capacitors still predicts ~4pA/rtHz noise at 29.5 MHz, so the conclusion about shot noise remains valid I think... One option is to change the attenuation in this path and send more light onto the WFS heads.
   The transimpedance gain and noise are now in Attachment #2. I just tweaked the L values to get a peak at 29.5 MHz and a notch at twice that frequency. For this I assumed a photodiode capacitance of 225pF and the shown transimpedance gain has the voltage gain of the MAX4106 stages divided out. The current noise is input referred.
2. The imbalanced power on WFS heads may have some motivation - it may be that the W/rad TF for one of the two modes we are trying to sense (beam plane tilt vs beam plane translation) is not equal, so we want more light on the head with weaker response.
3. The 45 degree mounting of the heads is actually meant to decouple PIT and YAW.

This is the doc from Keita Kawabe on why the WFS heads should be rotated.

OK so the QPD segments are in the "+" orientation when the 40m IMC WFS heads are mounted at 45 deg. I thought "+" was the natural PIT/YAW basis but I guess in the the LIGO parlance, the "X" orientation was considered more natural.

Summary:

I implemented an ASC servo for the PRC, with the POP QPD as a sensor, and the PRM as the actuator. This has improved the stability of the lock (longer locks are possible), and also reduced the RIN of the arm transmission.

Details:

Attachment #1 shows the in-loop error signal suppression, and some out-of-loop monitors (POP22 and POPDC).

• To practise and get some workable servo settings, I locked the PRMI with carrier resonant (no ETMs).
• Then, I compare the beam motion witnessed by the POP QPD with and without the feedback loop enabled.
• I also look at the spectra of the POPDC and POP22 signals, as out-of-loop proxies, to get an estimate of how much noise is being injected out of band.
• In this toy study, both the in-loop and out of loop monitors show good performance.
• However, when repeating the same diagnostics with the PRFPMI locked, I note that while the in-loop suppression looks good, POPDC and POP22 report elevated noise, relative to the PRMI carrier case.
• I don't have a comparison to the PRFPMI locked with the feedback disabled, because of stability reasons. Plus, for the PRMI, the angular feedforward loops were engaged, but for the PRFPMI traces, they were disabled.
• Nevertheless, the arm RIN goes down by ~2.5 in RMS, so this is doing something good.

Attachment #2 compares the arm transmission RIN with the PRFPMI locked, with and without PRC ASC. The 3 Hz bump is definitely squished, but I think we can do better yet. 

Attachments #3-5 are in the style of elog15361. No Oplev signals yet, I'll add them soon.

Summary:

In ELOG 15368, I had claimed that the POP QPD based feedback servo actuating on the PRM stabilized the lock. I now believe this scheme of sensing using the POP QPD and feeding back to the PRM is not a good topology for stabilizing the PRC angular motion.

Details:

• I was never able to get a measurement of the OLTF of this loop that made sense 
  • the loop was initally commissioned with the PRMI locked on the carrier, and the settings hence inferred to give a ~5 Hz UGF loop were used in the PRFPMI lock.
  • In the PRFPMI configuration, however, the loop gain seemed way too low when I measured using the usual IN1/IN2 method.
  • So it is critical for the lock stability that the angular feedforward works well, which it kind of does now (not that I have changed anything, but the glitches in the seismometer have not resurfaced recently).
  • Hopefully, this becomes less of an issue once we replace the TTs with SOS and OSEM based damping.
• To get some more insight, I did some finesse modeling
  • Attachment #1 shows the sensing response at the QPDs we have available currently (POP and TR). 
  • I included the telescopes (propagation distances, in-air lenses) to these QPDs as best as I could.
  • A simplified model (3 mirror coupled cavity) is used, so there isn't really a common/differential mode in this picture, but we still get some insight I think.
  • Specifically, once the full lock is realized, the PRC optic motion isn't sensed well with our QPDs, and so it was some fluke that turning on these PRC angular feedback loops worked. 
  • Attachment #2 shows the same info as Attachment #1, but with the pendulum transfer functions (and radiation pressure effects) included. The SOS suspensions are modelled as f0=0.7/0.8 Hz (for P/Y), Q=5, while the tip-tilts have f0~5 Hz, Q~10. The high frequency phase is 0 degrees and not 180 as expected because of the pendulum complex pole pair because of the way the quantity is computed in Finesse.
• The current scheme I use is:
  • DC couple the ITM oplevs, using their individual Oplev QPDs.
  • Use the TR QPDs, mixed to actuate on the ETMs in a common/differential way.
  • I think the system is under-determined with the sensors we currently have - we wan't to sense the 10 angular modes - PIT and YAW for the PRC, Csoft, Chard, Dsoft and Dhard (using the terminology from Kate's thesis), but we only have 6 sensors of the same field (POP, TRX and TRY QPDs, PIT and YAW from each).
  • So we need more sensors?
• One thing that can easily be improved I think is to make the ASS system work at high power. 
  • I think this should be as simple as scaling the gain for the loops to work for the high power.
  • Then we can counteract the input pointing drift at least.
  • But the ITM Oplev DC coupling would need to be turned OFF and then ON again, I'm not sure if this will introduce some transient that will destroy the lock...

I would also like to bring up the topic of implementing some WFS for the interferometer fields again, there doesn't seem to be any mention of this in the procurement/planning for the BHD. It is not obvious to me yet that we need WFS and not just DC QPDs from a noise point of view, but at least we should discuss this.

Summary:

I want to be able to run the dither alignment servo with the PRFPMI locked - I've been thinking about what the scheme should be, and I list here some questions I had while thinking about this.

Details:

1. ITM Oplev DC coupling
   • In the current scheme, I DC couple the ITM Oplev servos after the arms have been aligned to maximize POX/POY transmission.
   • However, looking back at data from when the CARM offset is reduced (e.g. Attachment #1), it looks like the ITMs are being torqued quite a bit during this process (ITMX PIT changes by ~20urad, ITMY YAW by ~10urad in this particular lock attempt). 
   • So the spots are not actually being centered on the test-masses? I guess the spot position on ITMX isn't actually controlled because we have only one actuator (BS) for the XARM beam axis. Is it unexpected that ITMY gets torqued so much? 
   • It is unclear what would happen if the ITM Oplev servos are not DC coupled. I wonder if I'd still be able to reach the high circulating powers and then rely solely on the TR QPDs for the arm cavity angular control.
   • Another possibility is to offload the DC part of the control signal to the optic's slow bias voltage slider, and then turn off the DC coupling. After that, the dither alignment can optimize the cavity alignment.
2. Dither alignment at high circulating power
   • I think that the system should work with the same settings as for the POX/POY locking, with the following changes:
     • Scale the overall loop gain by the arm transmission.
     • Change LSC2ASS matrix element from XARM/YARM ---> DARM.
       Does this sound right?
   • In light of the above, I was thinking that we should introduce a gain scaling field in the c1ass RTCDS model (like we have for the LSC power normalization matrix). Is it worth to go through the somewhat invasive process of model recompilation etc?
   • With the PRFPMI locked, I am wondering if I can simultaneously run the dither alignment loops for all the DoFs. Probably not, especially for MICH, since the actuator is the BS, which is also the actuator for the XARM loop?

Where do we want to install the interface and readout electronics for the AS port WFS? Options are:

• 1Y1 / 1Y3  (i.e. adjacent to the LSC rack) - advantage is that 55 MHz RF signal is readily available for demodulation. But space is limited (1Y2, where the RF signal is, is too full so at the very least, we'd have to run a short cable to an adjacent rack), and we'd have a whole bunch of IPC channels between c1lsc and c1ioo models.
• 1X1/1X2. There's much more space and we can directly digitize into the c1ioo model, but we'd have to route the 55 MHz signal back to this rack (kind of lame since the signal generation is happening here). I'm leaning towards this option though - thinking we can just open up the freq generation box and take a pickoff of the 55 MHz signal...

There isn't much difference in terms of cable length that will be required - I believe the AS WFS is going to go on the AP table even in the new optical layout and not on the ITMY in-air oplev table? 

The project requires a large number of new electronics modules. Here is a short update and some questions I had:

1. WFS head and housing. Need to finalize the RF transimpedance gain (i.e. the LC resonant part), and also decide which notches we want to stuff. Rich's advise was to not stuff any more than is absolutely necessary, so perhaps we can have at first just the 2f notch and add others as we deem necessary once we look at the spectrum with the interferometer locked. Need to also figure out a neat connector solution to get the signals from the SMP connectors on the circuit board to the housing - I'm thinking of using Front-Panel-Express to design a little patch board that we can use for this purpose, I'll post a more detailed note about the design once I have it.
2. WFS interface board + soft-start board (the latter provides a smooth ramp up of the PD bias voltage). These go in a chassis, the assembly is almost complete, just waiting on the soft-start board from JLCPCB. One question is how to power this board - Sorensens or linear? If we choose to install in 1X1/1X2, I guess Sorensen is the only option, unless we have a couple of linear power supplies lying around spare.
3. Demod board (quad chassis). Assembly is almost complete, need to install the 4 way RF splitter, some insulating shoulder washers. (to ensure the RF ground is isolated from the chassis), and better nuts for the D-sub connectors. A related question is how we want to supply the electrical LO signal for demodulation. The "nominal" level each demod board wants is 10 dBm. This signal will be sourced inside the chassis from a 4-way RF splitter (~7 dB insertion loss). So we'd need 17dBm going into the splitter. This is a little too high for a compact amplifier like the ZHL-500-HLN to drive (1dB compression point is 16 dBm), and the signal level available at the LSC rack is only ~2 dBm. So do we want a beefy amplifier outside the chassis amplifying the signal to this level? Or do we want to use the ZHL-500-HLN, and amplify the signal to, say 13 dBm, and drive each board with ~6 dBm LO? The Peregrine mixer on these boards (PE4140) are supposed to be pretty forgiving in terms of the LO level they want... In either case, I think we should avoid having an amplifier also inside the chassis, it is rather full in there with 4 demod boards, regulator board, all the cabling, and an RF splitter. It may be that heat dissipation becomes an issue if we stick an RF amplifier in there too...
4. Whitening chassis. Waiting for front panels to arrive, PCBs and interface board are in hand, stuffed and ready to go. A question here is how we want to control the whitening - it's going to be rather difficult to have fast switchable whitening. I think we can just fix the whitening state. Another option would be to control the whitening using Acromag BIO channels.
5. AI chassis - will go between whitening and ADC.
6. Large number of cables to interconnect all the above pieces. I've asked Chub to order the usual "Deluxe" shielded Dsub cables, and we will get some long SMA-SMA cables to transmit the RF signals from head to demod board from Pasternack (or similar), do we need to use Heliax or the Times Microwave alternative for this purpose? What about the LO signal? Do we want to use any special cable to route it from the LSC rack to the IOO rack, if we end up going that way? 

Approximately half of the assembly of the various electronics is now complete. The basic electrical testing of the interface chassis and demod chassis are also done (i.e. they get power, the LEDs light up, and are stable for a few minutes). Detailed noise and TF characterization will have to be done.

Attachment #1 - Proposed mods for 40m RF freqs. 

• I followed Rich's suggestion of choosing an inductor that has Z~100 ohms at the frequency of interest.
• The capacitor is then chosen to have the correct resonant frequency.
• Voltronix trim caps are used for fine tuning the resonances. 2 variants are used, one with a range of 4-20 pF, and a Q of 500 per spec, while the other has range of 8-40 pF, and a Q of 200 per spec.
• In the table, the first capacitance is the fixed one, and the second is the variable one. We're not close to the rail for the variable caps.
• For the first trials, I think we can try by not populating all of the notches - just the 2f notch. We can then add notches if deemed necessary. Probably these notches are more important for a REFL/POP port WFS.
• One thing I noticed is that the aLIGO WFS use ceramic capacitors for the LC reactances. i haven't checked if there is any penalty we are paying in terms of Q of the capacitor. anyways, i'm not going to redesign the PCB and maybe ceramic is the only option in the 0805 package size?

Attachment #2 - Modelled TFs for the case where all the notches are stuffed, and where only the 2f notch is stuffed.

• The model uses realistic composite models for the inductors from coilcraft, but the capacitors are idealized parts.
• I also found the library part for LMH6624, so this should be a bit closer to the actual circuit than Rich's models which subbed in the MAX4107 in place.
• The dashed vertical lines indicate some frequencies of interest.
• Approx 1 kohm transimpedance is realized at 55 MHz. I don't have the W/rad number for the sensitivity at the AS port, but my guess is this will be just fine.
• If the 44 MHz and 66 MHz notches are stuffed, then there is some interaction with the 55 MHz notch, which lowers the transimpedance gain somewhat. So if we decide to stuff those notches, we should do a mroe careful investigation into whether this is problematic.

Attachment #3 - Modelled TFs for the case where all the notches are stuffed, and where only the 2f notch is stuffed.

• Initially, I found the (modelled) noise level to be rather higher than expected. It persisted despite making the resistors in the model noiseless. Turns out there is some leakage from the "Test Input" path. Some documents in the DCC suggest that there should be an "RF Relay" that allows one to isolate this path, but afaik, the aLIGO WFS does not have this feature. So maybe what we should do is to remove C9 once we're done tuning the resonances. Better yet, just tune the resonance with the Jenne laser and not this current-injection path.
• Horizontal dashed lines indicate shot noise for the indicated DC photocurrent levels. It is unlikely we will have even 1 mW of light on a single quadrant at the AS port, so the AS port WFS will not be shot noise limited. But I think that's okay for initial trials.
• The noise level of ~20 pA/rtHz input referred is in agreement what I would expect using Eq 3 of the LMH6624 datasheet. The preamp has a gain of 10, so the source impedance seen by it is ~100 ohms (since the overall gain is 1kohm). The corresponding noise level per Eq 3 is ~2 nV/rtHz, or 20 pA/rtHz current noise referred to the photocurrent 👍 . 
• The LMH6624 datasheet claims that the OpAmp is stable for CLG >= 10. For reasons that aren't obvious to me, Koji states here that the CLG needs to be even higher, 15-20 for stability. Do the aLIGO WFS see some instability? Should I raise R14 to 900 ohms?

Any other red flags anyone sees before I finish stuffing the board?

Last week and this week I've been working on the characterization of the Q3000 QPDs. The QPDs were named 81, 82, 83, and 94.

• Dark current [OMC LAB ELOG 402]: All the segments looked similar and acceptable except for the seg1 of #82. It has a smaller reverse breakdown voltage (~6V) but even this is an acceptable level.
• Impedance [OMC LAB ELOG 403]: All the segments showed a ~300pF junction capacitance with no reverse bias. This looks quite normal.
• Dark noise [OMC LAB ELOG 404]: All the segments showed ~5pA/rtHz dark noise above 1Hz.

My recommendation is to use #81 and #84 as they have similar dark current characteristics between the segments. But basically, all the QPDs look fine.

The actual junction capacitance and the RF dark noise should be characterized by the actual WFS head circuit.

The QPD packages were labeled and returned to Gautam to be implemented in the WFS heads.

gautam: S/N #84 was installed as the AS WFS QPD. The remaining 3 are stored in the clean cabinet at EX (where the rest of the RF photodiodes are).

I am confused by the discussion during the call today. I revisited Hartmut's paper - the circuit in Fig 6 is essentially what I am calling "only 2f_2 notch stuffed" in my previous elog. Qualitatively, the plot I presented in Attachment #2 of the preceeding elog in this thread shows the expected behavior as in Fig 8 of the paper - the impedance seen by the photodiode is indeed lower. In Attachment #1, I show the comparison - the "V(anode)/I(I1)" curve is analogous to the "PD anode" curve in Hartmut's paper, and the "V(vout)/I(I1)" curve is analogous to the "1f-out" curve. I also plot the sensitivity analysis (Attachment #2), by varying the photodiode junction capacitance between 100pF and 200 pF (both values inclusive) in 20 pF steps. There is some variation at 55 MHz, but it is unlikely that the capacitance will change so much during normal operation? 

I understand the motivation behind stuffing the other notches, to reduce intermodulation effects. But the impression I got from the call was that somehow, the model I presented was wrong. Can someone help me identify the mistake?

I didn't bother to export the LTspice data and make a matplotlib plot for this quick analysis, so pardon the poor presentation. The colors run from green=100pF to grey=200pF.

An 8 channel whitening chassis was prepared and tested. I measured:

1. TF from input to output - there are 7 switchable stages (3 dB, 6 dB, 12 dB and 24 dB flat whitening gain, and 3 stages of 15:150 Hz z:p whitening). I enabled one at a time and measured the TF. 
2. Noise with input terminated.

In summary,

1. All the TFs look good (I will post the plots later), except that the 3rd stage of whitening on both boards don't show the expected transfer function. The fact that it's there on both boards makes me suspect that the switching isn't happening correctly (I'm using a little breakout board). I'm inclined to not debug this because it's unlikely we will ever use 3 stages of 15:150 whitening for the AS WFS. 
2. The noise measurement displayed huge (x1000 above the surrounding broadband noise floor) 60 Hz harmonics out to several kHz. My hypothesis is that this has to do with some bad grounding. I found that the circuit ground is shorted to the chassis via the shell of the 9pin and 15pin Dsub connectors (but the two D37 connector shields are isolated). This seems very wierd, idk what to make of this. Is this expected? Looking at the schematic, it would appear that the shields of the connectors are shorted to ground which seems like a bad idea. afaik, we are using the same connectors as on the chassis at the sites - is this a problem there too? Any thoughts? 

I don't think your simulation looked inaccurate (at least not to me). In my opinion, we just want to minimize any excess noise from intermodulation. Of course, its possible that stuffing too many notches will make it difficult to have the same low noise as a simple circuit, so that's worth considering.

Also, the intermodulation is mainly a problem when the other peaks are not suppressed by some feedback: e.g. POP55_I can have excess noise if POP55_Q or POP11_I are not controlled by some MICH/PRCL/SRCL loops.

For the WFS, perhaps this is not a significant issue, but I'm not sure. My suggestion is to stuff 11 & 55 for sure, and then the others depending on the amplitude of the peaks and the consequent intermodulation. IF it works with all stuffed, that seems good. If its tricky to get it to work with all stuffed, I'd back off on a couple of them...but it probably takes more careful thought to figure out which ones are least important.

I'm thinking of making some modifications to the RF distribution box in 1X2, so as to have an extra 55 MHz pickoff. Koji already proposed some improvements to the layout in 2015. I've marked up his "Possible Improvement" page of the document in Attachment #1, with my proposed modifications. I believe it will be possible to get 15-16 dBm of signal into a 4 way RF splitter in the quad demod chassis. With the insertion loss of the splitter, we can have 9-10 dBm of LO reaching each demod board, which will then be boosted to +20 dBm by the Teledyne on board. The PE4140 mixer claims to require only -7 dBm of LO signal. So we have quite a bit of headroom here - as long as we limit the RF signal to 0dBm (=0.5 Vpp from the LMH6431 opamp at 55 MHz, we shouldn't be having a much larger signal anyways), we should be just fine with 15 dBm of LO power (which is what we will have after the division into the I and Q paths, and nominal insertion losses in the transmission path). These numbers may be slight overestimates given the possible degradation of the RF amps over the last 10 years, but shouldn't be a show-stopper.

Do the RF electronics experts agree with my assessment? If so, I will start working on these mods tomorrow. Technically, the splitter can be added outside the box, but it may be neater if we package it inside the box. 

I got a bit confused by your description.

The demod board claims that the nominal power at each LO port is 10dBm. So we want to give at least 16dBm to the (external?) 4way power splitter, but we only have 15dBm. As you said, the actual LO power reaching the FET mixier (PE4140) is the level of ~20dBm. But you said the requirement for the mixer is -7dBm. So are you proposing to reduce the LO level (slightly) than the LIGO recommendation because the minimum for PE4140 is -7dBm?
If that's the message, then I can say "yes". We supply 8~9dBm to the LO ports instead of 10dBm. I suppose the mixers don't care about this level of reduction.

Looking at my original post [40m ELOG 11817], the necessary modification is much larger than you have indicated in your post (as yours is the modification of my modification plan.)
If you do your modification you have to deal with the components rearrangement in the chassis. I think you can still accomplish it as you are going to remove an amplifier and gain the space from it.

The main RF line still has 5dBm Attn. How about to insert another 3dB power splitter there and create a spare 55MHz port for the future use?

Before doing any modification you should check how much the distributed powers are at the ports.
Also your modification will change the relative phase between 11MHz and 55MHz.
Can you characterize how much phase difference you have between them, maybe using the modulation of the main marconi? And you might want to adjust it to keep the previous value (or any new value) after the modification by adding a cable inside?

I removed the Frequency Generation box from the 1X2 rack. For the time being, the PSL shutter is closed, since none of the cavities can be locked without the RF modulation source anyways.

Prior to removal, I did the following:

1. Measured powers at each port on the front panel 
   • Gigatronix power meter was used, which has a maximum power rating of 20dBm, so for the EOM drive outputs which we operate closer to 25-27 dBm, I used a 20 dBm coupler to make the measurement.
   • Attachment #1 summarizes my findings - there doesn't seem to be anything majorly wrong, except that for the 11 MHz EOM drive channel, the "7" setting on the variable attenuator doesn't seem to work. 
   • We can probably get a replacement from MiniCircuits, but since we operate at 0dBm variable attenuation nominally, maybe we don't need to futz around with this.
2. Measured the relative phasing between the 11 MHz and 55 MHz signals using an oscilloscope.
   • I measured the relative phase for the EOM drive channels, and also the demod channels.
   • The scope can accept a maximum of 5V RMS signal with 50ohm input impedance. So once again, I couldn't make a direct measurement at the nominal setting for the EOM drive channel. Instead, I used the variable attenuator to set the signal amplitude to ~2V RMS. 
   • I will upload the time-domain plots later. But we now have a record of the relative phasing that we can try and reproduce after making modifications. FWIW, my measured phase difference of 139 degrees is reasonably consistent with Koji's inferred from the modulation spectrum.

One thing I noticed was that we're using very stiff coax cabling (RG405) inside this box? Do we need to stick with this option? Or can we use the more flexible RG316? I guess RG405 is lower loss, so it's better. I can't actually find any measurement of the shielding performance in my quick google searching but I think the claim on the call yesterday was that RG405 with its solder soaked braids offer superior shielding.

Let's use RG405 for better shielding. It is not too stiff. The bending  (just once) does not break the cable.

Are you going to full replacement of the 55MHz system? Or just remove the 7dBm and then implement the proposed modification for the 55MHz line?

I'm open to either approach. If the full replacement requires a lot of machining, maybe I will stick to just the 55 MHz line. But if only a couple of new holes are required, it might be advantageous to do the revamp while we have the box out? What do you think?

BTW, now that I look more closely at the RF chain, I have several questions:

1. The 1 dB compression power of the ZHL-2 amplifiers is ~29 dBm, and we are driving it at that level. Is this okay? I thought we always want to be several dBm away from the 1dBm compression point?
2. Why do we have an attenuator between the Marconi input and the first ZHL-2 amplifier? Can't we just set the Marconi to output 8 or 9 dBm?
3. The Wenzel frequency multiplier is rated to have 13dBm input and 20 dBm output. We operate it with 12 dBm input and 19 dBm output. Why throw away 1 dBm?

I guess it is feasible to have +17 dBm of 55 MHz signal to plug into the Quad Demod chassis - e.g. drive the 55 MHz input with 20 dBm, pick off 3dBm to the front panel for ASC. Then we can even have several "spare" 55 MHz outputs and still satisfy the 9 dBm input that the ZHL-2 in the 55 MHz chain wants (though again, isn't this dangerously close to the 1dB compression point?). The design doc claims to have done some Optickle modeling, so I guess there isn't really any issue? 

1. That's true. But we are already in that regime with the Var attn at 0dB, aren't we? We can reduce the input to the amp by 1-2dBm sacrificing the EOM out by that amount (we can compensate this for the demo out by removing the 1dB attn).

2. Not 100% sure but one possible explanation is that we wanted to keep the Marconi output large (or as large as possible) to keep the SNR between the signal and the noise of the driver in Marconi. The attenuator is less noisy compared to the driver noise.

3. My guess is that theoretically we were supposed to have 13dBm input and 20dBm output in design. However, the actual input was as such.  We can restore it to the 13dBm input.

This turned out to be a much more involved project than I expected. The layout is complete now, but I found several potentially damaged sections of cabling (the stiff cables don't have proper strain relief near the connectors). I will make fresh cables tomorrow before re-installing the unit in the rack. Several changes have been made to the layout so I will post more complete details after characterization and testing.

I was poring over minicircuits datasheets today, and I learned that the minicircuits bandpass filters (SBP10.7 and SBP60) are not bi-directional! The datasheet clearly indicates that the Male SMA connector is the input and the Female SMA connector is the output. Almost all the filters were installed the other way around 😱 . I'll install them the right way around now.

This work is now complete. The box was characterized and re-installed in 1X2. I am able to (briefly) lock the IMC and see PDH fringes in POX and POY so the lowest order checks pass.

Even though I did not deliberately change anything in the 29.5 MHz path, and I confirmed that the level at the output is the expected 13 dBm, I had to lower then IN1 gain of the IMC servo by 2dB to have a stable lock - should confirm if this is indeed due to higher optical gain at the IMC error point, or some electrical funkiness. I'm not delving into a detailed loop characterization today - but since my work involved all elements in the RF modulation chain, some detailed characterization of all the locking loops should be done - I will do this in the coming week.

After tweaking the servo gains for the POX/POY loops, I am able to realize the single arm locks as well (though I haven't dont the characterization of the loops yet).

I'm leaving the PSL shutter open, and allowing the IMC autolocker to run. The WFS loops remain disabled for now until I have a chance to check the RF path as well.

Unrelated to this work: Koji's swapping back of the backplane cards seems to have fixed the WFS2 issue - I now see the expected DC readbacks. I didn't check the RF readbacks tonight.

Update 7 Dec 2020 1 pm: A ZHL-2 with heat sink attached and a 11.06 MHz Wenzel source were removed from the box as part of this work (the former was no longer required and the latter wasn't being used at all). They have been stored in the RF electronics cabinet along the east arm.

The assembly of the head is nearly complete, I thought I'd do some characterization before packaging everything up too nicely. I noticed that the tapped holes in the base are odd-sized. According to the official aLIGO drawing, these are supposed to be 4-40 tapped, but I find that something in between 2-56 and 4-40 is required - so it's a metric hole? Maybe we used some other DCC document to manufacture these parts - does anyone know the exact drawings used? In the meantime, the circuit is placed inside the enclosure with the back panel left open to allow some tuning of the trim caps. The front panel piece for mounting the SMA feedthroughs hasn't been delivered yet so hardware-wise, that's the last missing piece (apart from the aforementioned screws).

Attachment #1 - the circuit as stuffed for the RF frequencies of relevance to the 40m.

Attachment #2 - measured TF from the "Test Input" to Quadrant #1 "RF Hi" output.

• There is reasonable agreement, but not sure what to make of the gain mismatch at most frequencies.
• The photodiode itself hasn't been installed yet, so there will be some additional tuning required to account for the interaction with the photodiode's junction capacitance.
• I noticed that the Qs of the resonances in between the notches is pretty high in this config, but the SPICE model also predicts this, so I'm hopeful that they will be tamed once the photodiode is installed.
• One thing that is worrying is the feature at ~170 MHz. Could be some oscillation of the LM opamp. All the aLIGO WFS test procedure documentation shows measurements only out to 100 MHz. Should we consider increasing the gain of the preamp from x10 to x20 by swapping the feedback resistor from 453 ohms to 1 kohm? Is this a known issue at the sites? 
• Any other comments?

Update 11 Dec: For whatever reason, whoever made this box decided to tap 4-40 holes from the bottom (i.e. on the side of the base plate), and didn't thread the holes all the way through, which is why I was unable to get a 4-40 screw in there. To be fair the drawing doesn't specify the depth of the 4-40 holes to be tapped. All the taps we have in the lab have a maximum thread length of 9/16" whereas we need something with at least 0.8" thread length. I'll ask Joe Benson at the physics workshop if he has something I can use, and if not, I'll just drill a counterbore on the bottom side and use the taps we have to go all the way through and hopefully that does the job.

The front panel I designed for the SMA feedthroughs arrived today. Unfortunately, it is impossible for the D-sub shaped holes in this box to accommodate 8 insulated SMA feedthroughs (2 per quadrant for RF low and RF high) - while the actual SMA connector doesn't occupy so much space, the plastic mold around the connector and the nut to hold it are much too bulky. For the AS WFS application, we will only need 4 so that will work, but if someone wants all 8 outputs (plus an optional 9th for the "Test Input"), a custom molded feedthrough will have to be designed. 

As for the 170 MHz feature - my open loop modeling in Spice doesn't suggest a lack of phase margin at that frequency so I'm not sure what the cause is there. If this is true, just increasing the gain won't solve the issue (since there is no instability at least by the phase margin metric). Could be a problem with the "Test Input" path I guess. I confirmed it is present in all 4 quadrants.

Summary:

I think the WFS head performs satisfactorily.

• The (input-referred) dark noise level at the operating frequency of 55 MHz is ~40pA/rtHz (modelled) and ~60 pA/rtHz (measured, converted to input-referred). See Attachment #1. Attachment #5 has the input referred current noise spectral densities, and a few representative shot noise levels.
• The RF transimpedance gain at the operating frequency is ~500 ohms when driving a 50 ohm load (in good agreement with LTspice model). See Attachment #2 and Attachment #3.
• The resonant gain to notch ratios are all > 30 dB, which is in line with numbers I can find for the WFS installed at the sites (and in good agreement with the LTspice model as well).
• There are a few lines visible in the noise measurement. But these are small enough not to be a show-stopper I think.

Details and remarks:

1. Attachment #4 shows a photo of the setup. 
   • The QPD used was S/N #84.
   • The heat sinks have a bunch of washers because the screw holes were not tappe at time of manufacture.
   • There isn't space to have 8 SMA feedthroughs in the D-shaped cutouts, so we can only have the 4 "RF HI" outputs without some major metalwork.
   • C9 has been remvoed in all channels (to isolate the "TEST INPUT").
2. I found that some quadrants displayed a ~35 MHz sine-wave of a few mV pk-pk when I had the back of the enclosure off (for tuning the notches). The hypothesis is that this was due to some kind of stray capacitance effect. Anyways, once I closed everything up, for the noise measurement, this peak was no longer visible. With an HP8447A preamp, I measured an RMS voltage of ~2mV rms on an oscilloscope. After undoing the 20 dB gain of the amplifier, each quadrant has an output voltage noise of ~200 uVrms (as returned by the "measure" utility on the scope, I don't know the specifics of how it computes this). Point is, there wasn't any clear sine-wave oscillations like I saw on two channels when the lid was off. 
3. Some of the lines are present during some measurement times but not others (e.g. Q4 blue vs red curve in Attachment #1). I was doing this work in the elec-bench area of the lab, right next to the network switches etc so not exactly the quietest environment. But anyway, I don't see anything in these measurements that suggest something is seriously wrong.
4. In the transfer function measurements, above 150 MHz, there are all sorts of features. But I think this is a measurement artefact (stray cable capacitance etc) and not anything real in the RF signal path. Koji saw similar effects I believe, and I didn't delve further into it.
5. The dark noise of the circuit is such that to be shot noise limited, each quadrant needs 10 mA of DC photocurrent. The light bulb we have has a max current rating of 0.25A, with which I could only get 3 mA DC per quadrant. So the 55 MHz sideband power needed to be shot noise limited is ~50 mW - we will never have such high power. But I think to have better performance will need a major re-work of the circuit design (finite Qs of inductors, capacitors etc).
6. Regarding the transimpedance gains - in my earlier plots, I omitted the 50ohm input impedance of the AG4395A network analyzer. The numbers I report here are ~half of those earlier in this thread for this reason. In any case, I think this number is what is important, since the ADT-1-1 on the demod board RF input has an input impedance of 50ohm. 
7. Regarding grounding - the RF ground on the head is actually isolated from the case pretty well. Two locations of concern are (i) the heat sinks for the voltage regulator ICs and (ii) the DB15 connector shield. I've placed electrically insulating (but thermally conducting) pads from TO220 mounting kits between both sets of objects and the case. However, for the Dsub connector, the shape of the pad doesn't quite fit all the way round the connector. So if I over-tighten the 4-40 mounting bolts, at some point, the case gets shorted to the RF ground, presumably because the connector deforms slightly and touches the case in a spot where I don't have the isolating pad installed. I think I've realized a tightness that is mechanically satisfying but electrically isolating.
8. I will do the fitting at my leisure but the eye-fit is already suggesting that things are okay I think.

If the RF experts see some red flags / think there are more tests that need to be performed, please let me know. Big thanks to Chub for patiently supporting this build effort, I'm pleasantly surprised it worked.

On Friday, I felt that the ASC performance when the PRFPMI was locked was not as good as it used to be, so I looked into the situation a bit more. As part of my ASC model revamp in December, I made a bunch of changes to the signal routing, and my suspicion was that the control signals weren't even reaching the ETMs. My log says that I recompiled and reinstalled the c1rfm model (used to pipe the ASC control signals to the ETMs), and indeed, the file was modified on Dec 21. But for whatever reason, the C1RFM.ini (=Dolphin receiver since the ASC control signals are sent to this model over the Dolphin network from the c1ioo machine which hosts the C1:ASC- namespace, and RFM sender to the ETMs, but this path already existed) file never picked up the new channels. Today, I recompiled, re-installed, and restarted the models, and confirmed that the control signals actually make it to the ETMs. So now we can have the QPD-based ASC loops engaged once again for the PRFPMI lock. The CDS system did not crash 🎉 . See Attachments #1-3.

I checked the loop performance in the POX/POY locked config by first deliberately misaligning the ETMs, and then engagin the loops - seems to work (Attachment #4). The loop shapes have to be tweaked a bit and I didn't engage the integrators, hence the DC pointing wasn't recovered. Also, added a line to the script that turns the ASC loops on to set limits for all the loops - in the testing process, one of the loops ran away and I tripped the ETMY watchdog. It has since been recovered. I SDFed a limit of 100cts just to be on the conservative side for model reboot situations - the value in the script can be raised/lowered as deemed necessary (sorry, I don't know the cts-->urad number off the top of my head).

But the hope is this improves the power buildup, and provides stability so that I can begin to commission the AS WFS system a bit.

1. Added rough cts2mW calibration filters to the quadrants, see Attachment #1. The number I used is:
             0.85 A/W         *       500 V/A            *          10 V/V                              *         1638.4 cts/V
   (InGaAs responsivity)     (RF transimpedance)  (IQ demod conversion gain)      (ADC calibration)
2. Recovered FPMI locking. Once the arms are locked on POX / POY, I lock MICH using AS55_Q as a sensor and BS as an actuator with ~80 Hz UGF.
3. Phased the digital demod phases such that while driving a sine wave in ETMX PIT, I saw it show up only in the "I" quadrant signals, see Attachment #2.

The idea is to use the FPMI config, which is more easily accessed than the PRFPMI, to set up some tests, measure some TFs etc, before trying to commission the more complicated optomechanical system.

[anchal, paco]

We picked up AS WFS comissioning for daytime work as suggested by gautam. In the end we want to comission this for the PRFPMI, but also for PRMI, and MICH for completeness. MICH is the simplest so we are starting here.

We started by restoromg the MICH configuration and aligning the AS DC QPD (on the AS table) by zeroing the C1:ASC-AS_DC_YAW_OUT and C1:ASC-AS_DC_PIT_OUT. Since the AS WFS gets the AS beam in transmission through a beamsplitter, we had to correct such a beamsplitters's aligment to recenter the AS beam onto the AS110 PD (for this we looked at the signal on a scope).

We then checked the rotation (R) C1:ASC-AS_RF55_SEGX_PHASE_R and delay (D) angles C1:ASC-AS_RF55_SEGX_PHASE_D (where X = 1, 2, 3, 4 for segment) to rotate all the signal into the I quadrature. We found that this optimized the PIT content on C1:ASC-AS_RF55_I_PIT_OUT and YAW content on C1:ASC-AS_RF55_I_YAW_OUTMON which is what we want anyways.

Finally, we set up some simple integrators for these WFS on the C1ASC-DHARD_PIT and C1ASC-DHARD_YAW filter banks with a pole at 0 Hz, a zero at 0.8 Hz, and a gain of -60 dB (similar to MC WFS). Nevertheless, when we closed the loop by actuating on the BS ASC PIT and ASC YAW inputs, it seemed like the ASC model outputs are not connected to the BS SUS model ASC inputs, so we might need to edit accordingly and restart the model.

[Anchal, Yuta]

We tried to re-tune Yarm ASS today. It cannot be fully closed as of now. I think we need to play with signs.

Motivation:
 - We want to make sure Yarm ASS work with current ITMY coil matrix (40m/16899).
 - ASS makes the beam positions on test masses to be the same every day.

What we did:
 - Adjusted A2L paths of C1:ASS-YARM_OUT_MTRX based on cavity geometry. For the paths to maximize the transmission using TT1 and TT2, we just assumed they are correctly calculated by someone in the past.
 - Adjusted OSC_CLKGAINs so that ITMY and ETMY will be shaken in the same amplitude in terms of radians. The ratio of the excitation was determined to take into account for the oscillator frequency difference between DOFs.
 - Checked the time constant of A2L paths by turning on A2L paths only, and checked that of max-transmission paths by turining on them only.
 - Adjusted DEMOD_SIG_GAINs so that their time constants will be roughly the same, with C1:ASS-YARM_SEN_MTRX fully identity matrix and all servo GAINs to be +1.
 - Re-tuned DEMOD_PHASEs to minimize Q signal. C1:ASS-YARM_ITM_PIT_L_DEMOD_PHASE and C1:ASS-YARM_ITM_YAW_T_DEMOD_PHASE were re-tuned within +/- 5 deg.
 - These changes are recorded in /opt/rtcds/caltech/c1/Git/40m/scripts/ASS/ASS_DITHER_ON.snap now.

Result:
 - A2L loops seems to be working, but max-transmission paths seems to diverge at some point. I think we need to play with the signs/gains of max-transmission paths for C1:ASS-YARM_OUT_MTRX.
 - Attached is the current configuration we achieved so far.

[Anchal, Yuta]

We are still in the progress of re-commissioning Yarm ASS.
Today, we tried to adjust output matrix by measuring the sensing matrix at DC.
Turning on yaw loops kind of works, but pitch does not. It seems like there is too much coupling in pitch to yaw.
We might need to adjust the coil output matrix of ITMY and ETMY to go further, and/or try measuring the sensing matrix including pitch - yaw coupling.

What we did:
 - Confirmed that turning on TT1 and TT2 loops (max-transmission loops) work fine. When we intentionally misalign TT1/2, the ASS loops correct it. So, we moved on to measure the sensing matrix of A2L paths, instead of using theoretical matrix caluclated from cavity geometry we used last week (40m/16909).
 - Instead of +/-1's, we put +/-2's in the ITMY coil output matrix to balance the actuation between ETMY and ITMY to take into account that ITMY is now using only two coils for actuating pitch and yaw (40m/16899).
 - Measured the change in C1:ASS-YARM_(E|I)TM_(PIT|YAW)_L_DEMOD_I_OUT16 error signals when offset was added to C1:SUS-(E|I)TMY_ASC(PIT|YAW)_OFFSET. We assumed pitch-yaw coupling is small enough here. Below was the result.

                            ETM PIT error  ITM PIT error
ETM PIT OFFSET of +100cnts: -3.0cnts       -2.99cnts
ITM PIT OFFSET of +100cnts: -11.94cnts      -5.38cnts

                            ETM PIT error  ITM PIT error
ETM YAW OFFSET of +100cnts: -3.42cnts      -16.93cnts
ITM YAW OFFSET of +10 cnts: +1.41cnts      +0.543cnts

 - Inverted the matrix to get A2L part of C1:ASS-YARM_OUT_MTRX. Attachment #1 is the current configuration so far.
 - With this, we could close all yaw loops when pitch loops were not on. But vise versa didn't work.
 - Anyway, we aligned the IFO by centering the beams on test masses by our eyes and centered all the oplevs (Attachment #2).

Next:
 - Do coil balancing to reduce pitch-yaw coupling
 - Measure sensing matrix also for pitch-yaw coupling
 - Xarm ASS is also not working now. We need to do similar steps also for Xarm

I finally got YARM AS to work today. It is hard to describe what worked, I did a lot of monkey business and some dirty offset measurements to create the ASS output matrix that gave results. Note that I still had to leave out ITMY PIT L error signal, but transmission was maximizing without it. The beam does not center fully on ITMY in Pit direction right now, but we'll mvoe on from this problem for now. Future people are welcome to try to make it work for this last remaining error signal as well.

commit

In the attachment please find IMC ASC simulation plots. Let me know what you think, if you want some other plots, and if you need any clarification.

In the attachment please find a comparison of error signals of simulation and reality. For C1:IOO-WFS1/2_PIT_IN1 excess signal ('belly') between a few Hz up to 70-80 Hz might be caused by air turbulence (which is not included in the simulation).

In the attachment please find a comparison of error signals of simulation and reality after including air turbulence as input noise.

In the attachment please find plots comparing controller output, local damping output, and error signals.

Input noises of the simulation are seismic noise, osem noise, input power fluctuations, sensing noises of WFSs and QPD, and air turbulence noise for WFSs. There is also optical torque noise (radiation pressure effect). 

The procedure to get optical gains and sensing noises:
Having the actuator response A rad/cnts @ 3 Hz. I was shaking MC1/2/3 in pitch with B cnts @ 3 Hz and getting WFS1/2 QPD signals of C cnts @ 3 Hz, which means WFS1/2 QPD optical gain is D cnts/rad = C / (A * B) cnts/rad. So, if WFS1/2 QPD IN1 has a noise spectrum (at higher freqs) of E cnts/rtHz, that corresponds to E/D rad/rtHz of sensing noise for WFS1/2 QPD.

Actuator response [rad/cts] I was getting shaking mirrors at 3 Hz and measuring amplitudes of OSEM output (knowing the geometry of the mirror). I scaled it to DC. From here I was getting ct2tau_mc (knowing the mirror's moment of inertia, Q, and natural pitch frequencies). OSEM calibration factors [cts/rad] I was getting from the input matrix and geometry of the mirror.

The flat noise at higher frequencies from the local damping and controller output channels is presumably quantization/loss of digits/numerical precision noise which I don't include in simulations for now?!

Regarding air turbulence, in KAGRA it has been reported that air turbulence introduces phase fluctuations in laser fields that propagate in air. According to Kolmogorov’s theory, the PSD of phase fluctuations caused by air turbulence scales as ∝ L*V^(5/3)*f^(−8/3). Here, L is the optical path length and V is a constant wind speed. Since it is not obvious how can one estimate typical V in the beam paths I was taking this excess noise from the error signals data between 10 Hz and 50 Hz, extrapolated it taking into account ∝ f^(−8/3) (not for frequencies below 2 Hz, where I just put constant, since it would go too high). I expect that I won't be able to get a parameterized model that also predicts the absolute value. The slope is all I can hope to match, and this I already know. QPD chamber is much smaller (and better isolated?) and there is no this excess noise.

Regarding other things in simulations (very briefly): beam-spots are calculated from angular motions, length change is calculated from beam-spots and angular motion, cavity power depends on length change and input power, and torque on the mirrors depends on beam-spots and cavity power. From other things, local-sensor basis conversion (and vice versa) is worth noting.

Inspected the lab to see what we can do about the IFO WFS:

• WFS heads
  • 1 functional WFS head (tuned at 11/55MHz) @AS Table [40m ELOG 15736]
  • 1 WFS head case (empty) @Section Y10 below the tube, plastic box
  • 2 WFS PCBs, components stuffed, tuning freq unknown @Section Y10 below the tube, plastic box
• Deomdulators
  • no 4ch IQ demod unit (some component possibly spare)
  • Build 4 iLIGO demods?
• Whitening / AA
  • No permanent unit: Maybe we can borrow something from the BHD
• ADC CHs
  • c1ioo seems to have just 8 more spare channels.
  • Borrow a card from bhd? This will require an AI. But their location would be close to the final positions.

To check out the bandwidths and cross-coupling in the WFS loops, I made a script (attached) to step the offsets around, sleeping between steps. Its also in the scripts/MC/WFS/ dir.

You can see from the steps that there is some serious cross coupling from WFS1-PIT to MC_TRANS PIT. This cross-coupling is not a disaster because we run the MC2 centering loop with such a low gain. This gain hirearchy means that you can effectively consider the IMC with the WFS loops closed to be an "open loop" plant that the MC TRANS loop is trying to control.

I've started another run at 4:40 UTC since my previous one only paused for 30 seconds after turning each offset OFF/ON. This is clearly not long enough to grab the MC_TRANS loop; although you can tell sort of how slow it is from the slope of the error signal after the step is applied.

To make the plot, I used diaggui in the time series mode, with a 3 Hz BW. I applied a 4th order Butterworth filter at 0.3 Hz to low pass the data using the foton string in the time series tool.

In the middle of aportioning gains and signs in the IMC WFS screen, so beware. More updates soon.

On Wednesday, I did some rework of the MC WFS gains. I think it should still work as before as long as the overall input gain is set to 0.1 (not 1.0 as the button on the screen sets it to).

1. The MC_TRANS P/TY signals were very small because they are normalized by the SUM. I added a '+80 dB' gain filter to the MC2_TRANS_PIT and MC2_TRANS_YAW filter banks which increase the signal gain before the digital signals are sent from the MC2 model to the MC_WFS control screen's Input Matrix. Now if you plot the MC_TRANS and WFS signals on dataviewer, the time series all have roughly the same magnitude.
2. I put a "-80 dB" gain button into the MC2_TRANS servo filter banks. This should make it have the same overall gain as before, since the (sensor to servo) Input Matrix is diagonal.
3. The servo gains (WFS1_PIT, WFS2_YAW, etc.) had some negative signs. To make all the servo gains positive, I moved those signs into the Output Matrix.
4. The Output Matrix had some values with 4-5 significant digits. I think its not necessary to have more than 2 places after the decimal point since out measurements are not that accurate, so I rounded them off. We can/should change that screen to reduce the PREC field on the matrix element display.
5. Now, if the overall INPUT_GAIN slider is increased beyond 0.1, there is some pitch oscillation. I think that is happening because the Output Matrix is not that great. In principle, if we have diagonalized the system, putting offsets into the various loops' error points won't make offsets in the other loops, but this is not the case. The pitch loops have a lot of cross coupling (my guess is that the off-diagonal elements are of order 0.1); the yaw loops are several times better. I suggest someone redo the Output Matrix diagonalization and then use the error point offset method to check that they are diagonal.

We mainly want these loops to work well at DC, so it is perhaps better if we can measure the matrix at DC. Its less automatic than at 13 Hz, but I think it could be done with a script and some iterative matrix inversion:

1. IMC locked, IMC ASC loops all open (by setting the overall input gain slider to zero)
2. apply an offset in the WFS1_P basis (turn off the integrators in all the servo loops, and apply a ~400 count offset in the error point)
3. tweak the WFS1_P output matrix until the WFS2_P and MC2_TRANS_P signals go to zero.
4. repeat for all 6 loops.

I haven't tried this procedure before, but I think it should work. You can use something like "cdsutils servo" to slowly adjust the Output Matrix values.

I tried following the steps and the method I was using converged to same output matrix upto 2 decimal points but there is still left over cross coupling as you can see in Attachment 1. With the new output matrix, WFS loop can be turned on with full overall gain of 1.

Changes:

• I switched off +20dB FM2 on C1IOO-WFS1_PIT and increased gain C1:IOO-WFS1_PIT_GAIN from 0.1 to 1 to be uniform with other filters.
• Output matrix change:
  • Old matrix:

    -2.   4.8 -7.3
     3.6  3.5 -2. 
     2.   1.  -6.8

  • New Matrix:

    3.44  4.22 -7.29
    0.75  0.92 -1.59
    3.41  4.16 -7.21

• I think the main change that allowed the WFS loop to become stable was the 0,0 element sign change.

Method:

• I made overall gain C1:IOO-WFS_GAIN 0
• Switched of (0:0.8) FM3 on PIT filter modules (IOO-WFS1_PIT, IOO-WFS2_PIT, IOO-MC2_TRANS_PIT)
• Changed ramp time to 2 seconds on all these modules
• Used offset of 10000 for WFS2 and MC2_TRANS, and 30000 for WFS1 (for some reason, response to WFS1 step was much lower than others)
• Measured the following sensor channels
  • C1:IOO-WFS1_I_PIT_OUT
  • C1:IOO-WFS2_I_PIT_OUT
  • C1:IOO-MC_TRANS_PIT_OUT
• First I took 30s average of these channels, then applied the offsets in the three modules one by one and recorded steps in each sensor.
• Measured step from reference value taken before, and normalized each step to the DOF that was actually stepped to get a matrix.
• Inverted this matrix and multiplied with existing output matrix. Made sure column norm1 is same as before and column signs are same as before.
• Repeated a few times.

Note: The standard deviation on the averages was very high even after averaging for 30s. This data should be averaged after low passing high frequencies but I couldn't find the filter module medm screens for these signals, so I just proceeded with simple averaging of full rate signal using cdsultis avg command.

Fri Nov 25 12:46:31 2022

The WFS loop are unstable again. This could be due to the matrix balancing done while vacuum was disrupted. The above matrix does not work anymore.

In Attachment 1, I give a plan for the proposed path of AS beam into the IMC WFS heads to use them temporarily as AS WFS. Paths shown in orange are the existing MC REFL path, red for the existing AS path, cyan for the proposed AS path, and yellow for the existing IFO refl path.  We plan to overlap AS beam to the same path by installing the following new optics on the table:

• M1 will be a new mirror mounted on a flipper mount reflecting 100% of AS beam to SW corner of the table.
• M2 will be a new fixed mirror for steering the new AS beam path to match with MC WFS path.
• M3 will be the existing beamsplitter used to pick off light for MC refl camera. We'll just mount this on a flipper so that it can be removed from the path. Precaution will be required to protect the CCD from high intensity MC reflection by putting on more ND filters.
• The AS beam would need to be made approximately 1 mm in beam width. The required lenses for this would be placed between M1 and M2.

I request people to go through this plan and find out if there are any possible issues and give suggestions.

PS: Thanks JC for the photos. I got it from foteee google photos. It would be nice if these are also put into the 40m wiki page for photos of optical tables.

RXA: Looks good. I'm not sure if ND filters can handle the 1 W MC reflection, so perhaps add another flipper there. It would be good if you can measure the power on the WFS with a power meter so we know what to put there. Ideally we would match the existing power levels there or get into the 0.1-10 mW range.

Today I did a lot of steps to eventually reach to WFS locking stably for long times and improving and keeping the IMC transmission counts to 14400. I think the main culprit in thw WFS loop going unstable was the offset value set on MC_TRANS_PIT filter module  (C1:IOO-MC_TRANS_PIT_OFFSET). This value was roughly correct in magnitude but opposite in sign, which created a big offset in MC_TRANS PIT error signal which would integrate by the loops and misalign the mode cleaner.

WFS offsets tuning

• I ran C1:IOO-WFS_MASTER > Actiona > Correct WFS DC offsets script while the two WFS heads were blocked.
• Then I aligned IMC to maximize transmission. I also made PMC transmission better by walking the input beam.
• Then, while IMC is locked and WFS loops are off, I aligned the beam spot on WFS heads to center it in DC (i.e. zeroing C1:IOO-WFS1_PIT_DC, C1:IOO-WFS1_YAW_DC, C1:IOO-WFS2_PIT_DC, C1:IOO-WFS2_YAW_DC)
• Then I ran C1:IOO-WFS_MASTER > Actiona > Correct WFS DC offsets script while keeping IMC locked (note the script says to keep it unlocked, but I think that moves away the beam). If we all agree this is ok, I'll edit this script.
• Then I checked the error signals of all WFS loops and still found that C1:IOO-MC_TRANS_PIT_OUTPUT and C1:IOO-MC_TRANS_YAW_OUTPUT have offsets. I relieved these offsets by averaging the input to these filter moduels for 100s and updating the offset. This is where I noticed that the PIT offset was wrong in sign.

WFS loops UGF tuning

• Starting with only YAW loops, I measured the open loop transfer functions (OLTFs) for each loop by simultaneously injecting gaussian noise from 0.01 Hz to 0.5 Hz using diaggui at the loop filter module excitation points and taking ration of IN1/IN2 of the filter modules.
• Then I scaled the YAW output matrix columns to get UGF of 0.1 Hz when YAW loop was along turned on.
• Then I tried to do this for PIT as well but it failed as even with overall gain of 0.1, the PIT loops actuate a lot of YAW motion causing the IMC to loose lock eventually.
• So I tried locking PIT loops along with YAW loops but with 0.1 overall gain. This worked for long enough that I could get a rough estimate of the OLTFs. I scaled the columns of PIT output matrix and slowly increased the overall gain while repeating this step to get about 0.1 Hz UGF for all PIT loops too.
• Note though that the PIT loop shape did not come out as expected with a shallower slope and much worse coherence for same amount of excitation in comparison to YAW loops. See attached plots.
• Never the less, I was able to reach to an output matric which works at overall gain of 1. I tested this configuration for atleast 15 minutes but the loop was working even with 6 excitations happening simultaneously for OLTF measurement.
• We will need to revisit PIT loop shapes, matrix diagonalization, and sources of noise.

OLTF measurements were done using this diaggui file. The measurement file got deleted by me by mistake, so I recreated the template. Thankfully, I had saved the pdf of the measurements, but I do not have same measurement results in the git repo.

Today, I worked on WFS loop output matrix for PIT DOFs.

• I began with the matrix that was in place before Nov 15.
• I followed the same method as last time to fist get all UGFs around 0.06 Hz with overall gain of 0.6 on the WFS loops.
• This showed me that MC2_TRANS_PIT loop shape matches well with the nice working YAW loops, but the WFS1 and WFS2 loops still looked flat like before.
• This indicated that output matrix needs to be fixed for cross coupling between WFS1 and WFS2 loops.
• I ran this script WFSoutMatBalancing.py which injects low frequency (<0.5 Hz) oscillations when the loops are open, and measures sensing matrix using error signals. I used 1000s duration for this test.
• The direct inverse of this sensing matrix fixed the loop shape for WFS1 indicating WFS1 PIT loop is disentangled from WFS2 now.
• Note this is a very vague definition of diagonalization, but I am aiming to reach to a workign WFS loop asap with whatever means first. Then we can work on accurate diagonalization later.
• I simply ran the script WFSoutMatBalancing.py again for another 1000s and this time the sensing matrix mostly looked like an identity.
• I implemented the new output matrix found by direct inversion and took new OLTF.Again though, the WFS2_PIT loop comes out to be flat. See Attachment 1.
• Then noting from this elog post, I reduced the gain values on MC2 TRANS loops to 0.1 I think it is better to use this place to reduce loop UGF then the output matrix as this will remind us that MC2 TRANS loops are slower than others by 10 times.
• I retook OLTF but very unexpected results came. The overall gain of WFS1_YAW and WFS2_YAW seemed to have increased by 6. All other OLTFs remained same as expected. See attachment 2.
• To fulfill the condition that all UGF should be less than 0.1 Hz, I reduced gains on WFS1_YAW and WFS2_YAW loops but that made the YAW loops unstable. So I reverted back to all gains 1.
• We probably need to diagonalize Yaw matrix better than it is for letting MC2_TRANS_YAW loop to be at lower UGF.
• I'm leaving the mode cleaner in this state and would come back in an hour to see if it remains locked at good alignment. See attachment 3 for current state.

Sun Dec 4 17:36:32 2022 AG: IMC lock is holding as strong as before. None of the control signals or error signals seem to be increasing monotonously over the last one hour. I'll continue monitoring the lock.

Mon Dec 5 11:11:08 2022 AG: IMC was locked all night for past 18 hours. See attachment 4 for the minute trend.

Also reply to: 40m/17255

I ran the toggleWFSoffsets.py script to generate a step response of the WFS loops in operation. Attachment 1 shows the diaggui measured time response following the parameters mentioned in 40m/17255. There are few things to quickly note from this measurement without doing detailed analysis:

• WFS2_PIT is heavily cross-coupled with WFS1_PIT and MC2_TRANS_PIT. This was also the inference from the previous post based on loop shape for WFS2_PIT loop. This needs to be fixed.
• Weirdly enough, it seems that WFS2_PIT is also cross coupled with MC2_TRANS_YAW.
• MC2_TRANS_PIT is not coupled to WFS1_PIT or WFS2_PIT. This was the major issue in last measurement in 40m/17255.
• WFS1_PIT is coupled to MC2_TRANS_PIT by about half, but is not cross-coupled to WFS2_PIT.
• For YAW, the DOFs are mostly disentangled except for a cross coupling of WFS1_YAW to MC2_TRANS_YAW by about 60%.

To get out the UGF of the loops from the step responses, I need to read this into python and apply the same filters and analyze time constants. I still have to do this part, but I thought I'll put out the result before spending more time on this.

GPSTIME: 1354314478

I took transfer function measurement of WFS2 SEG4 photodiode between 1 MHz to 100 MHz in a linear sweep.

Measurement details:

• The reincarnated Jenne laser head was used for this test. The laser diode is 950 nm though, which should just mean a different responsivity of the photodiode while we are mainly interested in relative response of the WFS heads at 11 MHz and 55 MHz with respect to 29.5 MHz.
• See attachment 2 for how the laser was placed on AP table.
• The beam was injected in between beam splitter for MC reflection camera and beam splitter for beam dump.
• The input was aligned such that all the light of the laser was falling on Segment 4 of WFS2.
• Using moku, I took RF transfer function from 1 MHz to 100 MHz, 512 points, linearly spaced, with excitation amplitude of 1 V and 100,000 cycles of averaging.
• Measurement data and settings are stored here.

Results:

Relative to 29.5 MHz, teh photodiode response is:

• At 11 MHz: -20.4 dB
• At 55 MHz: -36.9 dB
• At 71.28 MHz: -5.9 dB

I'm throwing in an extra number at the end as I found a peak at this frequency as well. This means to use these WFS heads for arm ASC, we need to have 10 times more light for 11 MHz and roughly 100 times more light for 55 MHz. According to Gautam's thesis Table A.1 and this elog post, the modulation depth for 11 MHz is 0.193 and for 55 MHz is 0.243 in comparison to 0.1 for 29.5 MHz., so the sideband TEM00 light available for beating against carrier TEM01/TEM10 is roughly twice as much for single arm ASC. That would mean we would have 5 times less error signal for 11 MHz and 40 times less error signal for 55 MHz. These are rough calculations ofcourse.

I tested teh WFS demod board for possibility of demodulating 11 MHz or 55 MHz signal with it. It definitely has some bandpass filter inside as the response is very bad for 11 MHz and 55 MHz. See attached the ASD curves for the excitations seens on I and Q inputs of WFS1 Segment 2 when it was demodulated with a clock of different frequencies but same amplitude of 783.5 mVpp (this was measured output of 29.5 MHz signal from RF distribution board). See attachments 2-4 for mokulab settings. Note for 29.5 MHz case, I added an additional 10 dB attenuator to output 1.

The measurement required me to change signal power level to see a signal of atleast 10 SNR. If we take signal level of 29.5 MHz as reference, following are the responses at other frequencies:

• At 11 MHz:
  • I: -92 dB
  • Q: -97 dB
• At 55 MHz:
  • I: -75 dB
  • Q: -72 dB

Note that I and Q outputs are unbalanced as well for the two different demodulation frequencies.

This means that if we want to use the WFS demodulation boards as is, we'll need to amplify the photodiode signal by the above amounts to get same level of outputs. I stil need to see the DCC document of these board and if the LO is also bandpassed. In which case, we can probably amplify the LO to improve the demodulation at 11 and 55 MHz. THe beatnote time series for the measured data did not show an obvious sinusoidal oscillation, so I chose to not show a plot with just noise here.