I used the CO2 profile measurement in aLOG 65382 to estimate the average radial CO2 intensity profile on the CP. The spatial scale on the CP was determined by using the 16 axial nodes in the HWS measurement in aLOG 65436 as fiducials to estimate the diameter on the CP. 

From this, I ended up with an average radial profile for intensity for the annular CO2 laser - which, when normalized to deliver 1W, looks like the following.

I put this into a 2D axially symmetric model of the coupled ITM+CP system in COMSOL and worked out the transient response for the defocus. The response looks like the following:

From this response, we estimate the steady-state defocus and can fit a weighted sum of exponential decays to the normalized response. The fitted time constants, tau, correspond to the poles in the transient response function, where the poles are 1/(tau*2*pi).

The COMSOL model predicts peak after about 2-3 hours and a slow decrease over 24 hours to settle around -9uD/W.

Steady state defocus = -8.91uD/W
amplitude = [-1.571, -0.846, 1.417]
tau = [798.6s, 7756.6s, 26491.9s]
poles = [199.30uHz, 20.52uHz, 6.01uHz]

Normalized response = 1 + sum[ amp(ii)*exp(-t/tau(ii) ) ]

The transient output of the annulus can be estimate by a weighted sum three single-pole LPF, where the weighting for each pole is just the "a" values given in the previous aLOG.

These are single-pass values.

Attaching the analysis used.

Note on the absolute power level for this simulation: it's a little unclear how to normalize the amount of power in the CO2 intensity profile. There is the power on the thermopile to consider, the aperture of the CP to consider (some power is lost as it falls off the edge of the CP) and the missing bits of the intensity on the paper on the camera. This will result in a calibration error in the magnitude in the simulation - the time constants should be relatively unaffected though.

Translated this into the following filter function: zpk([2.837e-05;2.691e-06],[6.01e-06;0.0001993;2.052e-05],1,"n")

Attached is the filter step response as given by foton in blue (red is the previsouly loaded filter.

New filters loaded into H1:TCS-SIM_ITMX_SUB_DEFOCUS_CO2_AN and H1:TCS-SIM_ITMY_SUB_DEFOCUS_CO2_AN at FM6.

FYI, the optical lever damping loop open loop gain transfer functions were taken with the M2 (triple acquisition, or TACQ) coil driver set to state 2 (ACQ ON, LP OFF), and -- importantly -- the optical lever damping loop filter bank limiters, H1:SUS-BS_M2_OLDAMP_P_LIMIT and H1:SUS-BS_M2_OLDAMP_Y_LIMIT is OFF (it's nominally set at 99e3 [ct]).

How to turn off RFSBs.

Disconnect the cable for 118MHz on the patch panel at the bottom of the PSL rack (1st picture).

On top of the patch panel there's a 24MHz amplifier, don't turn it off.

On top of the 24MHz thing, there are amplifiers for 9MHz and 45MHz. You will turn off the output of both (2nd picture showing the 45MHz unit with the RF output switch in OFF position).

If we just believe TCS frontend simulation, H1:TCS-SIM_ITMY_SUB_DEFOCUA_FULL_SINGLE_PASS_OUTPUT was ~17.05uD during the last OMC scan before we gave up.

We might be able to use this to distinguish between the two patches in the MM parameter space (update in https://alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=71477) but I'll wait for the OMC scan fitting results.

Executive Summary: The mode mis-match with no central heating on the ITM is 8.2%, the mode mis-match with central heating on the ITM is 3.6%.

For the first scan:

T0 = 1373734011

delta T = 87s

OMC scan is shown in the first png image.

Fitted C20/02 peak is shown in the first pdf.

We expect the HOM spacing to be 0.588 MHz as per this entry and DCC T1500060 Table 25.

The mode spacing is 148.796 - 149.388 = 0.592 MHz.

The ratio of second order to zeroth order carrier is (0.575 + 0.853)/(0.575 + 0.853 + 15.90) = 0.082 = 8.2 % mode mis-match

To run the code checkout git branch /dev of labutils and run measurement.

python OMCscan_nosidebands3.py 1373734011 87 "Sidebands off, 10W input, cold ITM + OM2" "single bounce" --verbose -m -o 2

and for the split peak fitting:

python fit_two_peaks_no_sidebands3.py

For the second scan:

T0 = 1373736206

delta T = 90s

OMC scan is shown in second png image.

Fitted C20/02 peak is shown in the second pdf.

The mode spacing is 148.741 - 149.338 = 0.597 MHz.

The ratio of second order to zeroth order carrier is (0.201 + 0.428)/(0.201 + 0.428 + 17.02) = 0.036 = 3.6 % mode mis-match

Run the following on the same git branch.

python OMCscan_nosidebands4.py 1373736206 90 "Sidebands off, 10W input, hot ITM + cold OM2" "single bounce" --verbose -m -o 2 -p 0.01

and for the split peak fitting:

python fit_two_peaks_no_sidebands4.py

data is in labutils/omc_scan/data/2023-07-18

files in labutils/omc_scan

figures in labutils/omc_scan/figures/2023-07-18

Summary:

Incorporated the fit results and updated the plot. Original analysis is in alog 71145.

In the attached, there are two pairs of patches, each pair comprising yellow and lighter blue, that represent the previous measurement (alog 71145 where ITMX single bounce was used with no TCS, OM2 hot/cold) and two pairs, each pair comprising greenish blue and darker blue, that represent the measurent done this time (ITMY single bounce, cold OM2, TCS ON/OFF).

Since it's impossible that the beam parameters of ITMX single bounce beam on the OMC are totally different from those of ITMY single bounce, you can just look at the distance between pairs and judge which ones represent the reality. In this case, the patches in the left half plane are the clear winners.

Details and caveats:

Calculation done for the ITMY single bounce is exactly the same as ITMX except that the measured losses are different and the mode actuator is ITMY central TCS instead of OM2.

As for the TCS optical power I  used H1:TCS-SIM_ITMY_SUB_DEFOCUS_FULL_SINGLE_PASS_OUTPUT~17uD for the central heating (zero for no heating). I simply doubled the number for double-pass effect. If this is grossly off the result might look different.

Since 1st order HOM power was not negligible in ITMY single bouncer scan, as a first order approximation, I used P2/(P0+P1+P2) as the measured mode matching loss where P0, P1 and P2 are the power of 00, 1st order and 2nd order mode (for the 2nd order mode, 20 and 02 were resolved by the fit code). I've done this to ITMX single bounce scan too just for consistency.

If the model is perfect and has everything, the difference between yellow "X, OM2" and greenish-blue "Y, OM2 Cold/TCS OFF" should be explained by the difference in the ITM ROC, substrate lensing/heating including the TCS (and IFO heating prior to lock loss, since we haven't waited for hours and hours after the IFO was unlocked). It would be interesting to see if ITM difference will make the plot look any different.

However, the model doesn't have ITMX and ITMY, it's just a single ITM at the average location. Though it's easy to implement that feature in principle, I have a suspicion that the numbers used for ITM substrate lens effect in the past could be off, and I've contacted GariLynn. Wait for the conclusion of that discussion.

A big caveat is that you cannot quickly draw conclusion about the full IFO mode matching from this. At the very least, you have to take into account that the arm mode is primarily determined by the HR and that the carrier coming to OMC from inside the arms only experience the ITM lensing once (-ish).

Another big caveat is that the ADC was railing for the 00 mode peak. Look at the 2nd attachment bottom where H1:OMC-DCPD_B_STAT_MIN=-(2^19). It's not as bad as the finesse measurement (alog 71888) as the scan was slower, but if we want a better data we need to redo it with lower power or w/o x10 gain.

Last attachment shows what happens when you change OM2 (left, 1 step in the plot = maximum range of the T-SAMS) or ITM heating (right, 1 step = 10uD single pass).

It appears that the VALID channel had not been added to the DAQ for the cameras migrated prior to this one. I told Dave and he is adding it now.

After the change of ETMY camera server, the sign of camera servo PIT3, which uses the ETMY camera, seems flipped. I changed the PIT3 gain from 300 to -400 in lscparams.

These are the plots for HAM2, only did X,Z,RY, and RZ. X and Z injections were ~2/3rds the amplitude of the LLO injections.

HAM3.

Here's pictures of WHAM1-D4

Here's pictures of WHAM1-D5

Here's pictures of WHAM1-D6

Here's pictures of WHAM1-D1

Here's pictures of WHAM1-D2
(which is in-between and beneath HAM1 and HAM2 which butt up against each other, so the pictures kinda stink. Sorry! But, it looks like there's quite litte on this feedthru anyways).

Here's pictures of WHAM1-D3

Here's pictures of WHAM1 "East" (-Y) door

Here's pictures of WHAM1 "South" (-X) door

Here's pictures of WHAM1 "West" (+Y) door
(with a lot of bellows going to ISCT1.)

Thanks Jeff for those pictures. I added a link to this alog from the WHAM1 flange layout: https://dcc.ligo.org/D1002872-v8 for reference.
If you spot any additional redlines from the posted -v8 'D1002872-v7-redline.pdf', please add them to the DCC.

Here's pictures of the feedthrus on the top WHAM1
The first three pictures (619-621) are viewed on a ladder in front of the "East" (-Y) door, looking toward the +Y direction.
The second two pictures (622-623) are viewed on a ladder in front of the the "South" (-X) door, looking toward the +X direction.

Here's the measurement of the DHARD_Y plant, together with a fit. The peak at 2.6 Hz is not yet well resolved, so we should target it with some additional noise injections.

Z, P, K of the fir in s-domain:

z = [-0.95136101+11.64945547j, -0.95136101-11.64945547j,
     -0.36478703 +3.20366341j, -0.36478703 -3.20366341j,
     -1.14203036 +0.27714772j, -1.14203036 -0.27714772j]
p = [-0.59076912+17.94263255j, -0.59076912-17.94263255j,
     -0.52161196+15.28151683j, -0.52161196-15.28151683j,
     -0.18999281 +6.5798622j , -0.18999281 -6.5798622j ,
     -0.41593773 +2.9252335j , -0.41593773 -2.9252335j ,
     -2.64441872 +0.j        , -0.0852773  +0.j        ]
k = -129105.8425258189

Here are the plots of ASC-AS_C_NSUM, OMC-QPD_A_NSUM, OMC-QPD_B_NSUM and OMC-REFL_A_LF, during these measurements. ASC-AS_C_NSUM shows between 22.8 and 32.1mW, OMC-QPD_A_NSUM 23.4mW, OMC-QPD_B_NSUM 23.0mW, and OMC-REFL_A_LF 24.8mW. According to Keita OMC-REFL_A_DC has an incorrect calibration and shows 25.2mW. The average of the 2 QPDs would be 23.2mW, which is about 6.5% lower than 24.8mW.

Second screen shots shows a time when the IMC was unlocked. The DC offsets are in the 10s of uW at most.

Using data from the scan I adapted labutils/OMCscan class to plot the fitted scan and adapted labutils/fit_two_peaks.py to fit a sum of two lorentzians functions for distinguishing carrier 20/02 modes.

The first graph is the OMC scan plot, the second is the curvefit for the second order carrier modes.

We expect the HOM spacing to be 0.588 MHz as per this entry and DCC T1500060 Table 25.

The spacing for the modes measured is 0.592 MHz.

From the heights of the two peaks this suggests mode-mismatch of the OMC to be C02+C20/C00 = (0.83+1.158)/(15.32+0.83+1.158) = 11.0% mode mis-match.

From the locked/unlocked powers on the OMC REFL PD the visibility on resonance is 1-(3.51+0.03/24.73+0.03) = 85.7% visibility.

If the total loss is 14.3%, this implies that the other non mode-matching losses are roughly 1.3%.

To run the OMC scan code go to 

/ligo/gitcommon/labutils/omc_scan/ and run 

python OMCscan_nosidebands.py 1370712036 100 "Sidebands off, 10W input" "single bounce" --verbose --make_plot -o 2
in the labutils conda environment and on git branch dev.

To do the double peak fitting run:

python fit_two_peaks_no_sidebands.py  
in the labutils conda environment and on git branch dev.

These scans were done with OM2 cold.

For comparison with new OMC measurements I used Sheila's code to process the visibility, but updated dit to use nds2utils instead of gwpy as I was having trouble using it to get data.

The code is attached and should be run in the nds2utils conda environment on the CDS workstations.

Power on refl diode when cavity is off resonance: 24.757 mW

Incident power on OMC breadboard (before QPD pickoff): 25.239 mW

Power on refl diode on resonance: 3.525 mW

Measured effiency (DCPD current/responsivity if QE=1)/ incident power on OMC breadboard: 70.4 %

assumed QE: 100 %

power in transmission (for this QE) 17.760 mW

HOM content infered: 13.472 %

Cavity transmission infered: 82.111 %

predicted efficiency () (R_inputBS * mode_matching * cavity_transmission * QE): 70.367 %

omc efficency for 00 mode (including pick off BS, cavity transmission, and QE): 81.323 %

round trip loss: 1605 (ppm)

Finesse: 371.769