Rana suggested in today's meeting to put in a notch filter in the XARM IR PDH loop to avoid suppressing the excitation line. We tried this today first with just one notch at 1069 Hz and then with an additional notch at 619 Hz and sent two simultaneous excitations.

Measurement and Analysis:

• We added notch filters with Q=10, depth=50dB, freq=619 Hz and 1069 Hz using foton in SUS-ETMX_LSC filter bank at FM10.
• We sent excitation signals with amplitudes 600cts and 1000 cts for 619 Hz and 1069 Hz signals respectively.
• We measured time series data of C1:SUS-ITMX_LSC_OUT_DQ and C1:ALS-BEATX_FINE_PHASE_OUT_HZ_DQ for 60s.
• Then, spectrum of both signals is measured with Hanning window using scipy.welch function with scaling set to  'spectrum', binwidth=1Hz.
• The beatnote signal was converted into length units by multiplying it by 1064nm * 37.79m / c.
• The ratio of the two spectrums at teh excitation frequency multiplies by excitation frequency squared gives us teh calibration constant in units of nm Hz^2/cts.
• At 619 Hz, we got nm/cts
• At 1069 Hz, we got nm/cts.
• The calibration factor in use is from  nm/cts from 13984.
• So, the calibration factor from this methos is about 23% smaller than measured using freeswinging MICH in 13984.
• One possiblity is that our notch filter is not as effective in avoiding suppresion of excitation.
  • We tried increasing the notch filter depths to 100 dB but got the same result within 2%.
  • We tried changing the position of notch filters. We put them in POX filter banks. Again the result did not change more than 2%.
• The open loop gain of green PDH at 619 Hz and 1069 Hz must be large enough for our assumption of green laser perfectly following length motion to be true. The UGF of green laser is near 11 kHz.
• The discrepancy could be due to outdated freeswinging MICH measurement that was done 3 years ago. Maybe we should learn how to do the ITMX calibration using this method and compare our own two measurements.

Plot description:

• We picked up three 10 min times belonging to the three different configurations:
  • 'Old Settings': IMC Suspension settings before Paco and I changed anything. Data taken from Apr 26, 2021, 00:30:42 PDT (GPS 1303457460).
  • 'New Settings': New input matrices uploaded on April 28th, along with F2A filters and AC coil balancing gains (see 16091). Data taken from May 01, 2021, 00:30:42 PDT (GPS 1303889460).
  • 'New settings with new gains' Above and new suspension damping gains uploaded on May5th, 2021 (see 16120). Data taken from May 07, 2021, 03:10:42 PDT (GPS 1304417460).
• Attachment 1  shows the RMS seismic noise along X direction between 1 Hz and 3 Hz picked from C1:PEM-RMS_BS_X_1_3 during the three time durations chosen. This plot is to establish that RMS noise levels were similar and mostly constant. Page 2 shows the mean ampltidue spectral density of seismic noise in x-direction over the 3 durations.
• Attachment 2 shows the transfer function estimate of seismic noise to MC_F during the three durations. Page 1 shows ratio of ASDs taken with median averaging while page 2 shows the same for mean averaging.
• Attachment 3 shows the transfer function estimate of seismic noise to MC_TRANS_PIT during the three durations. Page 1 shows ratio of ASDs taken with median averaging while page 2 shows the same for mean averaging.
• Attachment 4 shows the transfer function estimate of seismic noise to MC_TRANS_YAW during the three durations. Page 1 shows ratio of ASDs taken with median averaging while page 2 shows the same for mean averaging.

Inferences:

• From Attachment 2 Page 1:
  • We see that 'old settings' caused the least coupling of seismic noise to MC_F signal in most of the low frequency band except between 1.5 to 3 Hz where the 'new settings' were slightly better.
  • 'new settings' also show less coupling in 4 Hz to 6 Hz band, but at these frequencies, seismix noise is filtered out by suspension, so this could be just coincidental and is not really a sign of better configuration.
  • There is excess noise coupling seen with 'new settings' between 0.4 Hz and 1.5 Hz. We're not sure why this coupling increased.
  • 'new settings with new gains' show the most coupling in most of the frequency band. Clearly, the increased suspension damping gains did not behaved well with rest of the system.
• From Attachment 3 Page 1:
  • Coupling to MC_TRANS_PIT error signal is reduced for 'new settings' in almost all of the frequency band in comparison to the 'old settings'.
  • 'new settings with new gains' did even better below 1 Hz but had excess noise in 1 Hz to 6 Hz band. Again increased suspension damping gains did not help much.
  • But low coupling to PIT error for 'new settings' suggest that our decoupling efforts in matrix diagonalization, F2A filters and ac coil balancing worked to some extent.
• From Attachment 4 Page 1:
  • 'new settings' and 'old settings' have the same coupling of seismic noise to MC_TRANS_YAW in all of the frequency band. This is in-line witht eh fact that we found very little POS to YAW couping in our analysis before and there was little to no change for these settings.
  • 'new settings with new gains' did better below 1 Hz but here too there was excess coupling between 1 Hz to 9 Hz.
• Page 1 vs Page 2:
  • Mean and median should be same if the data sample was large enough and noise was stationary. A difference between the two suggests existence of outliers in the data set and median provides a better central estimate in such case.
  • MC_F: Mean and median are same below 4 hz. There are high frequency outliers above 4 Hz in 'new settings with new gains' and 'old settings' data sets, maybe due to transient higher free running laser frequency noise. But since, suspension settigns affect below 1 Hz mostly, the data sets chosen are stationary enough for us.
  • MC_TRANS_PIT: Mean ratio is lower for 'new settings' and 'old settings' in 0.3 hz to 0.8 Hz band. Same case above 4 Hz as listed above.
  • MC_TRANS_YAW:  Same as above.
• Conclusion 1:  The 'new settings with new gains' cause more coupling to seismic noise, probably due to low phase margin in control loops. We should revert back the suspension damping gains.
• Conclusion 2: The 'new settings' work as expected and can be kept when WFS loops are optimized further.
• Conjecture: From our experience over last 2 weeks, locking the arms to the main laser with 'new settings with new gains' introduces noise in the arm length large enough that the Xend green laser does not remain locked to the arm for longer than tens of seconds. So this is definitely not a configuration in which we can carry out other measurements and experiments in the interferometer.

Following the conclusion, we are reverting the suspension gains to old values, i.e.

While the F2A filters, AC coil gains and input matrices are changed to as mentioned in 16066 and 16072.

The changes can be reverted all the way back to old settings (before Paco and I changed anything in the IMC suspensions) by running python scripts/SUS/general/20210602_NewIMCOldGains/restoreOldConfigIMC.py on allegra. The new settings can be uploaded back by running python scripts/SUS/general/20210602_NewIMCOldGains/uploadNewConfigIMC.py on allegra.

Change time:

Unix Time = 1622676038

GPS Time = 1306711256

I fixed the PSL shutter button on Shutters summary page C1IOO_Mech_Shutter.adl. Now PSL switch changes C1:PSL-PSL_ShutterRqst channel. Earlier it was C1:AUX-PSL_ShutterRqst which doesn't do anything.

We found Mon7 in control room dead today afternoon. It's front power on green light is not lighting up. All other monitors are working as normal.

This monitor was used for looking at IMC camera analog feed. It is one of the most important monitors for us, so we should replace it with a different monitor.

Yehonathan and Paco disconnected the monitor and brought it down. We put it under the back table if anyone wants to fix it. Paco has ordered a BNC to VGA/HDMI converter to put in any normal monitor up there. It will happen this Wednesday. Meanwhile, I have changed the MON4 assignment from POP to Quad2 to be used for IMC.

We attempted to simulate "oscillator based realtime calibration noise monitoring" in offline analysis with python. This helped us in finding about a factor of sqrt(2) that we were missing earlier in 16171. we measured C1:ALS-BEATX_FINE_PHASE_OUT_HZ_DQ when X-ARM was locked to main laser and Xend green laser was locked to XARM. An excitation signal of amplitude 600 was setn at 619 hz at C1:ITMX_LSC_EXC.

Signal analysis flow:

• The C1:ALS-BEATX_FINE_PHASE_OUT_HZ_DQ is calibrated to give value of beatntoe frequency in Hz. But we are interested in the fluctuations of this value at the excitation frequency. So the beatnote signal is first high passed with 50 hz cut-off. This value can be reduced a lot more in realtime system. We only took 60s of data and had to remove first 2 seconds for removing transients so we didn't reduce this cut-off further.
• The I and Q demodulated beatntoe signal is combined to get a complex beatnote signal amplitude at excitation frequency.
• This signal is divided by cts amplitude of excitation and multiplied by square of excitation frequency to get calibration factor for ITMX in units of nm/cts/Hz^2.
• The noise spectrum of absolute value of  the calibration factor is plotted in attachment 1, along with its RMS. The calibration factor was detrended linearly so the the DC value was removed before taking the spectrum.
• So Attachment 1 is the spectrum of noise in calibration factor when measured with this method. The shaded region is 15.865% - 84.135% percentile region around the solid median curves.

We got a value of .  The calibration factor in use is from  nm/cts from 13984.

Next steps could be to budget this noise while we setup some way of having this calibration factor generated in realitime using oscillators on a FE model. Calibrating actuation of a single optic in a single arm is easy, so this is a good test setup for getting a noise budget of this calibration method.

We measured the Xend green laser PDH Open loop transfer function by following method:

• We first measured the feedback transfer function 'K' directly.
  • See attachment 2 for this measurement. We measured Out2/exc here.
• Then, we closed the loop as shown in attachment 1with SR560 as a summing juntion at error point.
  • We injected excitation through B channel in SR560 and measured transfer function Out1/Out2.
  • This measurement should give us by loop alegbra.
• Then we multiplied the two transfer function measurements to get open loop transfer function.

Result:

• Our measurement gives the same UGF of 10kHz and phase margin of 53.5 degrees as reported in 13238.
• The shape of measurement also follows 1/f above 10 Hz atleast.
• Our measurement might not be correct below 10 Hz but we did not see any saturation or loss of lock in 1Hz to 10 Hz measurement.
• This OLTF is different from the modelled OLTF here even though the UGF matches.
• The feedback gain is supposed to roll-off faster than 1/f in 30Hz to 1kHz region but it does not seem to in our measurement.
• This suggests that the actual uPDH box is shaping the loop different from what schematic suggests. This might mean that the gain is much lower in the low frequency region than we would like it to be.
• We will investigate the reason of difference between model and measurement unless someone has a better explaination for the descripancy.

We did a quick check to make sure there is no saturation in the C1:SUS-ITMX_LSC_EXC analog path. For this, we looked at the SOS driver output monitors from the 1X4 chassis near MC2 on a scope. We found that even with 600 x 10 = 6000 counts of our 619 Hz excitation these outputs in particular are not saturating (highest mon signal was UL coil with 5.2 Vpp). In comparison, the calibration trials we have done before had 600 counts of amplitude, so we can safely increase our oscillator strength by that much

Things that remain to be investigated -->

• What is the actual saturation level?
• Two-tone intermodulation?

Attachment 1 shows the closed loop of Xend Green laser Arm PDH lock loop. Free running laser noise gets injected at laser head after the PZT actuation as . The PDH error signal at output of miser is fed to a gain 1 SR560 used as summing junction here. Used in 'A-B mode', the B port is used for sending in excitation where .

We have access to three ports for measurement, marked at output of mixer, at output of SR560, and at PZT out monitor port in uPDH box. From loop algebra, we get following:

, where is the open loop transfer function of the loop.

So measurement of can be done in following two ways (not a complete set):

1. , if excitation amplitude is large enough such that over all frequencies.
   • In this method however, note that SR785 would be taking ratio of unsuppresed excitation at with suppressed excitation at
   • If the closed loop gain (suppression) is too much, the excitation signal might drop below noise floor of SR785 while measuring .
   • This would then appear as a flat response in the transfer function.
   • This happened with us when we tried to measure this transfer function using this method. Below few hundered Hz, the measurement will become flat at around 40 dB.
   • Increasing the excitation amplitude where suppression is large should ideally work. We even tried to use Auto level reference option in SR785.
   • But the PDH loop gets unlocked as soon as we put exciation above 35 mV at this point in this loop.
2. , if excitation amplitude is large enough such that over all frequencies.
   • In this method, channel 1 (denominator) on SR785 would remain high in amplitude throughout the measurement avoiding the above issue of suppression below noise floor.
   • We can easily measure the feedback transfer funciton with the loop open. Then multiplying the two measurements should give us estimate of open loop transfer function.
   • This is waht we did in 16194. But we still could not increase the excitation amplitude beyond 35 mV at injection point and got a noisy measurement.
   • We checked yesterday coherence of excitation signal with the three measurment points and it was 1 throughout the frequency region of measurement for excitation amplitudes above 20 mV.
   • So as of now, we are not sure why our signal to noise was so poor in lower frequency measurement.

Stephen and I discussed the in-vacuum OMC wiring.

- One of the OMCs has already been completed. (Blue)
- The other OMC is still being built. It means that these cables need to be built. (Pink)
- However, the cables for the former OMC should also be replaced because the cable harness needs to be replaced from the metal one to the PEEK one.
- The replacement of the harness can be done by releasing the Glenair Mighty Mouse connectors from the harness. (This probably requires a special tool)
- The link to the harness photo is here: https://photos.app.goo.gl/3XsUKaDePbxbmWdY7

- We want to combine the signals for the two OMCs into three DB25s. (Green)
- These cables are custom and need to be designed.

- The three standard aLIGO-style cables are going to be used. (Yellow)

- The cable stand here should be the aLIGO style.

Attachment 1 shows the case when excitation is sent at control point i.e. the PZT output. As before, free running laser noise  in units of Hz/rtHz is added after the actuator and I've also shown shot noise being added just before the detector.

Again, we have a access to three output points for measurement. right at the output of mixer (the PDH error signal), the feedback signal to be applied by uPDH box (PZT Mon) and the output of the summing box SR560.

Doing loop algebra as before, we get:

So measurement of can be done by

• For frequencies, where is large enough, to have an SNR of 100, we need that ratio of to integrated noise is 100.
• Assuming you are averaging for 'm' number of cycles in your swept sine measurement, time of integration for the noise signal would be where f is the frequency point of the seeping sine wave.
  • This means, the amplitude of integrated laser frequency noise at either or would be
  • Therefore, signal to laser free running noise ratio at f would be .
  • This means to keep a constant SNR of S, we need to shape the excitation amplitude as
  • Putting in numbers for X end Green PDH loop, laser free-running frequency noise ASD is 1e4/f Hz/rtHz, laser PZT actuation is 1MHz/V, then for 10 integration cycles and SNR of 100, we get:
• Assuming you are averaging for a constant time  in swept sine measurement, then the amplitude of integrated laser free noise would be
  • In this case, signal to laser free-running noise ratio at f would be
  • This means to keep a constant SNR of S, we need to shape the excitation amplitude as
  • Again putting in numbers as above and integration time of 1s, we need an excitation amplitude shape

This means at 100 Hz, with 10 integration cycles, we should have needed only 3 mV of excitation signal to get an SNR of 100. However, we have been unable to get good measurements with even 25 mV of excitation. We tried increasing the cycles, that did not work either.

This post is to summarize this analysis. We need more tests to get any conclusions.

We replaced the Mon 7 with an LCD monitor from back bench. It is fed the analog signal from BNC converted into VGS with a converter box that Paco bought. We can replace this monitor with another monitor if it is required on the back bench. For now, we definitely need a monitor to show IMC camera's up there.

We did the measurement of OLTF for Xend green laser PDH loop with excitation added at control point using a SR560 as shown in attachment 1 of 16202. We also measured coherence in our measurement, see attachment 1.

Measurement details:

• We took the measurement as per 16202.
• We did measurement in two pieces. First in High frequency region, from 1 kHz to 100 kHz.
  • In this setup, the excitation amplitude was kept constant to 5 mV.
  • In this region, the OLTF is small enough that signal to noise ratio is maintained in (SR560 sum output, measured on CH1). The coherence can be seen to be constant 1 throughout for CH1 in this region.
  • But for (PZT Mon, measured on CH2), the low OLTF actually starts damping both signal and noise and to elevate it above SR785 noise floor, we had a high pass (z:0Hz, p:100kHz, k:1000) SR560 amplifying before measurement (see attachment 2). This amplification has been corrected in Attachment 1. This allowed us to improve the coherence on CH2 to above 0.5 mostly.
• Second region is from 3 Hz to 1 kHz.
  • In this setup, the excitation was shaped with a low pass (p: 1Hz, k:5) SR560 filter with SR785 source amplitude as 1V.
  • We took 40 averaging cycles in this measurement to improve the coherence further.
  • In this freqeuency region, is mostly coherent as we shaped the excitation as  and due to constant cycle number averaging, the integrated noise goes as (see 16202 for math).
  • We still lost coherence in (CH1) for frequencyes below 100 Hz. the reason is that the excitation is suppressed by OLTF while the noise is not for this channel. So the shaping of excitation only helps fight against the suppression of OLTF somewhat and not against the noise.
    
  • We need shaping for this purpose but we were loosing lock with that shaping so we shifted back to shaping and captured whatever we could.
  • It is clear that the noise takes over below 100 Hz and coherence in CH1 is lost there.

Inferences:

• Yes, the OLTF does not look how it should look but:
• The green region in attachment 1 shows the data points where coherence on both CH1 and CH2 was higher than 0.75.  So the saturation measured below 1 kHz, particularly in 100 Hz to 500 Hz (where coherence on both channels is almost 1) is real.
• This brings the question, what is saturating. As has been suggested before, our excitation signal is probably saturating some internal stage in the uPDH box. We need to investigate this next.
  • It is however very non-intuitive to why this saturation is so non-uniform (zig-zaggy) in both magnitude and phase.
  • In past experiences, whenever I saw somehting saturating, it would cause a flat top response in transfer function.
• Another interesting thing to note is the reduced UGF in this measurement.
• UGF is about 40-45 kHz. This we believe is due to reduced mode matching of the green light to the XARM when temperature of the end increases too much. We took the measurement at 6 pm and Koji posted the Xend's temperature to be 30 C at 7 pm in 16206. It certainly becomes harder to lock at hot temperatures, probably due to reduced phase margin and loop gain.

I propose we set up a temperature sensor network as described in attachment 1.

Here there are two types of units:

• BASE-GATEWAY
  • Holds the processor to talk to the network through Modbus TCP/IP protocol.
  • This unit itself has a temperature sensor in it. It is powered by a power adaptor or PoE from the switch.
  • Each base unit can have at max 2 extended temperature probes ENV-TEMP.
• ENV-TEMP
  • This is just a temperature probe with no other capabilities.
  • It is powered via PoE from the BASE-GATEWAY unit.

Proposal is

• to put 2 ENV-TEMP sensors (#1 and #2) along the Y-arm at the end and midway. These are powered and read through a BASE-GATEWAY (#A) at the vertex. The BASE-GATEWAY (#A) will serve as temperature sensor for the vertex.
• We put one ENV-TEMP(#3) at the X-end powered and read through by another BASE-GATEWAY (#B) at the midpoint of X-arm.
• Both BASE-GATEWAY are connected by ethernet cables to the network switch. That's it.

These sensors can be configured over network by going to their assigned IP addresses. I'm not sure at the moment how to configure the dB files to get them to write on slow EPICS channels.

We will have an unused port on the BASE-GATEWAY (#B) which can be used to run another temperature sensor, maybe at an important rack, PSL table or somewhere else.

In future, if more sensors are required, there are expansion (network switch like) options for BASE-GATEWAY or daisy-chain options for the probes.

Edit Fri Jun 18 16:28:13 2021 :

See this [wiki page](https://wiki-40m.ligo.caltech.edu/Physical_Environment_Monitoring/Thermometers) for updated plan and final quote.

Today we went through LSC locking mechanics with Gautam and as a "Hello World" example, worked on locking michelson cavity.

MICH settings changed:

• Gautam at some point added 9 dB attenuation filters in MICH filter module in LSC to match the 9 dB pre-amplifier before digitization.
• This required changing teh trigger thresholds, C1:LSC-MICH_TRIG_THRESH_ON and C1:LSC-MICH_TRIG_THRESH_OFF.
• We looked at C1:LSC-AS55_Q_ERR_DQ and C1:LSC-ASDC_OUT_DQ on ndscope.
• The zero crossings in AS55_Q correspond to ASDC going to zero. We found the threshold values of ASDC by finding the linear region in zero crossing of AS55_Q.
• We changed the thresold values to UP: -0.3mW and DOWN -0.05mW. The thresholds were also changed in C1LSC_FM_TRIG.
• We also set FM2,3,6 and 8 to be triggered on threshold.

We characterized the loop OLTF, found the UGF to be 90 Hz and measured the noise at error and control points.

gautam: one aim of this work was to demonstrate that the "Lock Michelson (dark)" script call from the IFOconfigure screen worked - it did, reliably, after the setting changes mentioned above.

When both arms were locked, we found that ITMY optical lever was very off-center. This seems to have happened after the c1susaux rebooting we did in June 17th. I opened the ITMY table and realigned the OPLev beam to the center when the arm was locked. I repeated this process for BS, PRM and ETMY. I did PRM because I've known that we have been keeping its OpLev off. The reason was clear once I opened the table. The oplev reflection beam was hitting the PD box instead of the PD. After correcting, I was able to swithc on PRM opLev loops and saw normal functioning.

I worked in Yend station, trying to get the ETMY QPD to work properly. When I started, only one (quadrant #3) of the 4 quadrants were seeing any lights. By just changing the beam splitter that reflects some light off to the QPD, I was able to get some amount of light in quadrant #2. However, no amount of steering would show any light in any other quadrants.

The only reason I could think of is that the incoming beam gets partially clipped as it seems to be hitting the beam splitter near the top edge. So for this to work properly, a mirror upstream needs to be adjusted which would change the alignment of TRX photodiode. Without the light on TRX photodiode, there is no lock and there is no light. So one can't steer this beam without lossing lock.

I tried one trick, in which, I changed the YARM lock trigger to POY DC signal. I got it to work to get the lock going even when TRY was covered by a beam finder card. However, this lock was still bit finicky and would loose lock very frequently. It didn't seem worth it to potentially break the YARM locking system for ETMY QPD before running this by anyone and this late in evening. So I reset everything to how it was (except the beam splitter that reflects light to EMTY QPD. That now has equal ligth falling on quadrant #2 and #3.

The settings I temporarily changed were:

• C1:LSC-TRIG_MTRX_7_10 changed from 0 to -1 (uses POY DC as trigger)
• C1:LSC-TRIG_MTRX_7_13 changed from 1 to 0 (stops using TRY DC as trigger)
• C1:LSC-YARM_TRIG_THRESH_ON changed from 0.3 to -22
• C1:LSC-YARM_TRIG_THRESH_OFF changed from 0.1 to -23.6
• C1:LSC-YARM_FM_TRIG_THRESH_ON changed from 0.5 to -22
• C1:LSC-YARM_FM_TRIG_THRESH_OFF changed from 0.1 to -23.6

All these were reverted back to there previous values manually at the end.

Paco worked on alignign the beam splitter to get light on the ETMY QPD and was successful in centering it without any other changes in the settings.

This was a mistake. When arms are locked, PRM is misaligned by setting -800 offset in PIT dof of PRM. The oplev is set to function in normal state not this misalgined configuration. I undid my changes today by switching off the offset, realigning the oplev to center and then restoring the single arm locked state. The PRM OpLevs loops are off now.

We corrected the MICH locking snap file C1configure_MI.req and saved an updated C1configure_MI.snap. Now the 'Restore MICH' script in IFO_CONFIGURE>!MICH>Restore MICH works. The corrections included adding the correct rows of PD_DOF matrices to be at the right settings (use AS55 as error signal). The MICH_A_GAIN and MICH_B_GAIN needed to be saved as well.

We also were able to get to PRMI SB resonance. PRM was misalgined earlier from optimal position and after some manual aligning, we were able to get it to lock just by hitting IFO_CONFIGURE>!PRMI>Restore PRMI SB (3f).

We held the lab cleaning for the first time since the campus reopening (Attachment 1).
Now we can use some of the desks for the people to live! Thanks for the cooperation.
We relocated a lot of items into the lab.

• The entrance area was cleaned up. We believe that there is no 40m lab stuff left.
  • BHD BS optics was moved to the south optics cabinet. (Attachment 2)
  • DSUB feedthrough flanges were moved to the vacuum area (Attachment 3)
• Some instruments were moved into the lab.
  • The Zurich instrument box
  • KEPCO HV supplies
  • Matsusada HV supplies
• We moved the large pile of SUPERMICROs in the lab. They are around MC2 while the PPE boxes there were moved behind the tube around MC2 area. (Attachment 4)
• We have moved PPE boxes behind the beam tube on XARM behind the SUPERMICRO computer boxes. (Attachment 7)
• ISC/WFS left over components were moved to the pile of the BHD electronics.
  • Front panels (Attachment 5)
  • Components in the boxes (Attachment 6)

We still want to make some more cleaning:

- Electronics workbenches
- Stray setup (cart/wagon in the lab)
- Some leftover on the desks
- Instruments scattered all over the lab
- Ewaste removal

Last night Gautam walked us through the algorithm used to lock PRFPMI. We tried it several times with the PSL HEPA filter off between 10:00 pm July 7th to 1:00 am July 8th. None of our attempts were successful. In between, we tried to do the locking with old IMC settings as well, but it did not change the result for us. In most attempts, the arms would start to resonate with PRMI with about 200 times the power than without power recycling while the arms are still controlled by ALS beatnote. The handover of lock controls "CARM+DARM locked to ALS beatnote" to "Main laser + IMC locked to the CARM+DARM" would always fail. More specifically, we were seeing that as soon as we hand over the DC control of CARM from ALS beatnote to IR by feeding back to MC2, the lock would inevitably fail before the rest of the high-frequency control can be transferred over.

Nonetheless, Paco and I got a good demo of how to do PRFPMI locking if the need appears. With more practice and attempts, we should be able to achieve the lock at some point in the future. The issues in handover could be due to any of the following:

• Although it seems like ALS beatnote fed control of arms keep them within the CARM IR linewidth as we see the IR resonating, there still could be some excess noise that needs to be dealt with.
• Gautam conjectures, that the presence of high power in the arms connects the ITMs and the ETMs with an optical spring changing the transfer function of the pendula. This in turn changes the phase margin and possibly makes the CARM loop in IR PRFPMI unstable.
• We should also investigate the loop transfer functions near the handover point for the ALS beatnote loop and the IR CARM loop and calculate the crossover frequency and gain/phase margins there.

More insights or suggestions are welcome.

Note; An earthquake came around lunch time and tripped all watchdogs. Most suspensions were recovered without issues, but ITMX appeared to be stuck. We tried the shaking procedure, but after this we couldn't restore the XARM lock. From alignment, we tried optimizing the TRX but we only got up to ~0.5 and ASS wouldn't work as usual. In the end the issue was that we had forgotten to enable the LL coil output so after we did this, we managed to recover the XARM.

I did this analysis again by just doing demodulation go 5s time segments of the 60s excitation signal. The major difference is that I was not summing up the sine-cosine multiplied signals, so the error associated was a lot more. If I simply multpy the whole beatnote signal with digital LO created at excitation frequency, divide it up in 12 segments of 5 s each, sum them up individually, then take the mean and standard deviation, I get the answer as:
as opposed to that was calculated using MICH signal earlier by gautum in 13984.

Attachment 1 shows the scatter plot for the complex calibration factors found for the 12 segments.

My aim in the previous post was however to get a time series of the complex calibration factor from which I can take a noise spectral density measurement of the calibration. I'll still look into how I can do that. I'll have to add a low pass filter to integrate the signal. Then the noise spectrum up to the low pass pole frequency would be available. But what would this noise spectrum really mean? I still have to think a bit about it. I'll put another post soon.

[paco]

At 09:34 PST I noted a glitch in the controls room as the machines went down except for c1ioo. Briefly, the video feeds disappeared from the screens, though the screens themselves didn't lose power. At first I though this was some kind of power glitch, but upon checking with Jordan, it most likely was related to some system crash. Coming back to the controls room, I could see the MC reflection beam swinging, but unfortunately all the FE models came down. I noticed that the DAQ status channels were blank.

I ssh into c1ioo no problem and ran "rtcds stop c1ioo c1als c1omc", then "rtcds restart c1x03" to do a soft restart. This worked, but the DAQ status was still blank. I then tried to ssh into c1sus and c1lsc without success, similarly c1iscex and c1iscey were unreachable. I went and did a hard restart on c1iscex by switching it off, then its extension chassis, then unplugging the power cords, then inverting these steps, and could ssh into it from rossa. I ran "rtcds start c1x01" and saw the same blank DAQ status. I noticed the elog was also down... so nodus was also affected?

[paco, anchal]

Anchal got on zoom to offer some assistance. We discovered that the fb1 and nodus were subject to some kind of system reboot at precisely 09:34. The "systemctl --failed" command on fb1 displayed both the daqd_dc.service and rc-local.service as loaded but failed (inactive). Is it a good idea to try and reboot the fb1 machine? ... Anchal was able to bring elog back up from nodus (ergo, this post).

[paco]

Although it probably needs the DAQ service from the fb1 machine to be up and running, I tried running the scripts/cds/rebootC1LSC.sh script. This didn't work. I tried running sudo systemctl restart daqd_dc from the fb1 machine without success. Running systemctl reset-failed "worked" for daqd_dc and rc-local services on fb1 in the sense that they were no longer output from systemctl --failed, but they remained inactive (dead) when running systemctl status on them. Following from  15303   I succeeded in restarting the daqd services. Turned out I needed to manually start the open-mx and mx services in fb1. I rerun the restartC1LSC script without success. The script fails because some machines need to be rebooted by hand.
 

Used diaggui to get OLTF in preparation for optimal system identification / calibration. The excitation was injected at the control point of the XARM loop C1:LSC-XARM_EXC. Attachment 1 shows the TF (red scatter) taken from 35 Hz to 2.3 kHz with 201 points. The swept sine excitation had an envelope amplitude of 50 counts at 35 Hz, 0.2 counts at 100 Hz, and 0.2 at 200 Hz. In purple continous line, the model for the OLTF using all the digital control filters as well as a simple 1 degree of freedom plant (single pole at 0.99 Hz) is overlaid. Note the disagreement of the OLTF "model" at higher frequencies which we may be able to improve upon using vector fitting.

Attachment 2 shows the coherence (part of this initial measurement was to identify an appropriately large frequency range where the coherence is good before we script it).

this model doesn't seem to include the analog AA, analog AI, digital AA, digital AI, or data transfer delays in the system. I think if you include those you will get more accuracy at high frequencies. Probably Anchal has those included in his DARM loop model?

- Sat amp mod and test: on going (Tega)
- Coil driver mod and test: on going (Tega)

- Acromag: almost ready (Yehonathan)

- IDC10-DB9 cable / D2100641 / IDC10F for ribbon in hand / Dsub9M ribbon brought from Downs / QTY 2 for two ends -> Made 2 (stored in the DSUB connector plastic box)
- IDC40-DB9 cable / D2100640 / IDC40F for ribbon in hand / DB9F solder brought from Downs  / QTY 4 for two ends -> Made 4 0.5m cables (stored in the DSUB connector plastic box)

- DB15-DB9 reducer cable / ETMX2+ETMY2+VERTEX16+NewSOS14 = 34 / to be ordered

- End DAC signal adapter with Dewhitening (with DIFF/SE converter) / to be designed & built
- End ADC adapter (with SE/DIFF converter) / to be designed & built

MISC Ordering

• 3.5 x Sat Amp Adapter made (order more DSUB25 conns)
  • -> Gave 2 to Tega, 1.5 in the DSUB box
  • 5747842-4 A32100-ND -> ‎5747842-3‎ A32099-ND‎ Qty40
  • 5747846-3 A32125-ND -> ‎747846-3‎ A23311-ND‎ Qty40
• Tega's sat amp components
  • 499Ω P499BCCT-ND 78 -> Backorder -> ‎RG32P499BCT-ND‎ Qty 100
  • 4.99KΩ TNPW12064K99BEEA 56 -> Qty 100
  • 75Ω YAG5096CT-ND 180 -> Qty 200
  • 1.82KΩ P18391CT-ND 103 -> Qty 120
  • 68 nF P10965-ND 209
• Order more DB9s for Tega's sat amp adapter 4 units (look at the AA IO BOM) 
  • 4x 8x 5747840-4 DB9M PCB A32092-ND -> 6-747840-9‎ A123182-ND‎ Qty 35
  • 4x 5x 5747844-4 A32117-ND -> Qty 25
  • 4x 5x DB9M ribbon MMR09K-ND -> 8209-8000‎ 8209-8000-ND‎ Qty 25
  • 4x 5x 5746861-4 DB9F ribbon 5746861-4-ND -> 400F0-09-1-00 ‎LFR09H-ND‎ Qty 35
• Order 18bit DAC AI -> 16bit DAC AI components 4 units
  • 4x 4x 5747150-8 DSUB9F PCB A34072-ND -> ‎D09S24A4PX00LF‎609-6357-ND‎ Qty 20
  • 4x 1x 787082-7 CONN D-TYPE RCPT 68POS R/A SLDR (SCSI Female) A3321-ND -> ‎5787082-7‎ A31814-ND‎ Qty 5
  • 4x 1x 22-23-2021 Connector Header Through Hole 2 position 0.100" (2.54mm)    WM4200-ND -> Qty5

[paco, koji, tega, ian]

Today in the morning the name server / network file system running in chiara failed. This resulted in donatella/pianosa/rossa shell prompts to hang forever. It also made sitemap crash and even dropping into a bash shell and just listing files from some directory in the file system froze the computer. Remote ssh sessions on nodus also had the same symptoms.

A little after 1 pm, we started debugging this issue with help from Koji. He suggested we hook a monitor, keyboard, and mouse onto chiara as it should still work locally even if something with the NFS (network file system) failed. We did this and then we tried for a while to unmount the /dev/sdc1/ from /home/cds/ (main file system) and mount /dev/sdb1/ from /media/40mBackup (backup copy) such that they swap places. We had no trouble unmounting the backup drive, but only succeeded in unmounting the main drive with the "lazy" unmount, or running "umount -l". Running "df" we could see that the disk space was 100% used, with only ~ 1 GB of free space which may have been the cause for the issue. After swapping these disks by editing the /etc/fstab file to implement the aforementioned swapping, we rebooted chiara and we recovered the shell prompts in all workstations, sitemap, etc... due to the backup drive mounting. We then started investigating what caused the main drive to fill up that quickly, and noted that weirdly now the capacity was at 85% or about 500GB less than before (after reboot and remount), so some large file was probably dumped into chiara that froze the NFS causing the issue.

At this point we tried opening the PSL shutter to recover the IMC. The shutter would not open and we suspected the vacuum interlock was still tripped... and indeed there was an uncleared error in the VAC screen. So with Koji's guidance we walked to the c1vac near the HV station and did the following at ~ 5:13 PM -->

1. Open V4; apart from a brief pressure spike in PTP2, everything looked ok so we proceeded to
2. Open V1; P2 spiked briefly and then started to drop. Then, Koji suggested that we could
3. Close V4; but we saw P2 increasing by a factor of~ 10 in a few seconds, so we
4. Reopened V4;

We made sure that P1a (main vacuum pressure) was dropping and before continuing we decided to look back to see what the nominal vacuum state was that we should try to restore.

We are currently searching the two systems for diffrences to see if we can narrow down the culprit of the failure.

Attachment 1:
We are pumping the main volume with TP2. Once P1a reached the pressure ~2.2mtorr, we could open the PSL shutter. The TP2 voltage went up once but came down to ~20V. It's close to nominal now.
We wondered if we should use TP3 or not. I checked the vacuum pressure trends and found that the annulus pressures were going up. So we decided to open the annulus valves.

Attachment 2:
The current vacuum status is as shown in the MEDM screenshot.

There is no trend data of the valve status (sad)

[tega, paco]

We found the files that took excess space in the chiara filesystem (see Attachment 1). They were error files from the summary pages that were ~ 50 GB in size or so located under /home/cds/caltech/users/public_html/detcharsummary/logs/. We manually removed them and then copied the rest of the summary page contents into the main file system drive (this is to preserve the information backup before it gets deleted by the cron job at the end of today) and checked carefully to identify the actual issue for why these files were as large in the first place.

We then copied the /detcharsummary directory from /media/40mBackup into /home/cds to match the two disks.

Also deleted the ~50GB error files from ldas to prevent rsync from copying them to nodus again. With the new update to GWsumm, there are new error messages that initially didn't seem to affect the summary pages functionality, but in the extreme case can populated the error files the repeated warnings on the form "Loading: FrSerData", "Loading: FrSerData::n4294967295", "Loading: FrSummary","Loading: FrSerDataLoading: FrSerData" and many more combinations until we get file sizes of the order of ~50GB. So I have updated the checkstatus script to parse the error files and strip out the majority of these error messages. Work is ongoing to get them all.

In light of these large files generation, I decided to look in the summary pages folder to see if there are other large files that we need to keep track of and it turns there are indeed a collection of files in the archive folder that bloats the summary pages on ldas to ~1TB. Luckily these are not synced to nodus so no problem here. However, since the beginning of the year, the archive folders that hold data used for each day's computation have not been cleared. We have a script for doing this but it has not been run for a while now and it only delete archive files for a specific month which is hardcoded to two months from the date the file is run. I have modified the code to allow archive deletion for a range of months so we can clear data from Jan to July. 

[paco]

This morning, I spent some time restoring the jupyter notebook server running in allegra. This server was first set up by Anchal to be able to use the latest nds python API tools which is handy for the calibration stuff. The process to restore the environment was to run "source ~/bashrc.d/*" to restore some of the aliases, variables, paths, etc... that made the nds server work. I then ran ssh -N -f -L localhost:8888:localhost:8888 controls@allegra from pianosa and carry on with the experiment.

[paco, hang, tega]

We started a notebook under /users/paco/20210906_XARM_Cal/XARM_Cal.ipynb on which the first part was doing the following;

• Set up list of excitations for C1:LSC-XARM_EXC (for example three sine waveforms) using awg.py
• Make sure the arm is locked
• Read a reference time trace of the C1:LSC-XARM_IN2 channel for some duration
• Start excitations (one by one at the moment, ramptime ~ 3 seconds, same duration as above)
• Get data for C1:LSC-XARM_IN2 for an equal duration (raw data in Attachment #1)
• Generate the excitation sine and cosine waveforms using numpy and demodulate the raw timeseries using a 4th order lowpass filter with fc ~ 10 Hz
• Estimate the correct demod phase by computing arctan(Q / I) and rerunning the demodulation to dump the information into the I quadrature (Attachment #2).
• Plot the estimated ASD of all the quadratures (Attachment #3)

[paco, hang, tega]

Estimation of open loop gain:

• Grab data from the C1:LSC-XARM_IN1 and C1:LSC-XARM_IN2 test points
• Infer excitation from their differnce, i.e. C1:LSC-XARM_EXC = C1:LSC-XARM_IN2 - C1:LSC-XARM_IN1
• Compute the open loop gain as follows : G(f) = csd(EXC,IN1)/csd(EXC,IN2), where csd computes the cross spectra density of the input arguments
• For the uncertainty in G, dG, we repeat steps (1) to (3) with & without signal injection in the C1:LSC-XARM_EXC channel. In the absence of signal injection, the signal in C1:LSC-XARM_IN2 is of the form: Y_ref = Noise/(1-G), whereas with nonzero signal injection, the signal in C1:LSC-XARM_IN2 has the form: Y_cal = EXC/(1-G) + Noise/(1-G), so their ratio, Y_cal/Y_ref = EXC/Noise, gives the SNR, which we can then invert to give the uncertainty in our estimation of G, i.e dG = Y_ref/Y_cal.
• For the excitation at 53 Hz, our measurtement for the open loop gain comes out to about 5 dB whiich is consistent with previous measurement.
• We seem to have an SNR in excess of 100 at measurement time of 35 seconds and 1 count of amplitude which gives a relative uncertainty of G of 0.1%
• The analysis details are ongoing. Feedback is welcome.

[Koji, Stephen - updated 30 September]

Cable lengths task - in vacuum cabling for the green section (new, custom for 40m) and yellow section (per aLIGO, except likely with cheaper FEP ribbon cable material) from 40m/16198. These arethe myriad of cables extending from the in vacuum flange to the aLIGO-style on-table Cable Stand (think, for example, D1001347), then from the cable stand to the OMCs.

a) select a position for the cable stand.

 - Koji and I discussed and elected to place in the (-X, -Y) corner of the table (Northwest in the typical diagram) and near the table edge. This is adjacent to the intended exit flange for the last cable.

b) measure distances and cable routing approximations for cable bracket junctions

- Near OMC bracket to the cable stand, point to point = 17.2, routing estimate = 24.4.
- Far OMC bracket to the cable stand, point to point = 20.5, routing estimate = 32.2.

  - Recommendation = 48" for all green section cables (using one length for each OMC, with extra slack to account for routing variation).

c) (outdated - see item (b) and attachment 3) measure distances (point to point) and cable routing approximations for all items.

 +X OMC (long edge aligned with +Y beam axis) (overview image in Attachment 1)

- QPDs to the cable stand, point to point = 12, routing estimate = 20.
- DCPDs to the cable stand, point to point = 25, routing estimate = 32.
- PZTs to the cable stand, point to point = 21, routing estimate = 32.

+Y OMC (long edge aligned with +Y beam axis) (overview image in Attachment 1)

- QPDs to the cable stand, point to point = 16, routing estimate = 23.
- DCPDs to the cable stand, point to point = 26, routing estimate = 38.
- PZTs to the cable stand, point to point = 24, routing estimate = 33.

Cable stand to flange (Attachment 2) (specific image in Attachment 2)

- point to point = 35, routing estimate = 42

  - Recommendation = 120" for all yellow section cables, per Koji's preferences for zigzag cable routing on stack and coiling of slack.

Anchal mentioned it would be good to put more details about how I arrived at the values needed to configure the modbus drive for the temperature sensor, since this information is not in the manual and is hard to find on the internet, so here is a breakdown.

So the generic format is:

drvAsynIPPortConfigure("<TCP_PORT_NAME>","<UNIT_IP_ADDRESS>:502",0,0,1)
modbusInterposeConfig("<TCP_PORT_NAME>",0,5000,0)
drvModbusAsynConfigure("<PORT_NAME>","<TCP_PORT_NAME>",<slaveAddress>,<modbusFunction>,<modbusStartAddress>,<modbusLength>,<dataType>,<pollMsec>,<plcType>)

which in our case become:

drvAsynIPPortConfigure("c1pemxendtemp","192.168.113.240:502",0,0,1)
modbusInterposeConfig("c1pemxendtemp",0,5000,0)
drvModbusAsynConfigure("C1PEMXENDTEMP","c1pemxendtemp",0,4,199,2,0,1000,"ServerCheck")

As can be seen, the parameters of the first two functions "drvAsynIPPortConfigure" and "modbusInterposeConfig" are straight forward, so we restrict our discussion to the case of third function "drvModbusAsynConfigure". Well, after hours of trolling the internet, I was able to piece together a coherent picture of what needs doing and I have summarised them in the table below.

drvModbusAsynConfigure

Once the asyn IP or serial port driver has been created, and the modbusInterpose driver has been configured, a modbus port driver is created with the following command:

drvModbusAsynConfigure(portName,                # used by channel definitions in .db file to reference this unit)
                       tcpPortName,             # reference to portName created with drvAsynIPPortConfigure command
                       slaveAddress,            # 
                       modbusFunction,          # 
                       modbusStartAddress,      # 
                       modbusLength,            # length in dataType units
                       dataType,                # 
                       pollMsec,                # how frequently to request a value in [ms]
                       plcType);                #

Useful links

https://nodus.ligo.caltech.edu:8081/40m/16214

https://nodus.ligo.caltech.edu:8081/40m/16269

https://nodus.ligo.caltech.edu:8081/40m/16270

https://nodus.ligo.caltech.edu:8081/40m/16274

http://manuals.serverscheck.com/InfraSensing_Sensors_Platform.pdf

http://manuals.serverscheck.com/InfraSensing_Modbus_manualv5.pdf

https://community.serverscheck.com/discussion/comment/7419#Comment_7419

https://wiki-40m.ligo.caltech.edu/CDS/SlowControls

https://www.slac.stanford.edu/grp/ssrl/spear/epics/site/modbus/modbusDoc.html#Creating_a_modbus_port_driver

https://github.com/riptideio/pymodbus

https://en.wikipedia.org/wiki/Modbus

https://deltamotion.com/support/webhelp/rmctools/Communications/Ethernet/Supported_Protocols/Ethernet_Modbus_TCP.htm

For the past couple of days the 0.1 to 0.3 Hz RMS seismic noise along BS-X has increased. Attachment 1 shows the hour trend in the last ~ 10 days. We'll keep monitoring it, but one thing to note is how uncorrelated it seems to be from other frequency bands. The vertical axis in the plot is in um / s

Looks like this increase is correlated for BS/EX/EY. So it is likely to be real.

Comparison between 9/15 (UTC) (Attachment 1) and 9/10 (UTC) (Attachment 2)

Ordered compoenents are in.

- Made 36 more Sat Amp internal boards (Attachment 1). Now we can install the adapters to all the 19 sat amp units.

- Gave Tega the components for the sat amp adapter units. (Attachment 2)

- Gave Tega the componennts for the sat amp / coil driver modifications.

- Made 5 PCBs for the 16bit DAC AI rear panel interface (Attachment 3)

[yehonathan, paco, anchal]

We attempted to find any symptoms for actuation problems in the PRMI configuration when actuated through BS and PRM.

Our logic was to check angular (PIT and YAW) actuation transfer function in the 30 to 200 Hz range by injecting appropriately (f^2) enveloped excitations in the SUS-ASC EXC points and reading back using the SUS_OL (oplev) channels.

From the controls, we first restored the PRMI Carrier to bring the PRM and BS to their nominal alignment, then disabled the LSC output (we don't need PRMI to be locked), and then turned off the damping from the oplev control loops to avoid supressing the excitations.

We used diaggui to measure the 4 transfer functions magnitudes PRM_PIT, PRM_YAW, BS_PIT, BS_YAW, as shown below in Attachments #1 through #4. We used the Oplev calibrations to plot the magnitude of the TFs in units of urad / counts, and verified the nominal 1/f^2 scaling for all of them. The coherence was made as close to 1 as possible by adjusting the amplitude to 1000 counts, and is also shown below. A dip at 120 Hz is probably due to line noise. We are also assuming that the oplev QPDs have a relatively flat response over the frequency range below.

I suggest plotting all the traces in the plot so we can see their differences. Also remove the 1/f^2 slope so that we can see small differences. Since the optlev servos all have low pass filters around 15-20 Hz, its not necessary to turn off the optlev servos for this measurement.

I think that based on the coherence and the number of averages, you should also be able to use Bendat and Piersol so estimate the uncertainy as a function of frequency. And we want to see the comparison coil-by-coil, not in the DoF basis.

4 sweeps for BS and 4 sweeps for PRM.

This post serves as a summary and description of code to run to test the impacts of quantization noise on a state-space implementation of the suspension model.

Purpose: We want to use a state-space model in our suspension plant code. Before we can do this we want to test to see if the state-space model is prone to problems with quantization noise. We will compare two models one for a standard direct-ii filter and one with a state-space model and then compare the noise from both. 

Signal Generation:

First I built a basic signal generator that can produce a sine wave for a specified amount of time then can produce a zero signal for a specified amount of time. This will let the model ring up with the sine wave then decay away with the zero signal. This input signal is generated at a sample rate of 2^16 samples per second then stored in a numpy array. I later feed this back into both models and record their results.

State-space Model:

The code can be seen here

The state-space model takes in the list of excitation values and feeds them through a loop that calculates the next value in the output.

Given that the state-space model follows the form

     and   ,

the model has three parts the first equation, an integration, and the second equation.

1. The first equation takes the input x and the excitation u and generates the x dot vector shown on the left-hand side of the first state-space equation.
2. The second part must integrate x to obtain the x that is found in the next equation. This uses the velocity and acceleration to integrate to the next x that will be plugged into the second equation
3. The second equation in the state space representation takes the x vector we just calculated and then multiplies it with the sensing matrix C. we don't have a D matrix so this gives us the next output in our system

This system is the coded form of the block diagram of the state space representation shown in attachment 1

Direct-II Model:

The direct form 2 filter works in a much simpler way. because it involves no integration and follows the block diagram shown in Attachment 2, we can use a single difference equation to find the next output. However, the only complication that comes into play is that we also have to keep track of the w(n) seen in the middle of the block diagram. We use these two equations to calculate the output value

,  where w[n] is  

Bit length Control:

To control the bit length of each of the models I typecast all the inputs using np.float then the bit length that I want. This simulates the computer using only a specified bit length. I have to go through the code and force the code to use 128 bit by default. Currently, the default is 64 bit which so at the moment I am limited to 64 bit for highest bit length. I also need to go in and examine how numpy truncates floats to make sure it isn't doing anything unexpected.

Bode Plot: 

The bode plot at the bottom shows the transfer function for both the IIR model and the state-space model. I generated about 100 seconds of white noise then computed the transfer function as 

which is the cross-spectral density divided by the power spectral density. We can see that they match pretty closely at 64 bits. The IIR direct II model seems to have more noise on the surface but we are going to examine that in the next elog

I've updated the c1LSC simulink model to add the so-called UGF servos in the XARM and YARM single arm loops as well. These were earlier present in DARM, CARM, MICH and PRCL loops only. The UGF servo themselves serves a larger purpose but we won't be using that. What we have access to now is to add an oscillator in the single arm and get realtime demodulated signal before and after the addition of the oscillator. This would allow us to get the open loop transfer function and its uncertaintiy at particular frequencies (set by the oscillator) and would allow us to create a noise budget on the calibration error of these transfer functions.

The new model has been committed locally in the 40m/RTCDSmodels git repo. I do not have rights to push to the remote in git.ligo. The model builds, installs and starts correctly.

Here are some plots from analyzing the C1:LSC-XARM calibration. The experiment is done with the XARM (POX) locked, a single line is injected at C1:LSC-XARM_EXC at f0 with some amplitude determined empirically using diaggui and awggui tools. For the analysis detailed in this post, f0 = 19 Hz, amp = 1 count, and gain = 300 (anything larger in amplitude would break the lock, and anything lower in frequency would not show up because of loop supression). Clearly, from Attachment #3 below, the calibration line can be detected with SNR > 1.

We read the test point right after the excitation C1:LSC-XARM_IN2 which, in a simplified loop will carry the excitation suppressed by 1 - OLTF, the open loop transfer function. The line is on for 5 minutes, and then we read for another 5 minutes but with the excitation off to have a reference. Both the calibration and reference signal time series are shown in Attachment #1 (decimated by 8). The corresponding ASDs are shown in Attachment #2. Then, we demodulate at 19 Hz and a 30 Hz, 4th-order butterworth LPF, and get an I and Q timeseries (shown in Attachment #3). Even though they look similar, the Q is centered about 0.2 counts, while the I is centered about 0.0. From this time series, we can of course show the noise ASDs in Attachment #3.

The ASD uncertainty bands in the last plot are statistical estimates and depend on the number of segments used in estimating the PSD. A thing to note is that the noise features surrounding the signal ASD around f0 are translated into the ASD in the demodulated signals, but now around dc. I guess from Attachment #3 there is no difference in the noise spectra around the calibration line with and without the excitation. This is what I would have expected from a linear system. If there was a systematic contribution, I would expect it to show at very low frequencies.

I would expect to see some lower frequency effects. i.e. we should look at the timeseries of the demod with the excitation on and off.

I would guess tat the exc on should show us the variations in the optical gain below 3 Hz, whereas the exc off would not show it.

Maybe you should do some low pass filtering on the time series you have to see the ~DC effects? Also, reconsider your AA filter design: how do you quantitatively choose the cutoff frequency and stopband depth?

To reduce burden on c1lsc, I've shifted the added UGF block to to c1oaf model. c1lsc had to be modified to allow addition of an oscillator in the XARm and YARM control loops and take out test points before and after the addition to c1oaf through shared memory IPC to do realtime demodulation in c1oaf model.

The new models built and installed successfully and I've been able to recover both single arm locks after restarting the computers.

Now that we have a model of how the SS and IIR filters work we can get to the problem of how to measure the quantization noise in each of the systems. Den Martynov's thesis talks a little about this. from my understanding: He measured quantization noise by having two filters using two types of variables with different numbers of bits. He had one filter with many more bits than the second one. He fed the same input signal to both filters then recorded their outputs x_1 and x_2, where x_2 had the higher number of bits. He then took the difference x_1-x_2. Since the CDS system uses double format, he assumes that quantization noise scales with mantissa length. He can therefore extrapolate the quantization noise for any mantissa length.

Here is the Code that follows the following procedure (as of today at least)

This problem is a little harder than I had originally thought. I took Rana's advice and asked Aaron about how he had tackled a similar problem. We came up with a procedure explained below (though any mistakes are my own):

1. Feed different white noise data into three of the same filter this should yield the following equation: , where  is the power spectrum of the output for the ith filter,   is the noise filtered through an "ideal" filter with no quantization noise, and   is the power spectrum of the quantization noise. Since we are feeding random noise into the input the power of the quantization noise should be the same for all three of our runs.
2. Next, we have our three outputs:  ,  , and   that follow the equations: 

​

From these three equations, we calculate the three quantities: , , and  which are calculated by:

from these quantities, we can calculate three values: , , and  since these are just estimates we are using a bar on top. These are calculated using:

using these estimates we can then estimate    using the formula:

we can average the three estimates for    to come up with one estimate.

This procedure should be able to give us a good estimate of the quantization noise. However, in the graph shown in the attachments below show that the noise follows the transfer function of the model to begin with. I would not expect this to be true so I believe that there is an error in the above procedure or in my code that I am working on finding. I may have to rework this three-corner hat approach. I may have a mistake in my code that I will have to go through.

I would expect the quantization noise to be flatter and not follow the shape of the transfer function of the model. Instead, we have what looks like just the result of random noise being filtered through the model. 

Next steps:

The first real step is being able to quantify the quantization noise but after I fix the issues in my code I will be able to start liking at optimal model design for both the state-space model and the direct form II model. I have been looking through the book "Quantization noise" by Bernard Widrow and Istvan Kollar which offers some good insights on how to minimize quantization noise. 

[Anchal, Paco]

We had a second go at this with an increased number of averages (from 10 to 100) and higher excitation amplitudes (from 1000 to 10000). We did this to try to reduce the relative uncertainty a-la-Bendat-and-Pearsol

where are the coherence and number of averages respectively. Before, this estimate had given us a ~30% relative uncertainty and now it has been improved to ~ 10%. The re-measured TFs are in Attachment #1. We did 4 sweeps for each optic (BS, PRM) and removed the 1/f^2 slope for clarity. We note a factor of ~ 4 difference in the magnitude of the coil to angle TFs from BS to PRM (the actuation strength in BS is smaller).

For future reference:

With complex G, we get complex error in G using the formula above. To get uncertainity in magnitude and phase from real-imaginary uncertainties, we do following (assuming the noise in real and imaginary parts of the measured transfer function are incoherent with each other):

I have not been able to figure out a way to make the system that Aaron and I talked about. I'm not even sure it is possible to pull the information out of the information I have in this way. Even the book uses a comparison to a high precision filter as a way to calculate the quantization noise:

"Quantization noise in digital filters can be studied in simulation by comparing the behavior of the actual quantized digital filter with that of a refrence digital filter having the same structure but whose numerical calculations are done extremely accurately."
-Quantization Noise by Bernard Widrow and Istvan Kollar (pg. 416)

Thus I will use a technique closer to that used in Den Martynov's thesis (see appendix B starting on page 171). A summary of my understanding of his method is given here:

A filter is given raw unfiltered gaussian data  then it is filtered and the result is the filtered data  thus we get the result:   where  is the raw noise filtered through an ideal filter and  is the difference which in this case is the quantization noise. Thus I will input about 100-1000 seconds of the same white noise into a 32-bit and a 64-bit filter. (hopefully, I can increase the more precise one to 128 bit in the future) then I record their outputs and subtract the from each other. this should give us the Quantization error :

and since  because they are both running through ideal filters:


and since in this case, we are assuming that the higher bit-rate process is essentially noiseless we get the Quantization noise .

If we make some assumptions, then we can actually calculate a more precise version of the quantization noise:

"Since aLIGO CDS system uses double precision format, quantization noise is extrapolated assuming that it scales with mantissa length"
-Denis Martynov's Thesis (pg. 173)

From this assumption, we can say that the noise difference between the 32-bit and 64-bit filter outputs:    is proportional to the difference between their mantissa length. by averaging over many different bit lengths, we can estimate a better quantization noise number.

I am building the code to do this in this file

I have coded up the procedure in the previous post: The result does not look like what I would expect. 

As shown in Attachment1 I have the power spectrum of the 32-bit output and the 64-bit output as well as the power spectrum of the two subtracted time series as well as the subtracted power spectra of both. unfortunately, all of them follow the same general shape of the raw output of the filter. 

I would not expect quantization noise to follow the shape of the filter. I would instead expect it to be more uniform. If anything I would expect the quantization noise to increase with frequency. If a high-frequency signal is run through a filter that has high quantization noise then it will severely degrade: i.e. higher quantization noise. 

This is one reason why I am confused by what I am seeing here. In all cases including feeding the same and different white noise into both filters, I have found that the calculated quantization noise is proportional to the response of the filter. this seems wrong to me so I will continue to play around with it to see if I can gain any intuition about what might be happening.

I suggest that you

1. change the corner frequency to 10 Hz as I suggested last week. This filter, as it is, is going to give you trouble.
2. Put in a sine wave at 3.4283 Hz with an amplitude of 1, rather than white noise. In this way, its not necessary to do any subtraction. Just make PSD of the output of each filter.
3. Be careful about window length and window function. If you don't do this carefully, your PSD will be polluted by window bleeding.

[anchal, paco]

Here is a demonstration of the methods leading to the single (X)arm calibration with its budget uncertainty. The steps towards this measurement are the following:

1. We put a single line excitation through the C1:SUS-ETMX_LSC_EXC at 55.511 Hz, amp = 1 counts, gain = 300 (ramptime=10 s).
2. With the arm locked, we grab a long timeseries of the C1:LSC-XARM_IN1_DQ (error point) and C1:SUS-ETMX_LSC_OUT_DQ (control point) channels.
3. We assume the single arm loop to have the four blocks shown in Attachment #1, A (actuator + sus), plant (mainly the cavity pole), D (detection + electronics), and K (digital control).
   1. At this point, Anchal made a model of the single arm loop including the appropriate filter coefficients and other parameters. See Attachments #2-3 for the split and total model TFs.
   2. Our line would actually probe a TF from point b (error point) to point d (control point). We multiplied our measurement with open loop TF from b to d from model to get complete OLTF.
   3. Our initial estimate from documents and elog made overall loop shape correct but it was off by an overall gain factor. This could be due to wrong assumption on RFPD transimpedance or analog gains of AA or whitening filters. We have corrected for this factor in the RFPD transimpedance, but this needs to be checked (if we really care).
4. We demodulate decimated timeseries (final sampling rate ~ 2.048 kHz) and I & Q for both the b and d signals. From this and our model for K, we estimate the OLTF. Attachment #4 shows timeseries for magnitude and phase.
5. Finally, we compute the ASD for the OLTF magnitude. We plot it in Attachment #5 together with the ASD of the XARM transmission (C1:LSC-TRX_OUT_DQ) times the OLTF to estimate the optical gain noise ASD (this last step was a quick attempt at budgeting the calibration noise).
   1. For each ASD we used N = 24 averages, from which we estimate rms (statistical) uncertainties which are depicted by error bands () around the lines.

** Note: We ran the same procedure using dtt (diaggui) to validate our estimates at every point, as well as check our SNR in b and d before taking the ~3.5 hours of data.