[Anchal, Yuta]

We have measured OLTF of IMC loop, and revisited IMC error point calibration again.
Also, we have tried to break the ground loop between MC servo board and TTFSS, but didn't help.

IMC OLTF measurement:
 - IMC OLTF was measured using SR785 at TP1A and TP1B. MC servo board settings are the following.
   - +4 dB in IN1
   - 40 Hz pole, 4000 Hz zero filter was on
   - 0 boost
 - Eye-ball fit of OLTF gives zeros at [30e3,30e3] Hz, poles at [40,3e3,3e3] Hz (Attachment #1). 40 Hz pole is from 40:4000 Hz fiter in MC servo board and 4kHz zero is compensated by IMC cavity pole (~ 3.79 kHz). We are not sure where two 3k:30k are from.
 - Anyway, eye-ball fit gives OLTF gain of 1.7e5 at 60 Hz, which is accidentally roughly the same as previous estimate (40m/17446).

Revisiting IMC error point calibrations:
 - We realized that error signal calibration of 13kHz/V a while ago in 2018 (from 40m/14691, which is from 40m/13696) is a calibration for IN1.
 - So, 70 uV/rtHz at 60 Hz at TP1A corresponds to 70 uV/rtHz / 4dB / (4e3/60) * 13kHz/V = 0.009 Hz/rtHz, which corresponds to 1.2e-15 m/rtHz.
 - The estimated frequency noise at the output of IMC in terms of arm length is 1.2e-15 m/Hz * (1+G) = 2.0e-10 m/rtHz (or 1.4e-10 m RMS considering 0.5 Hz bandwith).
 - Noise measured with the same condition but PSL shutter closed was 7 uV/rtHz at 60 Hz (40m/17431). This correspond to 1.2e-16 m/rtHz (or 8.5e-17 m RMS), which is an estimated dark noise.

Summary of frequency noise measurements at 60 Hz:
 - 1.4e-10 m RMS (or 1.0e3 Hz RMS) as measured at TP1A (estimate of unsuppressed noise difference between IMC and PSL)
  - This being smaller than MC_F measurement is strange, as this should be an estimate of total unsuppressed noise (if 60 Hz noise is coherently cancelling each other, this can be explained).
 - 3.1e-9 m RMS (or 2.2e4 Hz RMS) as measured at MC_F
 - 4.3e-11 m RMS (or 3.1e2 Hz RMS)  as measured using XARM and YARM
 - 1.8e-10 m RMS as measured using FPMI DARM

Buffering MC servo board output to TTFSS:
 - We have inserted a battery-powered SR560 in between MC servo board output to TTFSS, trying to break the possible ground loop between 1X2 rack and PSL.
 - To do this, we had to lower IN1 gain to -6dB, to avoid saturation of SR560.
 - This didn't make any difference in MC_F or POY during YARM lock.

[Anchal, Yuta]

Yesterday, we have measured the frequency noise of PSL with IMC locked/unlocked using ALS BEATX/Y to narrow down where the 60 Hz is coming from.
All the measurements so far is consistent with a hypothesis that 60 Hz noise injected after MC_F is picked-off (it could be from MC_F DAQ readout or something in the IMC loop).

Method:
 - Measured YARM noise spectra when YARM is locked with POY11 to measure the frequency noise with respect to YARM, and compared with MC_F
 - Measured ALS BEATX and BEATY spectra when PSL is free running and when IMC is locked. Here, when "PSL is free running" is done with PSL shutter closed, but all the cables remained the same and FSS loop was in "down" state. Shutters at both ends were closed, and PZT inputs to AUX lasers were terminated to avoid noise injection from PDH locking with dark noise (this was necessary to reduce noise in BEATY).

Result:
 - Attachment #1 is YARM noise calibrated into Hz, and Attachment #2 is BEATX and BEATY spectra with PSL free running (solid lines) and IMC locked (dotted lines). Below are summary of noise level at 60 Hz (RMS is calculated using a bandwidth of 0.187493 Hz)

YARM (PSL locked vs Yarm): 6.5e2 Hz/rtHz (2.8e2 Hz RMS)
MC_F (sum of noises in IMC loop): 4.9e4 Hz/rtHz (2.2e4 Hz RMS)
BEATX free (PSL free vs Xend free): 3.3e3 Hz/rtHz (1.4e3 Hz RMS)
BEATX locked (PSL locked vs Xend free): 8.8e2 Hz/rtHz (3.8e2 Hz RMS)
BEATY free (PSL free vs Yend free): 1.6e4 Hz/rtHz (6.9e3 Hz RMS)
BEATY locked (PSL locked vs Yend free): 1.5e4 Hz/rtHz (6.5e3 Hz RMS)

Discussion:
 - "BEATX locked" measurement suggests that PSL locked to IMC (and Xend free) has noise less than 3.8e2 Hz RMS. This is roughly consistent with YARM measurement of frequency noise, and suggests that Yarm is stable enough to measure the PSL locked frequency noise.
 - "BEATX free" measurement suggests that PSL free run (with cables connected) has noise of 1.4e3 Hz RMS (note that Xend free is less than 3.8e2 Hz RMS).
 - MC_F measurement is the sum of noises in IMC loop, including IMC length noise + noise injected at error point (3.8e2 Hz RMS), PSL free run noise (1.4e3 Hz RMS), noise injected at feedback. Therefore, this suggests that 2.2e4 Hz RMS we see in MC_F is from noise injected after MC_F pickoff point (or in the MC_F DAQ readout).
 - BEATY having large 60 Hz noise probably comes from noise in the beat measurement.

Next:
 - Use BEATX to monitor 60 Hz noise.
 - Try terminating PZT input to see if 60 Hz noise reduces. Try different gains at different point of MC servo board and TTFSS when IMC is unlocked to see where exactly 60 Hz noise is coming from.

[Anchal, Yuta]

Measurements yesterday (40m/17458) suggested that 60 Hz noise is injected after MC_F is picked-off.
So, we terminated PSL PZT input at several points to see where 60 Hz noise is injected.
It seems like the 60 Hz frequncy noise we see in MC_F is from TTFSS box, but the 60 Hz noise we see in YARM is not limited by this.

The 60 Hz noise we see in YARM is probably limited by IMC length noise.

Method:
 - We terminated PZT input to the PSL laser at various points one by one and monitored 60 Hz frequency noise using BEATX. PSL shutter was closed and IMC was not locked.

Result:
 - Below is the result at 60 Hz (RMS is calculated using a bandwidth of 0.187493 Hz)

Reference from 40m/17458, YARM (PSL locked vs Yarm): 6.5e2 Hz/rtHz (2.8e2 Hz RMS)
Reference from 40m/17458, MC_F (sum of noises in IMC loop): 4.9e4 Hz/rtHz (2.2e4 Hz RMS)
MC_F when PSL shutter is closed but MC servo board configuration at IMC locked state: 2.7e2 Hz/rtHz (1.2e2 Hz RMS) -- this gives IMC loop gain enhanced sensing noise

BEATX free (PSL free vs Xend free): 3.5e3 Hz/rtHz (1.5e3 Hz RMS) -- consistent with previous measurements
With PZT input to NPRO terminated (Attachment #1): 8.1e2 Hz/rtHz (3.5e2 Hz RMS)
Connected a terminated small box (we see in Attachment #1) before NPRO PZT: 6.3e2 Hz/rtHz (2.7e2 Hz RMS)
Connected input terminated Thorlabs PZT driver (MDT694): 5.9e2 Hz/rtHz (2.6e2 Hz RMS)
Connected input terminated summing amp (Attachment#2): 4.4e2 Hz/rtHz (1.9e2 Hz RMS)
Connected input terminated TTFSS (C1:PSL-FSS_MGAIN=-10dB, C1:PSL-FSS_FASTGAIN=-10dB): 3.9e3 Hz/rtHz (1.7e3 Hz RMS) -- consistent with "BEATX free (PSL free vs Xend free)" measurement
Connected input terminated TTFSS (C1:PSL-FSS_MGAIN=-10dB, C1:PSL-FSS_FASTGAIN=+10dB): 7.6e3 Hz/rtHz (3.3e3 Hz RMS)
Connected input terminated TTFSS (C1:PSL-FSS_MGAIN=+4dB, C1:PSL-FSS_FASTGAIN=+19dB): 2.9e4 Hz/rtHz (1.3e4 Hz RMS) -- Nominal gains when IMC is locked; consistent with "MC_F" measurement 40m/17458
Connected input terminated TTFSS (C1:PSL-FSS_MGAIN=+19dB, C1:PSL-FSS_FASTGAIN=+4dB): 1.1e4 Hz/rtHz (4.8e3 Hz RMS)

Discussion:
 - Connecting TTFSS increased 60 Hz frequency noise, which suggests that TTFSS is creating this 60 Hz frequency noise.
 - Setting TTFSS gains to nominal gains to IMC locked, 60 Hz frequency noise matched with frequency noise measurement using MC_F. This quantitatively supports that TTFSS is creating this 60 Hz frequency noise.
 - Increasing C1:PSL-FSS_MGAIN and reducing C1:PSL-FSS_FASTGAIN reduced 60 Hz frequency nosie. This means that some portion of 60 Hz noise is from between these two gains.
 - Note that having 60 Hz noise in TTFSS does not necessarily mean that our YARM noise is limited by this, because IMC loop suppresses the TTFSS noise. Assuming all 1.3e4 Hz RMS is all from TTFSS noise, it is suppressed to less than 1.3e4 Hz RMS/2e5 = 6.5e-2 Hz RMS (where 2e5 is IMC loop gain without super boosts, but it is actually higher with them) as frequency noise we see in YARM. YARM noise is measured to be 6.5e2 Hz/rtHz (2.8e2 Hz RMS), so it is not limited by TTFSS noise.
 - Also dark noise measured at MC_F (1.2e2 Hz RMS) tells you that the dark noise is not limiting the frequency noise we see in YARM.

Touching various parts around TTFSS:
 - We moved on to touch various parts around TTFSS to see if 60 Hz noise reduces in MC_F. We removed unused cables around TTFSS interface, touched power cables into TTFSS (both at TTFSS interface in the rack and TTFSS box on PSL table), BNC cables into TTFSS, disconnected slow controls, tried to avoid grounding of cables going into EOM (there is a small box that sums FSS feedback signal and 33.5 MHz; Attachment #3), but 60 Hz noise we see in MC_F didn't change significantly.

Next:
 - Check grounding situation around TTFSS box.
 - Check IMC length noise and error point noise by monitoring BEATX.
 - Check coil drivers for MC1, MC2, MC3 by disconnecting drivers while IMC is locked.
 - Try feeding back IMC servo also to MC2 with 60 Hz resonant gain to cancel 60 Hz noise


Note added at 23:50 to clarify:
nIMC : IMC length noise in frequency
nPSL: PSL free run noise in frequency
ne: sensing noise in frequency
nf: feedback noise in frequency
G: IMC loop gain (estimated to be 2e5 at 60 Hz without boosts)

MC_F = G/(1+G) * (nIMC + nPSL + ne + nf) + [noises in MC_F DAQ]
 = 2.2e4 Hz RMS
 MC_F when dark, MC servo nominal gain = G * ne
 = 1.2e2 Hz RMS
PSL frequency noise after IMC lock = G/(1+G) * (nIMC + ne) + 1/(1+G) * (nPSL + nf)
YARM = [PSL frequency noise after IMC lock] + [noises from YARM loop]
 = 2.8e2 Hz RMS
BEATX when PSL is free run, TTFSS low gain connected = nPSL + [noises from Xend AUX and BEATX sensing]
 = 1.7e3 Hz RMS
BEATX when PSL is free run, TTFSS nominal gain connected = nPSL + nf + [noises from Xend AUX and BEATX sensing]
 = 2.9e4 Hz RMS
BEATX when IMC is locked = [PSL frequency noise after IMC lock] + [noises from Xend AUX and BEATX sensing]
 = 3.8e2 Hz RMS
 
So, our estimate is
ne ~ 1.2e2/G Hz RMS (small)
nPSL ~ 1.7e3 Hz RMS
nf ~ 2e4 Hz RMS (this dominates MC_F, but already suppressed enough in [PSL frequency noise after IMC lock])
[PSL frequency after IMC lock] ~ 3e2 Hz RMS (this dominates YARM and BEATX when IMC is locked)
nIMC ~ 3e2 Hz RMS (this dominates [PSL frequency noise after IMC lock])

[JC, Yuta]

We have found that MC1 coils are causing 60 Hz noise.
Tripping watchdogs for MC1 coils reduced 60 Hz noise seen in YARM by a factor of 100.

Method:
 - Locked YARM with POY11 and measured YARM sensitivity to use it for 60 Hz frequency noise monitor0.187493**0.5
 - Tripped MC1, MC2, MC3 coil output watchdogs to see if they are causing this 60 Hz frequency noise. IMC WFS were turned off.

Result:
 - Attachment #1 is YARM sensitivity and MC_F in Hz with MC1,2,3 untripped (dotted) and MC1 tripped (solid).

YARM (PSL locked vs Yarm), MC1,2,3 untripped: 6.0e2 Hz/rtHz (2.6e2 Hz RMS)
MC_F (sum of noises in IMC loop), MC1,2,3 untripped: 4.8e4 Hz/rtHz (2.1e4 Hz RMS)
YARM (PSL locked vs Yarm), MC1 tripped: 6.6e0 Hz/rtHz (2.9e0 Hz RMS) -- reduced by a factor of 100
MC_F (sum of noises in IMC loop), MC1 tripped: 4.7e4 Hz/rtHz (2.0e4 Hz RMS)

 - We have also tried tripping MC2 and MC3 coils, but they didn't make much difference.
 - Untripping only one of MC1 face coils created 60 Hz frequency noise, so all the face coils seem to have the same level of 60 Hz noise.

Next:
 - Inspect around MC1 coil driver

[Anchal, Yuta]

We think we have narrowed down the source of 60 Hz noise to one fo the following possibilities:

• Ground loop present along the MC1 suspension damping loop
• 60 Hz DAC noise on inputs of MC1 coil driver
• 60 Hz noise injected at dewhitening board before the dewhitening filter

The second and third cases are unlikely because we see 60 Hz noise present only in MC1 coils, not MC3 coils while they both share the same connection from DAC to SOS dewhitening filter boards as they share the SOS dewhitening board D000316-A. So it is unlikely that only the MC1 channels have this noise while the MC3 channels do not.

This inference was made from following observations:

Note: Turning ON analog dewhitenign on MC1 coil is done by turning off FM9 switch which is the simulated digital dewhitening filter. Also note that theanalog dewhitening filter has an attenuation of 30 dB at 60 Hz.

MC1 has an unconvetional setup where the satellite amplifier is from the new generation while the coil driver and dewhitening boards are from the old generation. The new generation satellite amplifiers sen PD signal through differential ended signals but the old generation PD whitening interface expects single ended inputs, so we ahve been using PD monitor outputs from the satellite amplifier which connects the ground of the two boards to each other. Maybe this is the reason for the ground loop.

Below are summary of electronics around MC1 and cable disconnection tests.
These suggest that the 60 Hz noise is probably from somewhere between DAC and the coil driver.
For now, we can work on IFO with SimDW off.

MC1 local damping electronics diagram:
Vacuum Flange
|| DB25 cable x2
Satellite Amp Chassis (LIGO-S2100029, LIGO-D1002818)
|| DB9 split cable
Suspension PD Whitening and Interface Board (LIGO-D000210)
||| 4pin LEMO x3
Anti-aliasing filter
|
ADC
|
CDS
 (SimDW is zpk([35.3553+i*35.3553;35.3553-i*35.3553;250],[4.94975+i*4.94975;4.94975-i*4.94975;2500],1,"n") gain(1.020); InvDW is the inverse)
|
DAC
|
SOS Dewhitening and Anti-Image Filter (LIGO-D000316) Shared with MC3
 (has 2ea. 800 Hz LPF & 5th order, 1 dB ripple, 50 dB atten, 28Hz elliptic LPF that can be turned on or bypassed)
||||| SMA-LEMO cable x5
 ("test in" are used; inputs can be disconnected with watchdogs)
SOS Coil Driver Module (LIGO-D010001, LIGO-D1700218)
 (HV offsets from Acromag are added at the output (independent from watchdogs))
|| DB9 split cable
Satellite Amp Chassis

Disconnecting cables:
 - Disconnecting cables between Satellite Amp Chassis and Suspension PD Whitening and Interface Board didn't help reducing 60 Hz noise.
 - Disconnecting LEMO cables between Suspension PD Whitening and Interface Board and Anti-aliasing filter didn't help reducing 60 Hz noise.
 - Turning off C1:SUS-MC1_SUSPOS/PIT/YAW/SIDE outputs didn't help reducing 60 Hz noise.
 - Turning off SimDW reduced 60 Hz noise.
 - Turning off watchdogs reduced 60 Hz noise.

Dewhitening filters:
 - When 60 Hz frequency noise was high, SimDW was on, but InvDW was off, which is in a weired state.
 - Now, all the MC suspensions have SimDW turned off and InvDW turned on (which supposed to turn on analog dewhitening filter, which is probably 28 Hz ELP which has a notch at 60 Hz)
 - Probably, when realtime model modifications for BH44 was made on Jan 17, coil dewhitening filter situation was not burt restored correctly, and we started to notice 60 Hz noise (which was already there but didn't notice because of dewhitening).
 - See 40m/17431 for the timeline, possibly related elogs 40m/17359, 40m/17361 about MC1 dewhitening switching on Dec 14-16.

Next:
 - Check if analong dewhitening filter actually has 28 Hz ELP by measuring transfer functions
 - Design SimDW and InvDW to correctly take into account of real dewhitening filters

Overtime the coil output filters on IMC optics have drifted into a bad configuration. Today at the meeting, Rana told us the correct configuration for these filters. I'll summarize this here and we have changes the filters on all IMC optics, MC1, MC2, and MC3 to match this configurations:

MC1 and MC3

Analog side:

Both MC1 and MC3 have a 28 Hz 5th order elliptical low pass filter as teh dewhitening filter in LIGO-D000316

Digital side:

At the coil output filters named as C1:SUS-MC1_ULCOIL, the filter module FM9 is connectd in RTCDS to the analog dewhitening filter such that only one of the two can remain ON. So For MC1 and MC3, we put a ellip("LowPass", 5, 1, 50, 28) filter on FM9 for all 5 coil output filters.

Note: We do not add a inverse dewhitening filter at FM10 like most other optics as inverting this filter will create resonant peaks at the dips of the elliptical filter which we want to avoid and we anyways do not use MC1 and MC3 optics for any kind of actuation above 20 Hz.

MC2

Analog side:

For MC2, the dewhitening filter is a 10 Hz pole, 30Hz zero like most other suspended optic.

Digital side:

At the coil output filters named as C1:SUS-MC2_ULCOIL, the filter module FM9 is connectd in RTCDS to the analog dewhitening filter such that only one of the two can remain ON. So For MC2 we put a SimDW filter which is matched to the anlog filter. We also put a InvDW filter on FM10, which is the analytical inverse of the SimDW filter. This filter does the anti-dewhitening required on the digital side and should be always ON.

To MC2 equivalent to other IMC optics in terms of overall transfer function for the local damping loops and ASC loops, we need additional 28 Hz elliptical low pass filter in these loops. But such a filter should not be in the path of LSC feedback when MC2 is used for locking CARM with a bandwidth of ~100 Hz. Thus, we put a ellip("LowPass", 5, 1, 50, 28) filter on FM6 of the following filters, which should be always ON as well:

• C1:SUS-MC2_ASCPIT
• C1:SUS-MC2_ASCYAW
• C1:SUS-MC2_SUSPOS
• C1:SUS-MC2_SUSPIT
• C1:SUS-MC2_SUSYAW
• C1:SUS-MC2_SUSSIDE

Effect on 60 Hz Noise

With the above changes, we see that the 60 Hz noise is same as the previous levels when we use the analog dewhitening filter (28 Hz elliptical filter) for MC1. We can move forward with our science experiments with that configuration but there is still something fishy about MC1 in comparison to MC3 which does not have this behavior. So this still needs to be looked at in future.

Wiki page for filter details and configurations

Information of this kind should be stored in a wiki page in my opinion. We should have a page where we list all common filter configurations for our suspensions and other loops, that can be generally classified and is useful for understanding legacy configuration for future folks who work here. I'm starting such a wiki page here, where I'll dump more information as I collect it and get time. Everyone is encouraged to update this in there free/procrastination times.

Also reply to: 40m/17352

Tomohiro, Anchal, and I did the following to make updates to the calibration constants for pitch and yaw on MC1, MC2 and MC3.

To acquire the data used for fitting a curve respective to the change in counts per change in mirror pitch and yaw, we utilized some code that Anchal has already developed.

The scripts used to take time averaged data points of the IMC mirrors can be found by entering the command $ s into a terminal window to enter the scripts folder. Then enter the path "SUS/angActCal"

The following scripts will be found there to be used for this experiment:

angActCal.py & parabolaFit.py

To take data we used the angActCal.py function with set values for the time averaging = 5 s, settle time = 5 s, and adjusted the offset such that we would acquire approximately 20 data points given our ASC Bias limits. We defined the limits for each plot based on where the transmission fall off from the maximum value reached an average range of 10,000 counts.

The "readChannel" for each was the "C1:IOO-MC_TRANS_SUMFILT_OUTPUT" and can be found from the site map at IOO>Lock MC> see MC2_TRANS

The adjustment channels for Pitch and yaw on each IMC mirror were entered as the offset value found in the IMC screen at ALIGNMENT OFFSETS > BIASPIT/BIASYAW > OFFSET

For the code to work, the offset switch must be turned on. parabolaFit.py 

The data from MC1, MC2, and MC3 for pitch and yaw was saved to individual text files which were then entered into the parabolaFit.py function to get the results seen in attachment 1 and 2.

The above images show the printout from the plot fitting function and one of the graphs produced.

From the fitted curve values we then derived the equations that will soon be described further by Tomohiro (see entry _____) to arrive at the final callibration constants.

Final Calibration Constants for MC1, MC2, & MC3

We then utilized our calculated calibration constants (as seen bellow) to adjust the following filter parameters in the IMC control panel.

To make the updates such that the IMC screens show the correct urad values at the output of the filter banks, we must do the following steps to MC1, MC2, and MC3:

First, to make changes to our calibration filters, we must first shut off the pitch and yaw feedback loop controls.

TO do so for the Lock Filters, we will set the pitch and yaw SUS ASC inputs to 0 but entering the sitemap > IOO > C1IOO_WFS_MASTER

Nex head to action at the top right, and we can select "MC WFS relief 60s", this will relieve the values from the pitch and yaw inputs to the 40m Mode Cleaner Alignment settings to save the overall alignment and allow us to turn off the WFS servos to make the necessary adjustments on the lock filters.

Once we have waited a sufficient amount of time for the values on the ASC inputs to hover around 0, select Turn WFS ON/OFF button and choose "Turn OFF MCWFS Servo"

Next, we will press on the "on/off" button (see attachment 3 - circled in orange) for pitch and yaw found in just the LOCK FILTERS windows.

Once these are off we will stay in the same screen and adjust the gain values (boxed in yellow) for pitch and yaw.

Next, we will take the current value and divide it by the newly found corresponding calibration constant. This is to adjust for the changes we will be making on the output end of the filter banks such that all values in the feedback controls are normalized to the same scale.

The changes made here can be seen bellow:

Now that these changes have been made in the damp and lock filter banks, with the pitch and yaw feedback loops STILL OFF, we may adjust the newly made calibration filters for pitch and yaw (as seen in attachment 4).

The "P" and "Y" filters may be opened (boxed in red) and we may adjust the gain (circled in yellow). Because each of these filters have just been created, the value is set to 1. This value can be completely replaced with the calibration constant found in our table above. Thus we will now change MC1 Pitch to have a "gain" of 12.66 and so forth.

Once each of the calibration filters have been updated, you may go back into the damp filters and reinitiate the feedback loops.

Once all values have been entered,

This concludes the updating of the IMC filter calibration constants at DC.

Alex, Anchal, and I did the following to make updated angular actuation calibration for IMC mirrors. This is the revised version of Anchal's: 40m/16125.

In order to make the calibration formulas, we consider a matrix : connecting displacements and rotations of the IMC's beam waist to PIT and YAW rotations of every mirror

The parameters used in the above equation are listed in the next table.

	horizontal displacement of beam waist position
	vertical displacement of beam waist position
	PIT of the beam axis and/or each mirror
	YAW of the beam axis and/or each mirror
(subscript)	parameters for the beam
(subscript)	parameters for

 are the flat mirrors and  is the curved mirror in IMC. Components in  are refered from F. Kawazoe+ 2011 (doi: 10.1088/2040-8978/13/5/055504). In the paper, displacement and/or rotation of the beam parameters obtained from the PIT and YAW of each mirror are obtained not by  but by common or differential rotation of both two flat mirrors . Therefore, we divide  into two parts  (relation ):

• : relation between the beam parameters and the PIT and YAW rotation with 

• : relation between  and 

 is represented by revewing F. Kawazoe+ (2011):

Here we use  as RoC of ,  as height from the shorter side of the isoscele triangle, and  as half-long length of the shorter side. Intuitive discussion about the components are written in the last of the log.

Transmitted power is reduced by the small displacement and/or the small rotation of the beam axis, and can be represented by the Gaussian factor. It is described in /users/OLD/kakeru/oplev_calibration/oplev.pdf by Takahashi-san:

• parallel displacement

where  is the small displacement of the beam waist. It corresponds to .  is beam waist diameter inside IMC.

• beam axis rotation

where  is the small rotation of the beam axis. It corresponds to .  is divergence angle of the beam and is written by  and wavelength of laser 

Total power reduction is measured by multiplied gaussian factor of the displacement and the rotation. We can obtain the calibration formulas  with summed reduction Gaussian factor

where  is the vector of the PIT and YAW rotation .  are the calibration fomulas of PIT and YAW in 40m/16125 defined by Anchal, respectively, and have a unit of . Every calibration fomula is expressed as follows:

We intuitively describe how to obtain the components in . The detail is discussed in F. Kawazoe+ (2011).

• : 2-flat mirrors rotate with differential YAW 

When the 2-flat mirrors rotate, the shape of the isoscele triangle is thick, that is, the beam waist does not rotate but slightly displaces from its original one. Considering that the longer side of the triangle are almost perpendicular to the shorter side and ,  can be obtained by focusing on the right triangle shown in the following picture

• : 2-flat mirrors rotate with common YAW 

From , new triangle beam line is very similar to the isoscele triangle by rotating  from original one. So  is approximated to , but actually the new one is breaked its symmetry. The result becomes as follows

• : curved mirror rotates by 

It is similar to the case of . But the pivot to rotate the triangle is near than the case , so  has bigger factor than that of 

• : curved mirror rotates by 

It is completely the same as the discussion of linear cavity which has flat end mirror and curved input mirror.

• : 2-flat mirrors rotate with common PIT 

It is also the same as the linear one except that 2-flat mirrors are angled by 45 degrees. Angled 45 degrees reduce the effective rotation by factor of . The detail is discussed in A. Freise (2010).

• : 2-flat mirrors rotate with differential PIT ​

The differential rotation with the effect of  directly reflects to the PIT rotation of the beam

I tried some LO PHASE noise coupling measurements today. With MICH locked using AS55_Q, I control the LO phase using the single RF (BH55_Q) or double RF (BH44_Q) demodulation error signals. The calibrated error and control points for single RF sideband sensing are shown in Attachment #1. In either case feedback loop is closed using FM5, FM8 first with a gain of 1.5 and then a "boost" using FM4. The actuation point is LO1 POS and the UGF was measured to be ~ 35 Hz for both.

** While doing this measurement, I noticed our LO_PHASE dark noise is significantly contributing 180 Hz, 300 Hz and other high line harmonics into the control signal rms so that may be something to look into soon.

I first thought I could use the remaining sensor to measure the noise coupling (e.g. BH44 locks LO phase and BH55 senses injected noise or viceversa), but these two sensing schemes give two different LO phase sensitivities so I decided to just use the calibrated control signals.

-- Noise coupling for BH55_Q --

After locking the LO_PHASE I inject 2 Hz wide uniform noise into three different frequency bands *within the control bandwidth* through C1:SUS-LO2_LSC_EXC, C1:SUS-AS1_LSC_EXC, and C1:SUS-AS4_LSC_EXC. The injected noise settings are captured by Attachment #2 (the screenshot of the excitation settings in diaggui).

I read back the calibrated C1:HPC-LO_PHASE_OUT_DQ representing the true LO_PHASE noise within the control bandwidth and also calibrate the injected noise spectra with the help of the actuation coefficients in [elog40m:17274]. The result is summarized in Attachment #3.

The diaggui template and data for this measurement are saved under /opt/rtcds/caltech/c1/Git/40m/measurements/BHD/BH55Q_NoiseCoupling.xml

-- Noise coupling for BH44_Q -- 

I repeat the same procedure as above and the injected noise settings, and the result is summarized in Attachment #4. 

The diaggui template and data for this measurement are saved under /opt/rtcds/caltech/c1/Git/40m/measurements/BHD/BH44Q_NoiseCoupling.xml

- Discussion -

It seems that noise injected along the AS beam path (AS1-AS4 dither) couples more into the control point of the LO phase. I also seem to be off in terms of calibrating the noise excitation (even though I scaled using the suspension actuation from [elog40m:17274]. General feedback on the methods used for this measurement are welcome of course. 

- Next steps - 

    - Extend this to single RF + audio dither scheme and double audio dither schemes (although it's hard because the control bandwidth is pretty low already)
    - Investigate line noise in RFPD + demod chain (present on the dark noise). 
    - Investigate other more interesting noise couplings, e.g. angular degrees of freedom, RIN, laser freq noise, etc...
    - Repeat under more relevant IFO configurations (e.g. FPMI)

[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).

[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 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).

• FIgure 1: PZT dither path. Most of the features in this plot are understood: There is a 2kHz high pass filter in the PZT drive which is otherwise flat. The resonance features above 5 kHz are believed to be the tombstones. I don't understand the extra motion from 1-2 kHz.
  
• Figure 2: PZT dither path zoom in. Since I want to dither the PZT to get an error signal, it helps to know where to dither. The ADC Anti-aliasing filter is a 3rd order butterworth at 10 kHz, so I looked for nice flat places below 10 KHz and settled on 8 kHz as relatively harmless.
  
• Figure 3: PZT LSC path. This path has got a 1^2:10^2 de-whitening stage in the hardware which hasn't been digitally compensated for. You can see its effect between 10 and 40 Hz. The LSC path also has a 160 Hz low path which is visible causing a 1/f between 200 and 500 Hz. I have no idea what the 1 kHz resonant feature is, though I am inclined to point to the PDH loop since that is pretty close to the UGF and there is much gain peaking at that frequency.
  

3  fsr =  33 195 439 Hz
12 fsr = 132 781 756 Hz
15 fsr = 165 977 195 Hz
18 fsr = 199 172 634 Hz

1.5 days of happy psl-ioo with litle bumps in C1:PSL-126MOPA_HTEMP

• Replace the cables from the board to the front panel connectors if this hasn't already been done.
  
• Replace the input opamps with 4131's. Be sure to test both positive and negative input signals.
  
• Check that all the compensation capacitors are in place and are 68 pF
  
• Make sure all the feedback loops have high frequency rolloff
  
• The ISS board reads the PDs differentially; make sure the PD sends differentially.
  
• Add a big (ie 10uF tantalum) capacitor to the PD to suppress power supply noise
  
• Add bigger power supply bypass caps to the ISS

# On Linux, "ezcastep" will interpret negative steps as command line arguments,
# because the GNU library interprets anything starting with a dash as a flag.
# There are two ways around this.  One is to set the environment variable
# POSIXLY_CORRECT and the other is to inject "--" as a command line argument
# before any dashed arguments you don't want interpreted as a flag.  The former
# is easiest to use here:

if (`uname` =~ m/Linux/) {
    # Add an environment variable for child processes
    $ENV{'POSIXLY_CORRECT'} = 1;
}

pushd /cvs/cds/caltech/users/tf/build/labca_2_1/bin/linux-x86
setenv PATH ${PATH}:`pwd`
cd /cvs/cds/caltech/users/tf/build/labca_2_1/lib/linux-x86
setenv LD_LIBRARY_PATH ${LD_LIBRARY_PATH}:`pwd`
popd

addpath /cvs/cds/caltech/users/tf/build/labca_2_1/bin/linux-x86/labca
help labca
foo = lcaGet('C1:PSL-FSS_RCTRANSPD')