[Rana, Koji]

1. The response of the IMC WFS board was measured. The LO signal with 0.3Vpp@29.5MHz on 50Ohm was supplied from DS345. I've confirmed that this signal is enough to trigger the comparator chip right next to the LO input. The RF signal with 0.1Vpp on the 50Ohm input impedance was provided from another DS345 to CH1 with a frequency offset of 20Hz~10kHz. Two DS345s were synced by the 10MHz RFreference at the rear of the units. The resulting low frequency signal from the 1st AF stage (AD797) and the 2nd AF stage (OP284) were checked.

Attachment 1 shows the measured and modelled response of the demodulator with various frequency offsets. The value shows the signal transfer (i.e. the output amplitude normalized by the input amplitude) from the input to the outputs of the 1st and 2nd stages. According to the datasheet, the demodulator chip provides a single pole cutoff of 340kHz with the 33nF caps between AP/AN and VP. The first stage is a broadband amplifier, but there is a passive LPF (fc=~1kHz). The second stage also provides the 2nd order LPF at fc~1kHz too. The measurement and the model show good agreement.

2. The output noise levels of the 1st and 2nd stages were meausred and compared with the noise model by LISO.
Attachment 2 shows the input referred noise of the demodulator circuit. The output noise is basically limited by the noise of the first stage. The noise of the 2nd stage make the significant contribution only above the cut off freq of the circuit (~1kHz). And the model supports this fact. The 6.65kOhm of the passive filter and the input current noise of AD797 cause the large (>30nV/rtHz) noise contribution below 100Hz. This completely spoils the low noiseness (~1nV/rtHz) of AD797. At lower frequency like 0.1Hz other component comes up above the modelled noise level.

3. Rana and I had a discussion about the modification of the circuit. Attachment 4 shows the possible improvement of the demod circuit and the 1st stage preamplifier. The demodulator chip can have a cut off by the attached capacitor. We will replace the 33nF caps with 1uF and the cut off will be pushed down to ~10kHz. Then the passive LPF will be removed. We don't need "rodeo horse" AD797 for this circuit, but op27 is just fine instead. The gain of the 1st stage can be increased from 9 to 21. This should give us >x10 improvement of the noise contribution from the demodualtor (Attachment 3). We also can replace some of the important resistors with the thin film low noise resistors.

Summary: The demodulator input noise level was improved by a factor of more than 2. This was not as much as we expected from the preamp noise improvement, but is something. If this looks OK, I will implement this modification to all the 16 channels.

The modification shown in Attachment 1 has actually been applied to a channel.

• The two 1.5uF capacitors between VP and AN/AP were added. This decreases the bandwidth of the demodulator down to 7.4kHz
• The offset trimming circuit was disabled. i.e. Pin18 of AD831 was grounded.
• The passive low pass at the demodulator output was removed. (R18, C34)
• The stage1 (preamp) chip was changed from AD797 to OP27.
• The gain of the preamp stage was changed from 9 to 21. Also the thin film resistors are used.

Attachment 2 shows the measured and expected output signal transfer of the demodulator. The actual behavior of the demodulator is as expected, and we still keep the over all LPF feature of 3rd order with fc=~1kHz.

Attachment 3 shows the improvement of the noise level with the signal reffered to the demodulator input. The improvement by a factor >2 was observed all over the frequency range. However, this noise level could not be explained by the preamp noise level. Actually this noise below 1kHz is present at the output of the demodulator. (Surprisingly, or as usual, the noise level of the previous preamp configuration was just right at the noise level of the demodulator below 100Hz.) The removal of the offset trimmer circuit contributed to the noise improvement below 0.3Hz.

more U4 gain, lesssss U5 gain

ELOG of the Wednesday work.

It turned out that the IMC WFS demod boards have the PCB board that has a different pattern for each of 8ch.
In addition, AD831 has a quite narrow leg pitch with legs that are not easily accessible.
Because of these, we (Koji and Rana) decided to leave the demodulator chip untouched.

I have plugged in the board with the WFS2-Q1 channel modified in order to check the significance of the modification.

WFS performance before the modification

Attachment 1 shows the PSD of WFS2-I1_OUT calibrated to be referred to the demodulator output. (i.e. Measured PSDs (cnt/rtHz) were divided by 8.9*2^16/20)
There are three curves: One is the output with the MC locked (WFS servos not engaged). The second is the PSD with the PSL beam blocked (i.e. dark noise). The third is the electronics noise with the RF input terminated and the nominal LO supplied.

This tells us that the measured PSD was dominated by the demodulator noise in the dark condition. And the WFS signal was also dominated by the demod noise below 0.1Hz and above 20Hz. There are annoying features at 0.7, 1.4, 2.1, ... Hz. They basically impose these noise peaks on the stabilized mirror motion.

WFS performance after the modification

Attachment 2 shows the PSD of WFS2-Q1_OUT calibrated to be referred to the demodulator output. (i.e. Measured PSDs (cnt/rtHz) were divided by 21.4*2^16/20)
There are three same curves as the other plot. In addition to these, the PSD of WFS2-I1_OUT with the MC locked is also shown as a red curve for comparison.

This figure tells us that the measured PSD below 20Hz was dominated by the demodulator noise in the dark condition. And the WFS signal is no longer dominated by the electronics noise. However, there still are the peaks at the harmonics of 0.7, 1.4, 2.1, ... Hz. I need further inspection of the FWS demod and whtening boards to track down the cause of these peaks.

ELOG of the work on Thursday

Gautam suggested looking at the preamplifier noise by shorting the input to the first stage. I thought it was a great idea.

To my surprise, the noise of the 2nd stage was really high compared to the model. I proceeded to investigate what was wrong.

It turned out that the resistors used in this sallen-key LPF were thick film resistors. I swapped them with thin film resistors and this gave the huge improvement of the preamplifier noise in the low frequency band.

Attachment 1 shows the summary of the results. Previously the input referred noise of the preamp was the curve in red. We the resistors replaced, it became the curve in magenta, which is pretty close to the expected noise level by LISO model above 3Hz (dashed curves). Unfortunately, the output of the unit with the demodulator connected showed no improvement (blue vs green), because the output is still limited by the demodulator noise. There were harmonic noise peaks at n x 10Hz before the resistor replacement. I wonder if this modification also removed the harmonic noise seen in the CDS signals. I will check this next week.

Attachment 2 shows the current schematic diagram of the demodulator board. The Q of the sallen key filter was adjusted by the gain to have 0.7 (butter worth). We can adjust the Q by the ratio of the capacitance. We can short 3.83K and remove 6.65K next to it. And use 22nF and 47nF for the capacitors at the positive input and the feedback, respectively. This reduces the number of the resistors.

I have implemented the modification to the demod boards (Attachment 1).
Now, I am looking at the noise in the whitening board. Attachment 2 shows the comparison of the error signal with the input of the whitening filter shorted and with the 50ohm terminator on the demodulator board. The message is that the whitening filter dominates the noise below 3Hz.

I am looking at the schematic of the whitening board D990196-B. It has an VGA AD602 at the input. I could not find the gain setting for this chip.
If the gain input is fixed at 0V, AD602 has the gain of 10dB. The later stages are the filters. I presume they have the thick film resistors.
Then they may also cause the noise. Not sure which is the case yet.

Also it seems that 0.7Hz noise is still present. We can say that this is coming from the demod board but not on the work bench but in the eurocard crate.

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.

Summary:

I got around to doing this measurement today, using a minicircuits bi-directional coupler (ZFBDC20-61-HP-S+), along with some SMA-LEMO cables.

• With the IMC "well aligned" (MC transmission maximized, WFS control signals ~0), the RF power per quadrant into the Demod board is of the order of tens of pW up to a 100pW.
• With MC1 misaligned such that the MC transmission dropped by ~10%, the power per quadrant into the demod board is of the order of hundreds of pW.
• In both cases, the peak at 29.5MHz was well above the analyzer noise floor (>20dB for the smaller RF signals), which was all that was visible in the 1MHz span centered around 29.5 MHz (except for the side-lobes described later).
• There is anomalously large reflection from Quadrant 2 input to the Demod board for both WFS
• The LO levels are ~-12dBm, ~2dBm lower than the 10dBm that I gather is the recommended level from the AD831 datasheet

Details:

I first aligned the mode cleaner, and offloaded the DC offsets from the WFS servos.

The bi-directional coupler has 4 ports: Input, Output, Coupled forward RF and Coupled Reverse RF. I connected the LEMO going to the input of the Demod board to the Input, and connected the output of the coupler to the Demod board (via some SMA-LEMO adaptor cables). The two (20dB) coupled ports were connected to the Agilent spectrum analyzer, which have input impedance 50ohms and hence should be impedance matched to the coupled outputs. I set the analyzer to span 1MHz (29-30MHz), IF BW 30Hz, 0dB input attenuation. It was not necessary to turn on averaging to resolve the peaks at ~29.5MHz since the IF bandwidth was fine enough.

I took two sets of measurements, one with the IMC well aligned (I maximized the MC Trans as best as I could to ~15,000 cts), and one with a macroscopic misalignment to MC1 such that the MC Trans fell to 90% of its usual value (~13,500 cts). The peak function on the analyzer was used to read off the peak height in dBm. I then converted this to RF power, which is summarized in the table below. I did not account for the main line loss of the coupler, but according to the datasheet, the maximum value is 0.25dB so there numbers should be accurate to ~10% (so I'm really quoting more S.Fs than I should be).

For the well aligned measurement, there was ~0.4mW incident on WFS1, and ~0.3mW incident on WFS2 (measured with Ophir power meter, filter out).

I am not sure how to interpret the numbers for quadrants #2 and #6 in the first table, where the reverse coupled RF power was greater than the forward coupled RF power. But this measurement was repeatable, and even in the second table, the reverse coupled power from these quadrants are more than 10x the other quadrants. The peaks were also well above (>10dBm) the analyzer noise floor 

I haven't gone through the full misalginment -> Power coupled to TEM10 mode algebra to see if these numbers make sense, but assuming a photodetector responsivity of 0.8A/W, the product (P₁P₂) of the powers of the beating modes works out to ~tens of pW (for the IMC well aligned case), which seems reasonable as something like P₁~10uW, P₂ ~ 5uW would lead to P₁P₂~50pW. This discussion was based on me wrongly looking at numbers for the aLIGO WFS heads, and Koji pointed out that we have a much older generation here. I will try and find numbers for the version we have and update this discussion.

Misc:

1. For the sake of completeness, the LO levels are ~ -12.1dBm for both WFS demod boards (reflected coupling was negligible)
2. In the input signal coupled spectrum, there were side lobes (about 10dB lower than the central peak) at 29.44875 MHz and 29.52125 MHz (central peak at 29.485MHz) for all of the quadrants. These were not seen for the LO spectra.
3. Attached is a plot of the OSEM sensor signals during the time I misaligned MC1 (in both pitch and yaw approximately by equal amounts). Assuming 2V/mm for the OSEM calibration, the approximate misalignment was by ~10urad in each direction.
4. No IMC suspension glitching the whole time I was working today

It was raised at the Wednesday meeting that I did not check the RF pickup levels while measuring the RF error signal levels into the Demod board. So I closed the PSL shutter, and re-did the measurement with the same measurement scheme. The detailed power levels (with no light incident on the WFS, so all RF pickup) is reported in the table below.

These numbers can be subtracted from the corresponding columns in the previous elog to get a more accurate estimate of the true RF error signal levels. Note that the abnormal behaviour of Quadrant #2 on both WFS demod boards persists.

we are thinking of doing a sprucing up of the input mode cleaner WFS (sensors + electronics + feedback loops)

1. WFS Heads
   1. it has been known since ~2002 that the RF circuits in the heads oscillate. 
   2. in the attached PDF you can see that 2 opamps (U3 & U4; MAX4106) are used to amplify the tank circuit made up of the photodiode capacitance and L6.
   3. due to poor PCB layout (the output of U4 runs close to the input of U3) the opamps oscillate if the if the Reed relay (RY2) is left open (not attenuating)
   4. we need to remove/disable the relay
   5. also remove U3 for each quadrant so that it has a fixed gain of (TBD) and a 50 Ohm output
   6. also check that all the resonances are tuned to 1f, 2f, & 3f respectively
2. Demod boards
3. DC quadrant readouts
4. Whitening
5. Noise budget of sensors, including electronics chain
6. diagonalization of sensors / actuators
7. Requirements -
8. Optical Layout
9. What does the future hold ?

1. what is our preferred pin-for-pin replacement for the MAX4106/MAX4107? internet suggests AD9632. Anyone have any experience with it? The Rabbott uses LMH6642 in the aLIGO WFSs. It has a lower slew rate than 9632, but they both have the same distortion of ~ -60 dB for 29.5 MHz.
2. the whole DC current readout is weird. Should have a load resistor and go into the + input of the opamp, so as to decouple it from the RF stuff. Also why such a fast part? Should have used a OP27 equivalent or LT1124.
3. LEMO connectors for RF are bad. Wonder if we could remove them and put SMA panel mount on there.
4. as usual, makes me feel like replacing with better heads...and downstream electronics...

The WFS loops were not maximizing the IMC transmission. The transmission counts remained stuck at around 12500 counts. The reflection DCMON from IMC had reached above 0.35 while nominally it had been around 0.2. So today, I manuaaly aligned the IMC to best transmission and lowest reflection, then unlocked IMC and reset the offsets on WFS1 and WFS2 RF readouts. After the offsets were changed, the error singals were fluctuating around 0 in best algined state. Then turning on the WFS loops made the transmissions slighlty higher to 13250 counts.

I wanted to check the functionality of the IMC WFS. I just turned on the WFS servo loops as they were. For the past two hours, they didn't run away. The servo has been left turned on. I don't think there is no reason to keep it turned off.

From the measured OLTF, the dynamics of the damped suspension was inferred by calculating H_damped = H_pend / (1+OLTF).
Here H_pend is a pendulum transfer function. For simplicity, the DC gain of the unity is used. The resonant frequency of the mode
is estimated from the OLTF measurement. Because of inprecise resonant frequency for each mode, calculated damped pendulum
has glitches at the resonant frequency. In fact measurement of the OLTF at the resonant freq was not precise (of course). We can
just ignore this glitchiness (numerically I don't know how to do it particularly when the residual Q is high).

Here is my recommended values to have the residual Q of 3~5 for each mode.

MC1 SUS POS current  75   -> x3   = 225
MC1 SUS PIT current   7.5 -> x2   =  22.5
MC1 SUS YAW current  11   -> x2   =  22
MC1 SUS SD  current 300   -> x2   = 600

MC2 SUS POS current  75   -> x3   = 225
MC2 SUS PIT current  20   -> x0.5 =  10
MC2 SUS YAW current   8   -> x1.5 =  12
MC2 SUS SD  current 300   -> x2   = 600

MC3 SUS POS current  95   -> x3   = 300
MC3 SUS PIT current   9   -> x1.5 =  13.5
MC3 SUS YAW current   6   -> x1.5 =   9
MC3 SUS SD  current 250   -> x3   = 750

This is the current setting in the end.

MC1 SUS POS 150
MC1 SUS PIT  15
MC1 SUS YAW  15
MC1 SUS SD  450

MC2 SUS POS 150
MC2 SUS PIT  10
MC2 SUS YAW  10
MC2 SUS SD  450


MC3 SUS POS 200
MC3 SUS PIT  12
MC3 SUS YAW   8
MC3 SUS SD  500

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.

We have spare WFS demods in a plastic box along the Y arm. So you don't need to modify the IMC demod boards, which we want to keep in the current state.

[Eric Koji]

We made sensing matrix measurements for the IMC WFS and the MC2 QPD.

The data is under further analysis but here is some record of the current state to show
IMC Trans RIN and the ASC error signals with/without IMC ASC loops

The measureents were done automatically running DTT. This can be done by

/users/Templates/MC/wfsTFs/run_measurements

The analysis is in preparation so that it provides us a diagnostic report in a PDF file.

Yesterday, Koji and I measured the transfer function of pitch and yaw excitations of each MC mirror, directly to each quadrant of each WFS QPD. 

When I last touched the WFS settings, I only used MC2 excitations to set the individual quadrant demodulation phases, but Koji pointed out that this could be incomplete, since motion of the curved MC2 mirror is qualitatively different than motion of the flat 1&3. 

We set up a DTT file with twenty TFs (the excitation to I & Q of each WFS quadrant, and the MC2 trans quadrants), and then used some perl find and replace magic to create an xml file for each excitation. These are the files called by the measurement script Koji wrote. 

I then wrote a MATLAB script that uses the magical new dttData function Koji and Nic have created, to extract the TF data at the excitation frequency, and build up the sensing elements. I broke the measurements down by detector and excitation coordinate (pitch or yaw).

The amplitudes of the sensing elements in the following plots are normalized to the single largest response of any of the QPD's quadrants to an excitation in the given coordinate, the angles are unchanged. From this, we should be able to read off the proper digital demodulation angles for each segment, confirm the signs of their combinations for pitch and yaw, and construct the sensing matrix elements of the properly rotated signals. 

The axes of each quadrant look consistent across mirrors, which is good, as it nails down the proper demod angle. 

The xml files and matlab script used to generate these plots is attached. (It requires the dttData functions however, which are in the svn (and the dttData functions require a MATLAB newer than 2012b))

It seems clever, but I wonder why use DTT and command line perl, instead of using the FE lockins or just demod the offline data or all of the other sensing matrix scripts made for the LSC (at 40m) or ASC (at LLO) ?

There are several non scientific reasons.

Lock ARMs

• Try IFO Configure ! Restore Y Arm (POY) and saw XARM lock, not YARM. Looks like YARM biases on ITMY and ETMY are not optimal, so we slide C1:SUS-ETMY_OFF from 3.0 --> -14.0 and watch Y catch its lock.
• Run ASS scripts for both arms and get TRY/TRX ~ 0.95
  • We ran X, then Y and noted that TRX dropped to ~0.8 so we ran it again and it was well after that. From now on, we will do Y, then X.

WFS1 noise injection

• Turn WFS limits off by running switchOffWFSlims.sh
• Inject broadband noise (80-90 Hz band) of varying amplitudes from 100 - 100000 counts on C1:IOO-WFS1_PIT_EXC
• After this we try to track its propagation through various channels, starting with
  • C1:LSC-XARM_IN1_DQ / C1:LSC-YARM_IN1_DQ
  • C1:SUS-ETMX_LSC_OUT_DQ / C1:SUS-ETMY_LSC_OUT_DQ
  • C1:IOO-MC_F_DQ
  • C1:SUS-MC1_**COIL_OUT / C1:SUS-MC2_**COIL_OUT / C1:SUS-MC3_**COIL_OUT
  • C1:IOO-WFS1_PIT_ERR / C1:IOO-WFS1_YAW_ERR
  • C1:IOO-WFS1_PIT_IN2

** denotes [UL, UR, LL, LR]; the output coils.

• Attachment 1 shows the power spectra with IMC unlocked
• Attachment 2 shows the power spectra with the ARMs (and IMC) locked

Rana came and helped us figure us where to inject the noise. Following are the characteristics of the test we did:

• Inject normal noise at C1:IOO-MC1_PIT_EXC using AWGGUI.
• Excitation amplitude of 54321 in band 12-37Hz with Cheby1 8th order bandpass filter with same limits.
• Look at power spectrum of C1:IOO-MC_F_DQ, C1:IOO-WFS1-PIT_OUT_DQ and the C1:IOO-MC1_PIT_EXC itself.
• Increased the gain of the noise excitation until we see some effect in MC_F.
• Diaggui also showed coherence plot in the bottom, which let's us have an estimate of how much we need to go further.

Attachment 1 shows a screenshot with awggui and diaggui screens displaying the signal in both angular and longitudinal channels.

Attachment 2 shows the analogous screenshot for MC2.

We redid the WFS noise injection test and have compiled some results on noise contribution in arm cavity noise and IMC frequency noise due to angular noise of IMC.

Attachment 1: Shows the calibrated noise contribution from MC1 ASCPIT OUT to ARM cavity length noise and IMC frequency noise.

• For calibrating the cavity length noise signals, we sent 100 cts 100Hz sine excitation to ITMX/Y_LSC_EXC, used actuator calibration for them as 2.44 nm/cts from 13984, and measured the peak at 100 hz in time series data. We got calibration factors: ETMX-LSC_OUT: 60.93 pm/cts , and ETMY-LSC_OUT: 205.0 pm/cts.
• For converting IMC frequency noise to length noise, we used conversion factor given by where L is 37.79m and lambda is wavelength of light.
• For converting MC1 ASCPIT OUT cts data to frequency noise contributed to IMC, we sent 100,000 amplitude bandlimited noise (see attachment 3 for awggui config) from 25 Hz to 30 Hz at C1:IOO-MC1_PIT_EXC. This noise was seen at both MC_F and ETMX/Y_LSC_OUT channels. We used the noise level at 29 Hz to get a calibration for MC1_ASCPIT_OUT to IMC Frequency in Hz/cts. See Attachment 2 for the diaggui plots.
• Once we got the calibration above, we measured MC1_ASCPIT_OUT power spectrum without any excitaiton and multiplied it with the calibration factor.
• However, something must be wrong because the MC_F noise in length units is coming to be higher than cavity length noise in most of the frequency band.
  • It can be due to the fact that control signal power spectrum is not exactly cavity length noise at all frequencies.  That should be only above the UGF of the control loop (we plan to measure that in afternoon).
  • Our calibration for ETMX/Y_LSC_OUT might be wrong.

We today measured the calibration factors for XARM_OUT and YARM_OUT in nm/cts and replotted our results from 16117 with the correct frequency dependence.

Calibration of XARM_OUT and YARM_OUT

• We took transfer function measurement between ITMX/Y_LSC_OUT and X/YARM_OUT. See attachment 1 and 2
• For ITMX/Y_LSC_OUT we took calibration factor of 3*2.44/f² nm/cts from 13984. Note that we used the factor of 3 here as Gautum has explicitly written that the calibration cts are DAC cts at COIL outputs and there is a digital gain of 3 applied at all coil output gains in ITMX and ITMY that we confirmed.
• This gave us callibration factors of XARM_OUT: 1.724/f² nm/cts , and YARM_OUT: 4.901/f² nm/cts. Note the frrequency dependence here.
• We used the region from 70-80 Hz for calculating the calibration factor as it showed the most coherence in measurement.

Inferring noise contributions to arm cavities:

• For converting IMC frequency noise to length noise, we used conversion factor given by where L is 37.79m and lambda is wavelength of light.
• For converting MC1 ASCPIT OUT cts data to frequency noise contributed to IMC, we sent 100,000 amplitude bandlimited noise  from 25 Hz to 30 Hz at C1:IOO-MC1_PIT_EXC. This noise was seen at both MC_F and ETMX/Y_LSC_OUT channels. We used the noise level at 29 Hz to get a calibration for MC1_ASCPIT_OUT to IMC Frequency in Hz/cts. This measurement was done in 16117.
• Once we got the calibration above, we measured MC1_ASCPIT_OUT power spectrum without any excitaiton and multiplied it with the calibration factor.
• Attachment 3 is our main result.
  • Page 1 shows the calculation of Angle to Length coupling by reading off noise injects in MC1_ASCPIT_OUT in MC_F. This came out to 10.906/f² kHz/cts.
  • Page 2-3 show the injected noise in X arm cavity length units. Page 3 is the zoomed version to show the matching of the 2 different routes of calibration.
  • BUT, we needed to remove that factor of 3 we incorporated earlier to make them match.
  • Page 4 shows the noise contribution of IMC angular noise in XARM cavity.
  • Page 5-6 is similar to 2-3 but for YARM. The red note above applied here too! So the factor of 3 needed to be removed in both places.
  • Page 7 shows the noise contribution of IMC angular noise in XARM cavity.

Conclusions:

• IMC Angular noise contribution to arm cavities is atleast 3 orders of magnitude lower then total armc cavity noise measured.

Edit Mon May 10 18:31:52 2021

See corrections in 16129.

A few corrections to last analysis:

• The first plot was not IMC frequency noise but actually MC_F noise budget.
  • MC_F is frequency noise in the IMC FSS loop just before the error point where IMC length and laser frequency is compared.
  • So, MC_F (in high loop gain frequency region upto 10kHz) is simply the quadrature noise sum of free running laser noise and IMC length noise.
  • Between 1Hz to 100 Hz, normally MC_F is dominated by free running laser noise but when we injected enough angular noise in WFS loops, due to Angle to length coupling, it made IMC length noise large enough in 25-30 Hz band that we started seeing a bump in MC_F.
  • So this bump in MC_F is mostly the noise due to Angle to length coupling and hence can be used to calculate how much Angular noise normally goes into length noise.
• In the remaining plots, MC_F was plotted with conversion into arm length units but this was wrong. MC_F gets suppressed by IMC FSS open loop gain before reaching to arm cavities and hence is hardly present there.
• The IMC length noise however is not suppresed until after the error point in the loop. So the length noise (in units of Hz calculated in the first step above) travels through the arm cavity loop.
• We already measured the transfer function from ITMX length actuation to XARM OUT, so we know how this length noise shows up at XARM OUT.
• So in the remaining plots, we plot contribution of IMC angular noise in the arm cavities. Note that the factor of 3 business still needed to be done to match the appearance of noise in XARM_OUT and YARM_OUT signal from the IMC angular noise injection.
• I'll post a clean loop diagram soon to make this loopology clearer.

• looking at some IMC WFS swept sines, it seems like there is poor margin around 1 Hz
• increasing the overall gain (input) by 2x makes the whole system shake a lot at ~1Hz
• increasing the input gain from 1 to 4 makes the lock break due to oscillations
• I have turned the input slider to 0.5 just now, but it will revert to 1 after the next lock loss for tonights testing
• we can use the observations from now for an hour or so to see if 0.5 is better for the 1 Hz behavior (lets look at the summary pages)

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.

IMC WFS tuning

- IMC was aligned manually to have maximum output and also spot at the center of the end QPD.
- The IMC WFS spots were aligned to be the center of the WFS QPDs.
- With the good alignment, WFS RF offset and MC2 QPD offsets were tuned via the scripts.

Last night the sensing matrix for IMC WFS&QPD were measured.

C1:IOO-MC(1, 2, 3)_(ASCPIT, ASCYAW)_EXC were excited at 5.01Hz with 100 count
The output of the WFS1/WFS2/QPD were measured. They all looked well responding
i.e. Pitch motion shows pitch error signals, Yaw motion shows yaw error signals.

The below is the transfer function from each suspension to the error signals

MC1P      MC2P     MC3P
-3.16e-4  1.14e-2  4.62e-3 -> WFS1P
 5.43e-3  8.22e-3 -2.79e-3 -> WFS2P
-4.03e-5 -3.98e-5 -3.94e-5 -> QPDP

MC1Y      MC2Y     MC3Y
-6.17e-4  6.03e-4  1.45e-4 -> WFS1Y
-2.43e-4  4.57e-3 -2.16e-3 -> WFS2Y
 7.08e-7  2.40e-6  1.32e-6 -> QPDY

Taking the inverse of these matrices, the scale was adjusted so that the dc response.



 I took some spectra of the error signals and MC2 Trans RIN with the loops off (blue) and on (red) during the current conditions of daytime seismic noise.

Today I started looking into the WFS problem and improvement, after being briefed by Koji and Nicholas. I started taking some measurements of open loop transfer functions for both PIT and YAW for WFS1, WFS2 and MC2_TRANS. For both WFS1 and 2 there is a peak in close proximity of the region with gain>1, and the phase margin is not very high. Tomorrow I will make measurements of the local damping open loop transfer functions, then we'll think how to improve the sensors' behaviour.

[Diego,Koji]

Today we took some measurements of transfer functions and power spectra of suspensions of the MC* mirrors (open loop), for all the DOFs (PIT, POS, SIDE, YAW); the purpose is to evaluate the Q factor of the resonances and then improve the local damping system.

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.

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

With all of the shaking (man-made and divine), it was a hard to debug this problem. Summary of fixes:

1. The beam was misaligned on the WFS 1 and 2 heads, as well as the MC2 trans QPD. I re-aligned the former with the IMC unlocked, the latter (see Attachment) with the IMC locked (but the MC2 spot centering loops disabled).
2. I reset the WFS DC and RF offsets, as well as the QPD offsets (once I had hand-aligned the IMC mirrors to obtain good transmission).

At least the DC indicators are telling me that the IMC locking is back to a somewhat stable state. I have not yet checked the frequency noise / RIN.

I resume my IMC ringdown activities now that the IMC is aligned again.

To avoid any accidental misalignments Gautam turned off all the inputs to the WFS servo.

I set up a PD and a lens as in attachment 1 (following Gautam's setup).

I connect the REFL, TRANS and INPut PDs to the oscilloscope.

I connect a Siglent function generator to the AOM driver. I try to shut off the light to the IMC using 1V DC waveform and pressing the output button manually. However, it produced heavily distorted step function in the PMC trans PD.

I use a square wave with a frequency of 20mHz instead with an amplitude of 0.5V offset of 0.25V and dutycycle of 1% so there will be minimal wasted time in the off state. I get nice ringdowns (attachment 2) - forgot to take pictures. The autolocker slightly misaligns the M2 every time it is acting, so I manually align it everytime the IMC gets unlocked.

Data analysis will come later.

I remove the PD and lens and reenable the WFS servo inputs. The IMC locks easily. The WFS outputs are very different than 0 now though.

changed some y-scale limits on the WFS summary pages to zoom in better

- Updated the circuit diagrams:

IMC WFS Demodulator Board, Rev. 40m https://dcc.ligo.org/LIGO-D1600503

IMC WFS Whitening Board, Rev. 40m https://dcc.ligo.org/LIGO-D1600504

- Measured the noise levels of the whitening board, demodboard, and nominal free running WFS signals.

- IMC WFS demod phases for 8ch adjusted

Injected an IMC PDH error point offset (@1kHz, 10mV, 10dB gain) and adjusted the phase to have no signal in the Q phase signals.

- The WFS2 PITCH/YAW matrix was fixed

It was found that the WFS heads were rotated by 45 deg (->OK) in CW and CCW for WFS1 and 2, respectively (oh!), while the input matrices were identical! This made the pitch and yaw swapped for WFS2. (See attachment)

- Measured the TFs MC1/2/3 P/Y actuation to the error signals

Noise analysis of the WFS error signals.

Attachment 1: All error signals compared with the noise contribution measured with the RF inputs or the whitening inputs terminated.

Attachment 2: Same plot for all the 16 channels. The first plot (WFS1 I1) shows the comparison of the current noise contributions and the original noise level measured with the RF terminated with the gain adjusted along with the circuit modification for the fair comparison. This plot is telling us that the electronics noise was really close to the error signal.

I wonder if we have the calibration of the IMC suspensions somewhere so that I can convert these plots in to rad/sqrtHz...?

WFS1 / WFS2 demod phases and WFS signal matrix

Signal transfer function measurements

C1:SUS-MC*_ASCPIT_EXC channels were excited for swept sine measurements.

The TFs to WFS1-I1~4, Q1~4, WFS1/2_PIT/YAW, MC2TRANS_PIT/YAW signals were recorded.

The MC1 and MC3 actuation seems to have ~30Hz elliptic LPF somewhere in the electronics chain.
This effect was compensated by subtracting the approximated time delay of 0.022sec.

The TFs were devided by freq^2 to make the response flat and averaged between 7Hz to 15Hz.
The results have been summarized in Attachment 3&4.

Attachment 4 has the signal sensing matrix. Note that this matrix was measured with the input gain of 0.1.

Input matrix for diagonalizing the actuation/sensor response

Pitch

e.g. To produce pure WFS1P reaction, => -1.59 MC1P + 0.962 MC2P + 0.425 MC3P

Yaw

Now, the output matrices in the previous entry were implemented.
The WFS servo loops have been engaged for several hours.
So far the REFL and TRANS look straight. Let's see how it goes.

It didn't go crazy at least for the past 24hours.

• For the rough calibration below 10 Hz, we can use the SUS OSEM cal: the SUSPIT and SUSYAW error signals are in units of micro-radians.
• It seems from the noise plots that the demod board is now dominating over the whitening board noise.
• If the RF signals at the demod input are low enough, we can consider either increasing the light power on the WFS or increasing the IMC mod. depth.
• We should look at the out-of-lock light power on the WFS and re-examine what the 'safe' level is. We used to do this based on the dissipated electrical power (bias voltage x photocurrent).

At Hanford, there is this issue with laser jitter turning into an IMC error point noise injection. I wonder if we can try out taking the acoustic band WFS signal and adding it to the MC error point as a digital FF. We could then look at the single arm error signal to see if this makes any improvement. There might be too much digital delay in the WFS signals if the clock rate in the model is too low.

Koji responding to Rana

> For the rough calibration below 10 Hz, we can use the SUS OSEM cal: the SUSPIT and SUSYAW error signals are in units of micro-radians.

I can believe the calibration for the individual OSEMs. But the input matrix looked pretty random, and I was not sure how it was normalized.
If we accept errors by a factor of 2~3, I can just naively believe the calibration factors.

> If the RF signals at the demod input are low enough, we can consider either increasing the light power on the WFS or increasing the IMC mod. depth.

The demod chip has the conversion factor of about the unity. We increased the gains of the AF stages in the demod and whitening boards. However, we only have the RMS of 1~20 counts. This means that we have really small RF signals. We should check what's happening at the RF outputs of the WFS units. Do we have any attenuators in the RF chain? Can we skip them without making the WFS units unstable?

The WFS gains are supposedly maximized already. If we remotely try to increase the gain, the two MAX4106 chips in the RF path will oscillate with each other.

We should insert a bi-directional coupler (if we can find some LEMO to SMA converters) and find out how much actual RF is getting into the demod board.

The whitening board saids it is Rev B, but the actual component values are more like Rev. C.

The input stage (AD602) has an input resistor of 909 Ohm.
This is causing a big attenuation of the signal (x1/10) because the input impedance of AD602 is not high. And this screws up the logarithm of the gain.
I don't think this is a right approach.