Alex, Anchal, and I adjusted the number of the MC2-TRANS column in the YAW output matrix. We used the same method in 40m/17504 but the amplitude of oscillator for Lock In Amplifier is increased from 1 to 4.

The corrected numbers of the column in the output matrix is as follows:

We did the step response test for the corrected output matrix. The sum of off-diagonal terms was 0.62, which is the minimum value. Attachment 1 is the step response test result. From the figure, the reduction of the sum is because the column MC2_TRANS can diagonalize better. We can find out the property from Attachment 2.

[Anchal, Yuta]

We have measured LO phase noise in ITMX single bounce, simple MICH and FPMI configurations with LO phase locked with BH55 or BH44.
We found that BH55 and BH44 have almost exactly same noise in ITMX single bounce, but BH44 is noisier than BH55 in MICH and FPMI configurations.
In any case, LO phase can be locked within 0.1 rad RMS, so optical gain fluctuations in BHD_DIFF should be fine for BHD locking.

Method:
 - We have locked ITMX single bounce vs LO, AS beam under MICH locked with AS55_Q vs LO, and AS beam under FPMI locked with REFL55 & AS55 vs LO, using BH55_Q or BH44_Q
 - In each IFO configuration, we have minimized I phase to set RF demodulation phases for BH55 and BH44.
 - In each IFO configuration, optical gain of BH55_Q and BH44_Q was measured by elliptic fit of X-Y plot for BH55_Q vs BHDC_A or BH44_Q vs BH55_Q.
 - For each LO_PHASE lock, feedback gain was adjusted to set the UGF to around 50 Hz, and actuator used was LO1.
 - LO_PHASE_IN1 was calibrated using the measured optical gain, and LO_PHASE_OUT was calibrated using LO1 actuator gain of 26.34e-9 /f^2 m/counts measured in 40m/17285.
 - To convert meters in radians, 2*pi/lambda is used (which means dark fringe to dark fringe is pi).
 - Below summarizes the result of RF demodulation phases and optical gains (whitening gains were 45 dB for BH55 and 39 dB for BH44). RF demod phases aligns well with previous measurement, but optical gain for BH44 seems higher by an order of magnitude compared with 40m/17478 (whitening gain changed??). Optical gain for BH55_Q is consistent with previous measurement in 40m/17506 (note the demodulation phase change).

LO_PHASE lock in ITMX single bounce
        Demod phase  Optical gain     filter gain
BH55_Q  -99.8 deg    7.6e9 counts/m   -0.3
BH44_Q  -6.5 deg     1.3e10 counts/m  -0.15

LO_PHASE lock in MICH
        Demod phase  Optical gain     filter gain
BH55_Q  -67.7 deg    6.1e8 counts/m   -3.9
BH44_Q  -31.9 deg    8.5e8 counts/m   -3.1

LO_PHASE lock in FPMI
        Demod phase  Optical gain     filter gain
BH55_Q  35.7 deg     3.4e9 counts/m   -0.65
BH44_Q  -9.3 deg     4.3e10 counts/m  -0.84

Result:
 - Attached are calibrated LO phase noise spectrum in different IFO configurations.
 - In ITMX single bounce, LO phase noise estimated using BH55 and BH44 are almost equivalent, and LO phase noise in-loop is ~0.04 rad RMS.
 - In MICH, LO phase noise estimated using BH44 is noisier than BH44 at around 20-60 Hz for some reason. LO phase noise in-loop is ~0.04 rad RMS for both cases.
 - In FPMI, LO phase noise estimated using BH44 is noisier than BH44 above ~20 Hz for some reason. LO phase noise in-loop is ~0.03 rad RMS for both cases. Dark noise is not limiting the measurement at least below 1 kHz.

Jupyter notebook: /opt/rtcds/caltech/c1/Git/40m/measurements/BHD/BH55_BH44_Comparison.ipynb

Next:
 - Lock MICH BHD with BH55 and BH44, and compare LO phase noise contributions to MICH sensitivity
 - Investigate why BH44 is noisier than BH55 in MICH and FPMI (offsets? contrast defect? mode-matching?)
 - Reduce 60 Hz + harmonics in BH55 and BH44

Purpose

• To adjust the components of the WFS2 column in the YAW output matrix.
• To check the value of the off-diagonal components of the WFS1 column.

Method

Alex, Anchal, and I used the same method in 40m/17504 to adjust the components of the WFS2 column. And we did the same step response test to check the value of the off-diagonal components in the YAW output matrix.

Used script & file

All the scripts & files are stored in /opt/rtcds/caltech/c1/Git/40m/scripts/MC/WFS/ directory.

• DiagnoalizatingMethod.ipynb: for adjusting the components and replacing the new output matrix,
• toggleWFSoffsets.py: for doing the step response test,
• IOO_WFS_YAW_STEP_RESPONSE_TEST.py: for analyzing the step response result.

Result

We changed the WFS2 column as follows

We can successfully diagonalize the WFS2 column. The sum of the off-diagonal components is slightly reduced. However, WFS1 has worse diagonalization.

The same step response test should be performed on a different day to see if the results change. It is because the multiple causes could exist: the influence of the changed other columns, the long time drift, the day to day change, and so on.

Tomohiro and I performed some tests under Rana's guidance to find cross corelations between WFS1 and WFS2 output signals in both pitch and yaw. We performed this test to further understand the degree to which our output matrices have been diagonolized.

Seen in attachment 1 is our base level with no injected noise source. In each figure, we also have inlcuded the coherence plot which compares each control signal to the overalll YARM power signal.

Attachments 2-5 display our results for injecting noise into each control signal individually.

We found the following corelations for each respective test:

We judged our corelated signals by the peaks seen from out noise injection on the power spectrum as well as by their coherence at the same frequencies of our noise (20Hz-30Hz) compared to the overall power spectrum of YARM.

Performing this measurement was done using diaggui and awggui. The diaggui files for each test are saved at: "users/Templates/singleArmCal/ArmCavityNoise_230317_2_WFS1_PIT"

To properly fix each of the control signals to the same magnitude plotted for YARM output, we callibrated each plot using the settings seen in Attachment 7. First the units were changed on the plots to represent the true scale of each measurement:

We found that the ETMY actuation strength is 10.843e-9 / f^2 (from 17376) and used this to clibrate the plots to the nanometer scale. Next the gain was adjusted such that each plot would align over the YARM output when noise was injected onto it, setting a basis for all four measurements.

Finally, some filtering poles were added to the callibration for each plot such that it resembled that of the filters seen by the YARM ouput signal. (RXA: this is the 28 Hz ELP filter to simulate the dewhitening filters)

The measurements were taken with the settings seen in Attachment 8, and noise injected using the parameters seen in attachment 9.

RXA: Some edits/comments:

The noise was injected as band-limited random noise with a Normal distribution. We used noise rather than lines so as to capture the linear and bilinear noise contributions. In the case where the coupling is mostly bilinear, we would not expect to see much coherence.

The first attachment is a ASC noise budget for the single arm - in the high gain mode, the noise does not limit the noise as seen by the arm. Next is to see if its due to the MC dewhitening filters being on/off?

[Paco, Yuta]

MICH was locked with balanced homodyne readout with LO phase locked using BH55_Q and BH44_Q.
It turned out that BH44_Q gives better LO phase in MICH configuration (in FPMI, BH55_Q is better; see 40m/17506).
LO phase noise seems to contribute to MICH sensitivity in 30-200 Hz region in BH55 case, and 30-100 Hz in BH44 case (this was not the case in FPMI BHD, see 40m/17392).
The mechanism for this coupling needs investigation.

MICH BHD sensing matrix:
 - MICH BHD sensing matrix was measured when MICH is locked with AS55_Q and LO_PHASE is locked with BH55_Q or BH44_Q.
 - MICH UGF was at around 50 Hz, and LO_PHASE UGF was at around 10 Hz.
 - BHDC_DIFF had better sensitivity to MICH when LO_PHASE was locked with BH44_Q.
 - BH44 component was not measured well.

MICH sensing matrix with MICH locked with AS55_Q and LO_PHASE locked with BH55_Q

Sensing matrix with the following demodulation phases (counts/m)
{'AS55': 2.1, 'REFL55': 76.01784975834194, 'BH55': -63.16236453101908, 'BH44': -39.01036239539396}
Sensors       MICH @311.1 Hz           LO1 @315.17 Hz           
AS55_I       (+0.40+/-6.23)e+07 [0]    (-0.83+/-3.01)e+07 [0]    
AS55_Q       (+1.38+/-0.26)e+09 [0]    (+0.76+/-6.58)e+07 [0]   
BH55_I       (-3.22+/-0.37)e+09 [0]    (-0.81+/-8.42)e+07 [0]    
BH55_Q       (+4.03+/-0.52)e+09 [0]    (-4.01+/-1.05)e+08 [0]    
BH44_I       (-0.06+/-4.22)e+10 [0]    (+0.29+/-4.63)e+10 [0]    
BH44_Q       (-0.03+/-3.21)e+11 [0]    (+0.21+/-3.12)e+11 [0]    
BHDC_DIFF       (-1.07+/-0.39)e+09 [0]    (-3.35+/-7.47)e+07 [0]    
BHDC_SUM       (+2.07+/-0.57)e+08 [0]    (+0.32+/-1.65)e+07 [0]

MICH sensing matrix with MICH locked with AS55_Q and LO_PHASE locked with BH44_Q

Sensing matrix with the following demodulation phases (counts/m)
{'AS55': 2.1, 'REFL55': 76.01784975834194, 'BH55': -63.16236453101908, 'BH44': -39.01036239539396}
Sensors       MICH @311.1 Hz           LO1 @315.17 Hz           
AS55_I       (+0.22+/-5.36)e+07 [0]    (+0.91+/-3.10)e+07 [0]    
AS55_Q       (+1.43+/-0.08)e+09 [0]    (-0.78+/-7.45)e+07 [0]   
BH55_I       (+4.92+/-5.18)e+08 [0]    (-5.20+/-7.93)e+07 [0]    
BH55_Q       (-1.45+/-0.75)e+09 [0]    (+1.76+/-0.59)e+08 [0]    
BH44_I       (+0.01+/-1.14)e+11 [0]    (+0.02+/-1.08)e+11 [0]    
BH44_Q       (+0.03+/-1.95)e+11 [0]    (+0.07+/-1.98)e+11 [0]    
BHDC_DIFF       (+3.05+/-0.17)e+09 [0]    (+1.70+/-2.51)e+07 [0]    
BHDC_SUM       (-2.33+/-0.23)e+08 [0]    (+0.19+/-1.53)e+07 [0]

  - Jupyter notebook: /opt/rtcds/caltech/c1/Git/40m/scripts/CAL/SensingMatrix/ReadSensMat.ipynb

MICH BHD locking:
 - MICH lock with AS55_Q was handed over to BHD_DIFF using following ratio:
C1:LSC-PD_DOF_MTRX_3_4 = 1 (AS55_Q to MICH_A)
C1:LSC-PD_DOF_MTRX_4_34 = -1.34 (BHDC_DIFF to MICH_B, when BH55_Q is used)
C1:LSC-PD_DOF_MTRX_4_34 = 0.47 (BHDC_DIFF to MICH_B, when BH44_Q is used)

MICH BHD noise budget:
 - FM2 of C1:CAL-MICH_CINV was updated to 1/1.4e9 = 7.14e-10 to use measured optical gain.
 - Dark noise was measured at C1:CAL-MICH_W_OUT with PSL shutter closed, PD DOF matrix at various settings for various readout scheme.
 - Attachment #1 shows MICH sensitivity with MICH locked using AS55_Q (green), BHD_DIFF under BH55_Q (blue), BHD_DIFF under BH44_Q (red). BH44 case gives the least noise due to larger optical gain. However, there are excess noise at around 100 Hz, when MICH is locked with BHD_DIFF. The excess noise (bump at around 50 Hz) was similar to what we saw in LO phase noise estimate (40m/17511).
 - At low frequencies below ~30 Hz, the MICH sensitivity is probably limited by seismic noise, as it alignes with FPMI DARM sensitivity (orange curve; measured in 40m/17468).
 - Attachemnt #2 and #3 show estimate of LO phase noise contribution to MICH sensitivity in BH55 case and BH44 case. The coupling was estimated by measuring a transfer fuction from BH55_Q/BH44_Q to MICH_W_OUT. As there was significant coherence in 30-200 Hz region in BH55 case, and 30-100 Hz in BH44 case, transfer function value in that regions was used to estimate the coupling.
 - The coupling was estimated to be the following

 2e-10 m/count for BH55_Q to MICH_W_OUT (0.035 m/m using BH55_Q calibration factor to LO1 motion of 1.76e8 counts/m)
 2e-11 m/count for BH44_Q to MICH_W_OUT

 - Diaggui file: /opt/rtcds/caltech/c1/Git/40m/measurements/LSC/MICH/MICH_Sensitivity_Live.xml

Next:
  - Calibrate BH44_Q to LO1 motion
  - Measure transfer function from LO1 motion to BHD_DIFF under BH44 and BH55
  - Find out the cause of 50 Hz bump in LO phase noise
  - Compare LO phase noise coupling with simulations

With Anchal's help, I have setup dither lines for Rana on MC1,2,3 that will be running overnight. The oscilations were set on MC1,2,3, oscillator screens.
The following table describes the current setup:

These frequencies and amplitudes were set on LOCKIN1 for each MC1,2,3. The output filters matrix for MC1,2,3 was also updated to reflect the degree of freedom being tested: PITCH.

The frequencies were picked to avoid the dewhitening frequency: 28Hz, and the Bounce/Roll frequencies: 16 Hz & 24 Hz. Furthermore, decimal value frequencies were utilized to avoid the multiples of 1 Hz.

The oscilators were originally started at 1363480200 and will be turned off at 1363535157.

See attachment 1 for the plot of the power spectrum. This test is done to find the beam offset for pitch.

I have organized the resulting data from running dither lines on MC1,2,3. The data has been collected from diaggui as shown in attachment 1.

Mirror		Avg Re (+/- 1000)	Avg Im (+/- 1000)	Peak Power ()	Cts/urad
MC1	21.12	7000	4000	8062	12.66
MC2	25.52	13000	10000	16401	6.83
MC3	27.27	4000	-600	4044	11.03

Next using the following equations we can find :

Where is the change in length in result of the dithering and is the overall change in beam spot position

Delta L can be calculated by:

where is the peak power of the line frequency and is found by taking the square root of the magnitude of the Real and imaginary terms, is frequency the laser light is traveling at (281 THz) and is the lenght of the IMC (13.5 meters).

can then be calculated by:

where  is the angle at which the mirror was shaken at a given frequency. We can find  by converting the amplitude of the frequency that the mirror was shaken at and converting it into radians using the conversion constants found here: 17481.

is then shown to be found by this angle diveded by the line frequency.

The final values are calculated and displayed bellow:

Mirror
MC1	157.9 urad	0.35 urad	0.38 nm	1.08 mm
MC2	146.4 urad	0.23 urad	0.78 nm	3.39 mm
MC3	226.7 urad	0.31 urad	0.19 nm	0.61 mm

[Paco, Yehonathan]

I took over the finesse calculations Yehonathan had set up for BHD. The notebook is here and for this post I focused on simulating what we might expect from our single RF vs dual RF sensors (55 MHz and 44 MHz respectively) in terms of LO phase control.

The configuration is simple, only MICH is included (no ETMs, no PRC, no SRC). The LO phase is changed by scanning LO1, the differential loss is changed by scanning the ITMXHR loss parameter (nominally at 25 ppm), and the microscopic DARM offset is changed by scanning the BS position by +- 6 nm.

Finesse estimates the sensor response by taking the demodulated sideband magnitude (BH55, BH44) with respect to a 1 Hz LO1 signal modulation. This can be done for a set of LO phase angles so as to get the nominal LO phase angle where the response is maximized.

I first replicated the plots from [elog17170] for the two sensors in question. This is just done as a sanity check and is shown in Attachment #1. This plot summarizes our expectation that the single RF sideband sensor should have a peak response to the LO phase around 90 deg away from the nominal BHD readout phase angle (0 deg in this plot). In contrast, the double RF demodulation scheme has a peak response around the nominal LO phase angle.

Attachment #2 looks at a family of similar plots representing differential loss changes between the two MICH arms. We tune this by changing the ITMX loss in finesse, and then repeat the calculation as described above. It seems that for the simple MICH, differential loss of ~ 10000 ppm does not impact the nominal LO phase angle where the responses are maximized for either sensor (note however that the response magnitude maybe changes for single RF sideband sensing at extremely high differential loss).

Finally, and most interestingly Attachment #3 looks at a family of similar plots representing a set of microscopic DARM offsets (+- 6 nm). This is tuned by changing the BS position ever so slightly, and the same calculation is repeated. In this case, the nominal LO phase angle does change, and it changes quite a lot for the single RF demod. It looks like this might be enough to explain how we can sense the LO phase angle with a single RF sideband, but I think the next interesting point would be to simulate the effect of contrast defect by changing the ITM RoCs (to scatter into HOMs) or the non-thermal ITM lenses (to probe the TEM00 contrast defect effect). Any comments / feedback at this point are welcome, as we move forward into other configurations where more serious thermal effects might be introduced (PRMI).

This is interesting. With the FPMI, the DARM phase shift is enhanced by the cavity. Therefore, I suppose the effect on the BH55 is also going to be enhanced (i.e. a much smaller displacement offset causes a similar LO phase rotation).

I have changed the MC SUS output matrices by a few % for some A2L decoupling - if it causes trouble, please feel free to revert.

Anchal came to me and said, "I think those beam offsets are a bunch of stinkin malarkey!", so I decided to investigate.

Instead of Alex's "method" of trusting the actuator calibration, I resolved to have less systematics by adjusting the SUS output matrices ot minimize the A2L and then see what's what vis a vis geometry.

The attached screenshot shows you the measurement setup:

1. copy the DoF vector from DoF column into the LOCKIN1 column.
2. Turn on the OSC/LOCKIN for the optics / DoF in question (in this example its MC2 PITCH)
3. Monitor the peak in the MC_F spectrum
4. Also monitor the mag and phase of the TF of MC_F/LOCKIN_LO
5. use the script stepOutMat.py to step the matrix

Next I'm going to modify the script so that it can handle input arguments for optic/ DOF, etc.

FYI, the LOCKIN screens do have a TRAMP field, but its not on the screens for some reason . Also the screens don't have the optic name on them. :

SUS>caput C1:SUS-MC2_LOCKIN1_OSC_TRAMP 3
Old : C1:SUS-MC2_LOCKIN1_OSC_TRAMP   0
New : C1:SUS-MC2_LOCKIN1_OSC_TRAMP   3

After finishing the tuning of all 3 IMC optics, I have discovered that 27.5 Hz is a bad frequency to tune at: the Mc1/MC3 dewhtiening filters have a 28 Hz cutoff, so they all have slightly different phase shifts at 27-28 Hz due to the different poles due to tolerances in the capacitors (probably).

*Also, I am not able to get a real zero coupling through this method. There always is an orthogonal phase component that can't be cancelled by adjusting gains. On MC3, this is really bad and I don't know why.
 

I drafted a calibrated LO Phase noise budget using diaggui whose template is saved under /opt/rtcds/caltech/c1/Git/40m/measurements/BHD/LO_PHASE_cal_nb.xml which includes new estimates for laser frequency and intensity noises at the LO phase when MICH is locked (whether they couple through MICH or the LO path is to be determined with noise coupling measurements in the near future, but we expect them to couple through the LO phat mostly).

Attachment #1 shows the result.

Laser Frequency Noise

To calibrate the laser frequency noise contribution, I used the LO PHASE error point away from the control bandwidth (~ 20 Hz) and the calibrated C1:IOO-MC_F control point (in Hz) which should represent the laser frequency noise above 100 Hz. and dithered MC2 at frequencies around to 130, 215, and 325 Hz to match the LO phase error point with the MC_F signal. I was expecting to use a single 0 Hz pole + gain (to get the phase equivalent of the laser frequency noise) but in the end I managed to calibrate with a single gain of 3.6e-7 rad/Hz and no pole. Since the way the laser frequency noise couples into our BHD readout may be complicated (especially when using BH55 RF sensor) I didn't think much of this for now.

Laser Intensity Noise

For the intensity noise, I followed more or less a similar prescription as for laser frequency noise. This time, I used the AOM in the PSL table to actuate on the 0th order intensity going into the interferometer. Attachments #2-3 show the connection made to the RF driver where I added a 50 mVpp sine (at an offset of 0.1 V) excitation in the AM port to inject intensity noise calibration lines at 215 and 325 Hz and matched the LO_PHASE error point with the BHDC_SUM noise spectrum.

[Paco, Yuta]

We locked PRMI in sideband using REFL55_I and REFL55_Q.
Lock is not quite stable probably due to alignment fluctuations, and power recylicing gain is breathing.

PRMI preparations:
 - We aligned PRM using PRY (PRM-ITMY) cavity. Aligning PRM to oplev QPD center or last PRM alignment values in May 2022 (! see 40m/16875) didn't work, but we were in the middle of these two, both in pitch and yaw.
 - After this, we centered PRM oplev, aligned REFL camera, POP RFPD (which provides POP22, POP110, and POPDC), and REFL11.

PRY/PRX locking:
 - PRY/X was locked using REFL55_I or REFL11_I. Locking configuration which gives UGF of ~100 Hz was as follows

REFL55_I (24 dB whitening gain, 76.02 deg demod angle) C1:LSC-PRCL_GAIN=-0.03
REFL11_I (18 dB whitening gain, 32.55 deg demod angle) C1:LSC-PRCL_GAIN=-0.8
FM4,5 used for acquisition, FM1,2,6,9 turned on triggered.

 - Attachment #1 is the measured OLTF when PRY was locked.
 - When PRY is flashing, ASDC_OUT, POPDC_OUT, POP22_I, POP11_Q flashes upto 0.33, 1000, 30, 80, respectively.

PRMI locking:
 - PRMI was locked using REFL55_I for PRCL and REFL55_Q for MICH using the following configurations to give UGF of ~100 Hz for both DoF.

PRCL
  REFL55_I (24 dB whitening gain, 76.02 deg demod angle) C1:LSC-PRCL_GAIN=-0.03
  FM4,5 for acquisition, FM1,2 turned on triggered using POPDC.
  Actuating on 1 * PRM

MICH
  REFL55_Q (24 dB whitening gain, 76.02 deg demod angle) C1:LSC-MICH_GAIN=+0.9
  FM4,5 for acquisition, FM1,2 turned on triggered using POPDC.
  Actuating on 0.5 * BS - 0.275 * PRM

 - REFL55 demodulation phase was the same as FPMI and PRY. We checked this is roughly enough by measuring the sensing matrix to minimize PRCL component in Q.
 - MICH actuation of PRM/BS ratio was roughly tuned by minimizing the sensing of MICH component in REFL55_I.
 - PRCL and MICH gain was estimated by measuring the amplitude of error signals in PRY or PRM-misalgined MICH, and comparing that in PRMI.
 - Attachment #2 shows the screenshot of the configuration.
 - Attachment #3 and #4 are measured OLTF for PRCL and MICH.
 - Attachment #5 shows the time series data when PRMI is locked.

Next:
 - Tune PRM local damping
 - Tune REFL55 demodulation phase better by measuring the sensing matrix
 - Measure PRM actuation efficiency to check what is the right BS/PRM balancing
 - Estimate power recycling gain and compare with expectations
 - Lock PRMI using REFL11, AS55
 - PRMI BHD

PRM actuator was calibrated using PRY by comparing the actuation ratio between ITMY.
It was measured to be

PRM : -20.10e-9 /f^2 m/counts

This is consistent with what we have measured in 2013! (40m/8255)

Method:
 - Locked PRY using REFL55_I using the configuration described in 40m/17521 (UGF of ~100 Hz)
 - Measured transfer function from C1:LSC-(ITMY|PRM)_EXC to C1:LSC-PRCL_IN1
 - Took the ratio between ITMY actuation and PRM actuation to calculate PRM actuation, as ITMY actuation is known to be 4.90e-9 /f^2 m/counts (40m/17285).

Result:
 - Attachment #1 is the measured TF, and Attachment #2 is the actuator ratio PRM/ITMY.
 - The ratio was -4.10 on average in 70-150 Hz region, and PRM actuation was estimated to be 4.90e-9 * -4.10 /f^2 m/counts.

MICH actuator for PRMI lock:
 - When BS moves in POS by 1, BS-ITMX length stays the same, but BS-ITMY length changes by sqrt(2), so MICH changes by sqrt(2) and PRCL changes by -sqrt(2)/2.
 - So PRM needs to be used to compensate for this, and the ratio will be BS + k * PRM, where

 k = 26.54e-9/sqrt(2) / -20.10e-9 * sqrt(2)/2 = -0.66

 - So, good MICH actuator will be 0.5 * BS - 0.33 * PRM, which is not quite consistent with the rough number we had yesterday (-0.275; 40m/17521), but agrees with the Gautam number (-0.34; 40m/15996).
 - PRMI sensing matrix for REFL55 needs to be checked again.

Summary of actuation calibration so far:
 They are all actuator efficiency from C1:LSC-{$OPTIC}_EXC

BS   : 26.54e-9 /f^2 m/counts in MICH (40m/17285)
ITMX :  4.93e-9 /f^2 m/counts (40m/17285)
ITMY :  4.90e-9 /f^2 m/counts (40m/17285)
LO1  : 26.34e-9 /f^2 m/counts (40m/17285)
LO2  :  9.81e-9 /f^2 m/counts (40m/17285)
AS1  : 23.35e-9 /f^2 m/counts (40m/17285)
AS4  : 24.07e-9 /f^2 m/counts (40m/17285)
ETMX : 10.91e-9 /f^2 m/counts (40m/16977, 40m/17014)
ETMY : 10.91e-9 /f^2 m/counts (40m/16977)
MC2 : -14.17e-9 /f^2 m/counts in arm length (40m/16978)
MC2 :   5.06e-9 /f^2 m/counts in IMC length (40m/16978)
MC2 :  1.06e+05 /f^2 Hz/counts in IR laser frequency (40m/16978)
PRM : -20.10e-9 /f^2 m/counts (40m/17522)

PRMI sensing matrix was measured under PRMI locked with REFL55_I and Q.
MICH actuator is 0.5*ITMX-0.5*ITMY (to have more pure MICH, according to 40m/15996) and PRCL actuator is PRM.
RF demod phases seem to be good within a degree or so to minimize PRCL component in Q.

Sensing matrix with the following demodulation phases (counts/m)
{'AS55': 2.1, 'REFL55': 76.02, 'REFL11': 32.63833493469488}
Sensors       MICH @311.1 Hz           PRCL @313.31 Hz           
AS55_I       (+0.31+/-1.48)e+09 [90]    (+6.56+/-2.23)e+10 [0]    
AS55_Q       (-3.49+/-0.87)e+08 [90]    (+4.62+/-1.80)e+09 [0]    
REFL55_I       (-1.52+/-5.61)e+09 [90]    (+3.21+/-1.36)e+11 [0]    
REFL55_Q       (+8.77+/-0.46)e+09 [90]    (+5.01+/-3.63)e+09 [0]    
REFL11_I       (-0.23+/-1.92)e+08 [90]    (+1.13+/-0.47)e+10 [0]    
REFL11_Q       (+0.39+/-2.14)e+07 [90]    (-4.00+/-9.79)e+07 [0]    

Phase for AS55 to minimize PRCL in Q is 6.14+/-2.08 deg (4.04+/-2.08 deg from current value)
Phase for REFL55 to minimize PRCL in Q is 76.91+/-0.75 deg (0.89+/-0.75 deg from current value)
Phase for REFL11 to minimize PRCL in Q is 32.44+/-0.50 deg (-0.20+/-0.50 deg from current value)

Next:
 - Lock PRMI in carrier
 - PRG is not so stable; Measure g-factor of PRC using Kakeru-Gupta method (40m/8235)

that is really a lot of high precision for the REFL_11 demod phase...

for this kind of measurement, I wish we had a python code that would plot this measurment relative to our Finesse/PyKat model so we know if this table is like "Oh, nothing to see here." or "Wow! that's a Nobel prize worthy measurement !!"

Yuta pointed out that the BH55 signal was weirdly never going to zero, so I actually tuned the demod angle and made sure I was reading the right (Q) quadrature. This doesn't affect our previous qualitative conclusion about DARM offsets, but here's an updated gif which also makes visualization easier (?).

but what about including the DC reflectivity imbalance of the arms? there would be another BH55 term from that field maybe.

I've updated c1ioo model with adding WFS sensor to optic angle matrix and output filter module option. The output filter modules are named like EST_MC1_PIT to signify that that these are "estimated" angles of the optic. We can change this naming convention if we don't like it. I've also started DQ on the outputs of these filter moduels at 512 Hz sampling rate.

No medm screens have been made for these changes yet. One can still access them through:

For SENS_TO_OPT_P Matrix

For SENS_TO_OPT_Y Matrix

For filter modules:

I repeated the calculations but with FPMI (last case was all MICH). The qualitative behavior is the same, the BH55 sensing is mostly affected by residual darm offset. If the darm offset is of a couple of nm, the single RF sideband may sense the LO phase at as much as > 20 deg away from the nominal phase angle. This is not too different from the MICH case; so maybe I overlooked something about how I define FPMI in the calculation.

Attachments #1-3 show the plots of the BH55 (single RF sideband) and BH44 (double RF sideband) sensitivity to LO phase fluctuations around various nominal LO phase angles. Attachment #1 looks at the effect of differential loss, Attachment #2 looks at the effect of differential dc reflectivity (of the ITMs), and Attachment #3 looks at the effect of residual darm offsets. Dashed lines show the orthogonal quadrature (I) of the demodulated RF signals (always minimized).

I confirmed that MC Length feedback path to MC2 position is present and has been turned off in recent history. Feedback filter module can be seen in sitemap>IOO>Lock MC>MC2_LSC where the bottom fitler module is for feeding back MC Length to MC2. See attached screenshot.

This feedback signal goes and gets added to MC2 suspension longitudnal signal through ALTPOS path which is nominally not shown in any of the suspension screens (including the old ones). Note that this path is different than the LSC path that comes into each suspension screen.

Today, I tried a quick turning ON of this apth without playing around with any of the filters to see if the feedback helps. On first glance, it does not seem to help. Probably the gain values and filter modules need ot be adjusted. See attachment 2.

I'm turning this off again and in future someone should take a look at this loop.

Stable lock of the X End green laser was recovered.

- The biggest issue was that the laser PZT input had been terminated with a 50ohm at the laser head. (See Attachment 1: The terminator has already been removed in the photo.) Since the PZT output of the servo box (output impedance 10Ohm) goes through 680Ohm at the summing node for the modulation, the PZT output was attenuated by a factor of 15. This made the required servo gain for locking more than the box could deliver. More importantly, the PZT range (in terms of the laser frequency) was also limited. Momentary locks were still possible with the reduced range and gain. However, the actuation signal hit the rail within a few seconds because of the pendulum motion.

Once the terminator was removed from the head, the Xarm was locked with the green laser like a charm.

- On the way to the resolution, I had to go through the full scrutinization of the loop components one by one. Here is the record of the findings:

• Inspected the green Refl PD (Thorlabs PFA36A). The gain setting of the PD was 40 dB, and the unlocked output voltage was 10.8 V. This is not only very close to saturation, but also the bandwidth drops below the modulation frequency (150 kHz according to Thorlabs' manual). The gain was changed to 20dB. This made the unlocked PD output to be 1.08V and the BW was expected to be 1MHz.
   
• Checked the LO setting. The box has a label saying "LO 7dBm". The function generator setting of "0.66 Vrms" resulted in 7.0dBm at the mixer LO input. So this number is used. Exactly the same amount goes to the PZT summing node.
   
• Checked the mod freq. The PDH error signal amplitude was maximized at 278.5kHz (mixer output observed with 50Ohm: 46.0mV), however, the signal looked distorted from the text-book shape of the PDF error. This means that the demod phase was not optimized.
  The mod freq of 287.5kHz made the PDH error signal look better while the response was weaker (mixer out: 31.2mV). It turned out that the cavity locking didn't like these mod freq between 280kHz~290kHz. The momentary lock stretches showed a lot of quasi-sinusoidal fluctuation ~600Hz in the error and transmission signals. Instead, the modulation of 210.5kHz was used. This made the error signal during lock stretches clean and tight. 
   
• Box inspection: Checked the signal ratio between the error in and the error mon. The monitor gain seemed x20~x21. The PZT output and the PZT mon had identical gains. The transfer function of the box was measured with the gain knob changed from 0.00 to 7.00 where the transfer function started to get distorted with the given input. The gain was increased by 5dB/turn (i.e., 1 turn increases the gain by 5dB). ? It does not match with the info on the schematic and the datasheet? Anyways, the gain knob is working fine.
   
• To resurrect the SLOW THERMAL servo, the monitor channels were connected to the DAQ interface. The existing slow channel servo/setting worked fine, wh
   
• Usual caution: a slight touch to the satellite amp caused the UR OSEM PD completely black out. It means that just your presence at the X end can make some changes to the suspension.
   

After the XAUX - XARM lock was recovered the C1:ALS-TRX_GAIN was set from 0.002 to 0.0006 to normalize the green transmission to 1 when the cavity is aligned. This situation was verified with YAUX as well. The green transmissions are now normalized to 1 when both arm cavities are aligned.

After this I took a reference ALS noise spectra (Attachment #1). The XALS rms noise is ~ 100 Hz (which is great compared to previous reference of > 250 Hz), while the YALS is slightly worse at high frequency but the rms is comparable to previous references (~ 250 Hz). This is somewhat encouraging for our future PRFPMI lock acquistions.

Here are our best estimates for the optic transmission (power) coefficients.

Assuming our input power to the IFO is 0.95 Watts, and the IMC transmission is 90%, about 855 mW should be incident on the PRM. Furthermore, following our recent estimates we can estimate our PRMI gain to be ~ 13.4.

• Using these numbers we expect a single pass AS power of 517.8 uW and LO power of 530.1 uW when the PRM is misaligned and MICH is free swinging, consistent with recent estimates. When the PRM is aligned we would then expect the max PRMI BHD single port flash to be 7.6 mW.
• Similarly, using these numbers we expect a single pass POPDC power of 1.01 mW, which then is expected to flash at a ~ 13.5 mW level when the PRM is aligned. The POP beam is split between the position sensor, our broadband POP22 and POP110 RFPD, and a CCD camera to monitor the POP beam.

POPDC calibration

I misaligned the PRM and ITMX to get a single ITMY bounce configuration. From the numbers above, I should expect a single ITMY bounce POPDC power of 255 uW. Instead, I measure a total of 173.5 uW = 78 uW (POP QPD) + 91 uW (POP RFPD) + 4.5 uW (POP camera) which is 50% less than expected .  The C1:LSC-POPDC_OUT level for this measurement was 335 counts, giving a rough empirical calibration of 1.931e6 counts / W. When the PRM is aligned and the MICH is free swinging, the POPDC flashes reach levels in excess of 14,500 counts implying 7.51 mW PRMI POPDC power. When PRM is misaligned the POP MICH flashes reach 1360 counts, implying 703 uW (which falls short by ~ 50% from our expectation).

There is probably an unaccounted BS in the ITMX table that may explain our observed difference. Nevertheless, our POPDC calibration should be good from here on.