Tagging this unique photo for EPO since these sorts of leak checks (on welds) you don't see everyday.  :)

I added a script to

... SusSVN/sus/trunk/HLTS/Common/FilterDesign/Estimator/

that uses autoquack to add the fits to the Foton file for H1 SR3.

The script is named

make_SR3_yaw_model.m

and it uses the fits mentioned in the logpost above, which are contained in the same folder, as

fits_H1SR3_2025-04-21.mat

The changes are current to the sus svn under revision 12277.

These filters have been loaded into the SR3_M1_YAW_EST_MODL_SUSP_Y_2GAP and SR3_M1_YAW_EST_MODL_DRV_Y_2GAP.

Attached are the plots that came up when I ran the matlab script that loaded them in, along with the log message that was created and the coeff diffs.

Small modification that will not affect the estimator test, so it is here for bookeeping.
I didn't clean up the zpk for the M1 to M1 transfer function, so it has a high frequency zero that is due to floating point errors in my fit.

the real zpks should be:

ST1 to M1

    'zpk([-0.068+20.398i,-0.068-20.398i,-0.099+11.454i,-0.099-11.454i,0,0],[-0.03+21.271i,-0.03-21.271i,-0.076+14.435i,-0.076-14.435i,-0.044+6.384i,-0.044-6.384i],-0.75)'

and M1 to M1

    'zpk([-0.089+8.28i,-0.089-8.28i,-0.113+19.058i,-0.113-19.058i],[-0.03+21.271i,-0.03-21.271i,-0.076+14.435i,-0.076-14.435i,-0.044+6.384i,-0.044-6.384i],71.17)'

I have uploaded the correct ones to the HLTS/Common/FilterDesign/Estimator with today's date (2025-04-23), svn revision 12279.

That filter change has been loaded in

Details and Methodology

Since the FARO decided it needed a Florida vacation we have to use the same alignment method employed during aLIGO install.  This is done using a total station for measuring X and Y axis position and ISI yaw, and an autolevel for measuring ISI height and level.

X Axis Position and Yaw

2 sets of crossed scales are used with the total station to make the required measurements.  These scales are mounted in such a way that one edge of the vertical scale lines up with the y-axis centerline of the ISI; a second scale is mounted horizontally to give a reading of the x-axis position of that location.  The 2 sets of scales are mounted to the outermost holes on the +Y and -Y side of the ISI, see the attached picture for an example (the right-most edge of the vertical scales are in line with the ISI y-axis centerline).  The -Y scale mount also has a mounting hole for a corner cube retroreflector, which gives us the ability to used the total station's Electronic Distance Measurement (EDM) function to measure the distance between the total station and the outermost -Y holes of the ISI.

There is a brass monument on the floor to the East of WHAM1 that the total station is set over; this is monument LV25, coordinates [-22726.7, -3050.7] mm.  The total station the sights monument LV26 (cooridnates [-2133.6, -3050.7] mm), which is down by WHAM4, and this line sets our horizontal angle to zero.  The total station is then turned -90° to point at the center of WHAM1.  We then use the total station to read the horizontal scale of each set of crossed scales to get a measurement to calculate x-axis position deviation and ISI yaw; the distance between the outermost holes, 2082.8 mm (taken from the SolidWorks model of the ISI), gives us the needed info to calculate the yaw.  Using the numbers for the final measurements from the above main alog as an example, the calculation looks like this:

• +Y scale reading: 0.0 mm
• -Y scale reading: +0.5 mm
• X axis position deviation: (0.5 + 0.0) / 2 = +0.25 mm
• Yaw: (0.5 - 0.0) / 2082.8 = 240 µrad CCW

Y Axis Position

A corner cube retroreflector is mounted to the -Y scale mount, designed in such a way so the measurement point of the corner cube lines up with the outermost row of holes.  From the SolidWorks model of the ISI this outermost row of holes is 1041.4 mm from the center of the ISI.  The total station occupies monument LV25, which has a y-axis coordinate of -3050.7 mm.  Since the ISI should be at a y-axis coordinate of 0.0 mm, we then use the total station's EDM function to measure the distance from the total station to the corner cube.  The target distance is the y-axis coordinate of monument LV25 minus the y-axis coordinate of the outermost -Y holes of the ISI, or |-3050.7 - (-1041.4)| = 2009.3 mm.  Using the numbers from the Initial measurements (since we did not take a final look at y-axis position yesterday afternoon) in the above main alog as an example, the calculation is:

• Total Station EDM: 2009.7 mm
• Target Distance: 2009.3 mm
• Y axis position deviation: 2009.7 - 2009.3 = +0.4 mm

Z Axis Position and Level

For the z-axis position deviation and ISI level we use an autolevel and a scale set at various points on the ISI.  The autolevel is set to +100.0 mm above the target ISI height using height mark 600 (on the East wall across from WHAM1).  From T1100187 the LHO local coordinate for this height mark is -249.7 mm.  We set a scale on this height mark, with 10.0 mm on the scale lining up with the height mark.  We can then calculate what scale reading required to set the autolevel at +100.0 mm above the target height of the ISI.  The LHO global z-axis coordinate for the WHAM1 ISI is -201.9 mm, but the height mark is in LHO local so we have to translate between the two coordinate systems.  This means we have to add 14.1 mm¹ to the LHO global coordinate to get the LHO local coordinate for the WHAM1 ISI; doing this, the LHO local coordinate for the ISI is -187.8 mm.  Now the delta between the WHAM1 ISI z-axis position and height mark 600 is calculated, then add 100.0 mm to that to set the autolevel 100.0 mm above the target ISI height; we have to also add 10.0 mm since that's where the scale was set on the height mark: |-249.7 - (-187.8)| + 100.0 + 10.0 = 171.9 mm.  So sighting 171.9 mm on the scale we mounted on height mark 600 puts the autolevel 100.0 mm above the target z-axis position of the ISI.

With the autolevel set, we then place a scale at several points on the ISI and use the autolevel to read the scale at each point.  The scale we have for this is in inches, and has tic marks at every 0.01".  Since the autolevel is 100.0 mm above the target ISI height we should be reading 3.94" (100.0 / 25.4 = 3.94) on the scale if the ISI is at the correct height; reading a lower number on the scale means the ISI is too high, and reading a higher number on the scale means the ISI is too low.  The scale is placed at the 4 corners of the ISI, with a reading taken at each point.  These 4 readings are averaged to give the height of the ISI table.  For the table level, the delta between the highest and lowest scale reading is used.  Using the numbers from the final measurements from the above main alog, this calculation looks like:

• -X/+Y scale reading: 3.905"
• -X/-Y scale reading: 3.915"
• +X/+Y scale reading: 3.915"
• +X/-Y scale reading: 3.915"
• Average: 3.913"
  • Z axis deviation: 3.94 - 3.913 = 0.027" => +0.69 mm
• Level: 3.915 - 3.905 = 0.01" => 0.25 mm

1: The 14.1 mm correction comes from removing the global x-axis tilt of -619.5 µrad, done by multiplying the x-axis tilt by the x-axis position of the WHAM1 chamber: -22726.7 * -.0006195 = +14.1 mm.

Tagging for EPO photos.

Adding a comment to talk about the L2P coupling in page 20. It appears as if we have a non-minimum phase zero that appears and dissappears between measurements [see page 20 of the original post above].

While I don't have a full explanation for this behavior, I remember seeing these shenanigans when I was testing the ISI feedforward many years ago. I was too young to make any coherent argument about it, but I remember seeing that the state of the ISI seemed correlated with the behavior. If the ISI is ISOLATED we have normal behavior, if it is DAMPED then we have the non-minimum phase behavior.

Here is a comparison between the last few years of successful ITMY  M0 to M0 transfer functions, with the ISI states retrieved from plotallquad_dtttfs.m. The color coding is selected to separate the situations with the ISI in 'ISO', and with the ISI in any other state. in pseudocode:

I got the same comparison done for ITMX and the ISI backreaction theory really does not seem to hold water.

There are two main regimes, same as ITMY. This time, the more recent ITMX TFs (after 2017-10-31) look more similar to the old (prior to 2021) ITMY TFs.

I am at a loss of what is making the change happen. Brian suggested it might be related to the vertical position of the suspension, maybe this is the next thing to test.

To back up Edgard's conclusion, I took measurments with the ISI in Fully Isolated and we didn't get the extra zero back 84083

J. Kissel

First, supporting Daniel's findings that the RM1 and RM2 HTTS OSEM sensor readbacks have been incorrectly negative for ages, I attach a trend of the OSEM ADC input values (and OSEMINF OFFSETS and GAINs) back to 2017.

Not said explicitly in the above aLOG -- Daniel / Fil / Marc installed fresh new DB25 Sat Amp to Vac Feedthru cables (D2100464) just after this aLOG as a part of cabling up the new signal chain for PM1. These cables are one-to-one pin-for-pin cables so it *should* have played no role in the sign of the sensors or how they're connected. 

However, it's now obvious that RM1 and RM2 have had the ADC input voltages as negative for a *very* long time. 

I reviewed the signal chains for the OSEM PDs; see G2500980.

The RMs are using a US 8CH satamps D1002818 / D080276.

I attach a screen-cap of page 4, which highlights that 
    - UK 4CH satamps D0900900 / D0901284 use 
        . a negative reverse bias configuration, with
        . anode connected to bias and cathode connected to the negative input of the TIA, and
        . an inverting differential amplifier stage
    - US 8CH satamps D1002818 / D080276 use 
        . a positive reverse bias configuration, with 
        . cathode connected to the bias and anode connected to the negative input of the TIA, and [hence the apparent "pin-flip" from the other two satamp types]
        . a non-inverting differential amplifier stage
    - US 4CH satamps D1900089 / D1900217use 
        . a negative reverse bias configuration, with
        . cathode connected to the bias and anode connected to the negative input of the TIA, and
        . a non-inverting differential amplifier stage [hence the overall "sign flip" from the other two]

I disagree with Daniel that "the polarity of the PD" i.e. how the anode and cathode are connected to the transimpedance amplifier.
All versions of the PD pinout + SatAmp configure the system in a reverse bias, be it negative or positive. 
In these configurations, even in a zero bias configuration, photocurrent always flows from from cathode to anode as light impinges on the PD. 
So if the anode is hooked up to the negative input of the transimpedance amp (as in D1002818), that signal will have a different sign than if the cathode is hooked up to the negative input (as in D0900900 and D1900089).

The RMs should have their *positive* bias from the D080276 circuit applied.
In 2011, we'd agreed in G1100856 to jumper all OSEM satamps to the "L" position, a.k.a. the LIGO OSEM a.k.a. AOSEM position, which uses a bias voltage and is thus in photo conductive or pc mode. This is mostly because we wanted to not have to think about keeping track of which satamps are jumpered and which are not, but also because the BOSEM PD didn't mind have a bias, even though it was designed to have no bias.

Given the "thought of 2nd to last, last, and never" history of the RMs as they traversed subsystem from ISC to SUS circa O1, moving from the ASC front-end to a SUS front-end circa O2, then never really appearing in wiring diagrams until O3, etc. it wouldn't surprise me if the RMs didn't get the memo to put the bias jumper in the "L" position jumpering pins 2 and 3.

I disagree with Daniel: only the US 4CH satamp D1900089 / D1900217 should read negative with light on it.

So, my guess is that that someone "in 2013" (i.e. during aLIGO install prior to O1) didn't understand these subtleties between the UK 4CH and US 8CH satamp, saw the "different from UK 4CH satamp" and tried fixing the pins of the in-air D25 from satamp to vacuum flange.

Regardless, the new cable has cleared up the issue, and ADC voltage from RM1 and RM2 is now positive.

I've attached a quick spectrum of SR3 yaw and pitch on M3 as seen by the optical lever. It's odd - the yaw looks very lightly damped - but the IFO was in observe. You can not see real motion above the 3.4 ish Hz yaw mode (it should be falling faster that 1/f^6). You might be seeing real motion between the peaks though - and we can use that (peaks at 1, 2.3, 3.4).

(environment was pretty quiet - BLRMS - EQ is 40-100 nm/sec, microseism is 200-400 nm/sec, wind speed below 1 m/s, anthropogenic is 20-30 nm/sec. It's 3 pm Saturday afternoon, local time. )

I've added 2 more plots. The first is to check that the Y damping is on, and it seems to be. This is a spectrum of the Y osem signal. Ignoring seismic input (which is completely fair), the signal here should just be yaw_osem_noise * (1/1-G) (the minus sign assumes you get all the loop gain signs directly from the control). You can see dips at the resonances, so the loop is on, and has some gain, but not much at the 1 Hz mode, more at 3.4 ish Hz. I've also added my yaw noise reference from G2002065 - you can see here that the noise is a bit larger than my estimate above 1 Hz.

LDVW shows that the gain on the M1_DAMP_Y control was already turned down to -0.5 at this time.

Here is a comparison of the spectra of three channels that can be used to monitor the performance of the estimator. We compare the motion when the M0 Yaw damping loop gain is at -0.5, versus when it is at the -0.1 (which is what we are aiming for with the estimator). The equivalent estimator plots should look somewhere in between the purple and blue curves in the images attached.

- The first one is the OPLEV on SR3. If the estimator works, we should be able to see a difference on the mode Qs. The oplev should see that we are able to damp (or control) the modes to the same level as the -0.5 damping.

- The second one is the M1 OSEM spectrum. The closed loop spectrum dips at the resonances of the plant at -0.5 gain (because of the sensitivity function), so we should be able to see that the sensitivity (as seen by the OSEM) is different, but the OPLEV sees good control of the modes.

- The third one is the total drive on M1. We should see that the total drive around the resonances is similar to the drive we get with the -0.5 gain, but the total drive should decrease rapidly above 3 or so Hz. We will need a faster channel than the one shown in the last attachment.

The plan is to make a full list of channels to monitor in conversation with Oli and Jeff, then run a pilot test with the fits from 84041 later in the week.

ECR E2400083
IIET 30642
WP 12453


Some "for the record" additional comments here:
- Sina refers to the "SPI-BS" above, which is the same as what we've now officially dubbed as "SPI-BS1."

- Lenses were identified to be needed after the initial measurement of the beam profile emanating from SPI-BS1. That initial beam profile measurement is cited in LHO:83956, and the lens also developed in JaMMT with the lenses that were available from the optics lab / PSL inventory.

- If anyone's trying to recreate the model of the beam profile from the two measurements (LHO:83956 with no lenses, and the above LHO:83983) just note that the "zero" position is different in the quoted raw data; in LHO:83956 is the front of the rail, on Column 159 of the table, and in LHO:83983 the zero position is the SPI-BS1 reflective surface which is on Column 149 of the table, i.e. a 10 inch = 25.4 cm difference.

- The real SPI-L1 installed to create this mode-shape / beam profile is labeled by its radius of curvature, which is R = 51.5 mm, and thus its focal length is more precisely f = R*2 = 103 mm. (We did find a lens that does have f = 60 mm for SPI-L2, and it's labeled by its focal length.)

- "the fiber" is that which is intended for permanent use, depicted as SPI_PSL_001 in the SPI optical fiber routing diagram D2400110, a Narrow Key PM-980 Optical Fiber "patch cord" from Diamond, whose length is 30 [m]. This fiber will run all the way out to SUS-R2, eventually, to be connected as the input to the SPI Laser Prep Chassis (D2400156).

- Per design, light going into this fiber is entirely p-pol, due to polarization via SPI-HWP1 and clean-up by SPI-PBS01 just upstream. We did not measure the polarization state of the light exiting the fiber.

- The raw data that informs the statement that "the power transmission thru the fiber has been measured to be 83%":
     : We measured the input to the fiber coupler, SPI-FC1, via the S140C low-power power meter we'd been using throughout the install. The output power was measured via a fiber-coupled power meter Sina had brought with her from Stanford (dunno the make of that one).

     : We measured the power input to the fiber twice several hours apart (with the change in fiber input power controlled via the SPI-HWP1 / SPI-PBS01 combo).,
         (1) 19.9 [mW] with PMC TRANS power at 104.1 [W] at 2025-04-17 16:35 UTC (while the PMC power was in flux from enviromental controls turn on)
         (2) 180 [mW] with PMC TRANS power at 103.5 [W] at 2025-04-17 14:00 UTC (while the PMC power was quite stable)

     : We measured the output power
         (1') 16.6 [mW] with PMC TRANS power at 103.7 [W] at 2025-04-17 17:35 UTC (an hour later than (1))
         (2') 150 [mW] with PMC TRANS power at 103.5 [W] at 2025-04-17 14:00 UTC (simultaneous to (2))

     : Thus derive the transmission to be 
         (1'') (16.6 / 19.9) * (104.1/103.7) = 0.837 = 83.7% and 
         (2'') (150 / 180) * (103.5/103.5) = 0.833 = 83.3%

In the attachment you will find the JAMMT model for the measured beam profile of the PSL pick off with the origin a SPI-BS1, as well as the lenses used to adjust the mode of the beam for the fiber collimator FC60-SF-4-A6.2-03.

Small correction to above is after installing SPI-HWP1 and SPI-PBS01, we adjusted HWP1 to have 20mW in transmission of PBS1 (not maximum quite yet) to start alignment into the fiber. Using the two steering mirrors downstream of PBS1 and the collimating lens in front of the fiber, Sina maximized the transmission as measured with the output of the fiber on a spare PD. We then took power measurements of the input and output of the fiber:

• Input: 19.4mW
• Output: 13.5mW
• Transmission ratio: 72.1%

This is a good start, but with a target ratio of >80%, there's still more work to be done here improving the beam into the fiber collimator. Out current mode-matching solution claims we should have 95% mode overlap into the fiber, so hopefully the issue is alignment, but it's entirely possible we'll revisit the mode-matching to see if improvements can be made there too.

The attached photo represents the optical layout as it stands as of where we stopped today, with the new SPI fiber in blue on the left (north) side of the table.

Re-post of Ryan's picture at the end of day 2, labeled with the almost entirely complete SPI pick-off path.

Critically here, this shows the PSL row/column grid, confirming that this whole ECR E1900246 ALS pick-off path is 2 rows "higher" in +Y than is indicated on the current version of the as built PSL drawing D1300348-v8.

Ryan grabbed another picture I attach here. This shows the ALS pick-off path on this day in order to support the identification that the beamline between ALS-M1, through the faraday ALS-FI1 and ALS-L1, etc stopping at ALS-M2 (not pictured) is on row 25 of the PSL table *not* row 23 as drawn in D1300348-v8. I attach both the raw picture and my labeled version. So, ya, ALS-M1 should have its HR surface centered on Row 25, Col 117.

Note, the grid in the picture is labeling bolt holes. Because the optical elements are all ~4 inches above the table, the beams appear offset from the way they travel on along the grid given that the photo was taken at a bit of an angle from vertical. May the future updater of D1300348 bear this in mind.

Just a quick trend of the SM1PD1A EXTERNAL PD in transmission of ALS-M9 after they throttled the s-pol power in the ALS/SQZ/SPI path to ~10 [mW]. 
In that trend, you can see the different in "lights on" vs. "lights off" highlighted with the magenta vertical lines.

Note, as you can see in the picture, the reflection of ALS-M9 is dumped so as to not have to think about how much power is or is not going into the ALS/SQZ fiber distribution collimator (ALS-FC2), so the INTERNAL monitor PD that's in the distribution chassis itself is "correctly" unexpectedly reading nothing, so I don't show it.

Correction to the last sentence of the main entry -- the ALS/SQZ fiber collimator is *not* an, but instead a Thorlabs Fiber Port PAF2-5A, pictured well in FinalInstall_ALSfiber.jpg from LHO:83989.

I had incorrectly assumed that this collimator would be a copy of ALS-FC1, which *is* listed in E1300483 as an F220 APC-1064.

In the attachment you will find the fit with JAMMT to the measured beam profile data with offset correction:

• Offset of measurement point to SPI-BS1: 10.2 cm
• Offset of measurement point to beam profiler surface: 7.3 cm

Before we started, Betsy and I replaced the septum plate VP cover we had removed yesterday 83798. 

Layout before: D1000313-v15

Added photo of myself, Betsy, Melina and Elenna before the HAM1 ISC removal work started. 

I had a brief look at some of this data to put bounds on losses and arm power in 83953:

The first attachment shows a plot of more of this data against models, focusing on the unexplained low frequency noise that we don't see with the filter cavity . The measured NLG matches the NLG infered from anti-squeezing and squeezing for the NLG 19 measurements, but for the NLG 35 measurements the infered NLG is 27.3, so that is what I've used here.  As Camilla wrote above, the NLG 35 measurements were made with a different SRC detuning than NLG19, so that is included in this model.  Squeezing angles are fit to the band from 2100 Hz to 2300 Hz. 

The first plot shows the measured data in solid lines, the quantum noise model in dashed lines, and the dotted lines show the non quantum noise from subtraction added to the quantum noise models.  There is a discrepancy where many of the measurements seem to have extra noise from 20-50 Hz, I've tried to make an easier to read version in the second plot, and finally removed some traces to try to make it easier to see.

In the above alog we thought perhaps that this could be explained as an excess noise that was larger with higher nonlinear gain but consistent with squeezing angle, the last attachment shows the residuals between the model and measurement for the measurements that had clear discrepancies, they all seem to be different, so this excess seems to depend both on squeezing angle and nonlinear gain. 

The script used to make these plots can be found at this repo

Here's a brief explanation of what was done.

Top left panel of the 1st attachment is the mode matching loss contour plot. loss=0 when [posDiffNormalized, sizeDiffNormalized]=[0.0]. Contours are not circular because the loss is calculated analitically, not by quadratic approximation.

Top right panel of the 1st attachment only shows the region close to the measured losses. Yelllow ring is when OM2 is cold, blue is when hot. Each and every point on these rings represent a unique waist size and waist position combination (relative to the OMC waist).

Since we are supposed to know the OMC-OM2 distance and ROC of the cold and hot OM2, you can choose any point on the yellow (cold) ring, back-propagate the beam to the upstream of OM2 (assuming the cold ROC), "heat" the OM2 by changing the ROC to the hot number, propagate it again to the OMC waist position, and see where the beam lands on the plot. If it's on the blue ring, it's consistent with the measured hot loss. If not, it's inconsistent.

Just for plotting, I chose 9 such points on the cold ring and connected them with their hot landing points on the top right panel. If you for example look at the point at ~[0, 0.4] on the plot ("beam too big but position is perfect when cold"), after heating OM2 the beam becomes smaller but the beam position doesn't change meaningfully, therefore the matching becomes better. In this case the improvement is much better than the measured (i.e the landing point is inside the blue ring), so we can conclude that this ~[0, 0.4] for cold is inconsistent with the measured hot loss.

By doing this for each and every point on the yellow ring we end up with a patch or two that are consistent with reality.

If you cannot visualize what's going on, see the 2nd attachment. Here I'm ploting the beam propagation of "beam too big but position is perfect when cold" case in the top panel. The beam between the OM2 and OMC is directly defined by the initial (cold) parameters. The beam upstream of the OM2 is back-propagation of that beam. On the bottom panel is the propagation diagram of when OM2 becomes hot. The beam upstream of OM2 is the same as the cold case. You propagate that beam to the OMC position using hot ROC. In this case the loss, which was ~12% when cold, was improved to 4.3%, that's inconsistent with the measured hot loss of (1+-0.1)*6.2%.

Further summary:

We can probably down-select the patch by 30uD single-path thermal lensing in ITM comp plate relative to the thermal lensing we had in previous scans (alogs 70502 and 71100). Start by a hot OM2. If we see a significant reduction in MM loss after ITM TCS, the actual beam parameters are on the patches in the left half plane.

Details 1:

In the 1st attachment, I took two representative points on the hot patches indicated by little green circles, which define the beam shape at the OMC waist position. I then back propagated the beam to the upstream of ITM (i.e., in this model, optics are correctly placed with correct ROC and things, but the input beam is bad). ITM is at the average ITM position. The  only lensing in the ITM is the nominal diversing lens due to ITM's curvature on the HR.

Then I added the thermal lens, once to the beam impinging the ITM HR and once to the beam reflected, and see what happens to the beam parameter at the OMC waist location. These parameters are represented by tiny crosses. Blue means negative diopters (annular heating) and red means positive (central heating). I changed the thermal lensing by 10uD steps (single-path number).

As you can see, if you start from the left half plane patch, central heating will bring you close to ~(-0.04, 0) with 30uD single-path (or 60uD double-path).

OTOH if you start from the right half plane, ITM heating only makes things worse both ways.

FYI, 2nd plot shows, from the left to the right, good mode matching, hot patch in the left half plane and in the right half plane. The beam size on the ITM is ~5.3cm nominally, 5.1cm if in the left half plane (sounds plausible), 6.8cm in the right (sounds implausible). From this alone, right half plane seems almost impossible, but of course the problem might not be the bad input beam.

Details 2:

Next, I start with (almost) perfectly mode-matched beam and change the optics (either change ROC/lens or move) to see what happens. We already expect from the previous plots that ITM negative thermal lensing will bring us from perfect to the hot patch in the left half plane, but what about other optics?

3rd attachment shows twice the Gouy phase separation between ITM and other optics. Double because we're thinking about mode matching, not misalignment. As is expected, there's really no difference between ITM, SR3 and SR2. OM1 is almost the opposite of ITM (172 deg), so this is the best optic to compensate for the ITM heating, but the sign is opposite. OM2 is about -31 deg, SRM ~36 deg. From this, you can expect that SR3 and SR2 are mostly the same as ITM as actuators.

4th attachment shows a bunch of plots, each representing the change of one DOF of one optic. (One caveat is that I expected that the green circles, which repsent the beam perfectly mode matched to the arm propagated to the OMC waist position, will come very close to (0, 0) with zero MM loss, but in this model it's ~(-0.4, 0.1) with ~1.2% loss. Is this because we need a certain amount of ITM self-heating to perfectly mode match?)

Anyway, as expected, ITM, SR3, SR2 all look the same. It doesn't matter if you move the position of SR3 and SR2 or change the ROC, the trajectory of the beam parameter points on these plots are quite similar. These optics all can transform the perfectly matched system to the blue patch in the left half plane.What is kind of striking, though not surprising, is that 0.025% error in SR3 ROC seem to matter, but this also means that that particular error is easily compensated by ITM TCS.

SRM, OM1 and OM2 are different (again as expected). Somewhat interesting is that if you move OM2, the waist size only goes smaller regardless of the direction of the physical motion.

From these plot, one can conclude that if you start from perfectly matched beam, you cannot just change one optic to reach the hot patch in the right half plane. You have to make HUGE changes in multiple optics at the same time e.g. SRM ROC and ITM thermal lensing.

Both Details 1 and 2 above suggest that, regardless of what's wrong as of now (input beam or the optics ROC/position), if you apply the central heating on ITM TCS and see an improvement in the MM loss, it's more likely that the reality is more like the patches on the left, not right.

Dan pointed me to their SRC single-path Gouy phase measurement for the completely cold IFO, which was 19.5+-0.4 deg (alog 66211).

In my model, 2*Gouy(ITM-SRM single path) was ~36deg, i.e. the SRC single-path Gouy phase is about 18 degrees. Seems like they're cosistent with each other.

ITM central heating plot was updated. See attached left. Now there are four points as the "starting points" without any additional TCS corresponding to both hot and cold patches.

According to this, starting with cold OM2, if the heating diopter (single path) is [0, 10, 20, 30, 40]uD, the loss will be [11.5, 7.1, 3.5, 1.1, 0.1]% if the reality is in the left half plane (attached right, blue), or [11.5, 9.9, 10.5, 13.1, 17.3] % if in the right half plane (attached right, red).

Updated to add cold OM2, ITMY single bounce, central CO2 OFF/ON case in alog 71457.

Jennie Wright, Keita Kawabe, Sheila Dwyer

Above Keita says "I assumed that the distance between OM2 and OMC waist is as designed (~37cm). "  37 cm is a typo here, the code actually uses 97 cm, which is also the value listed for OMC waist to OM2 in T1200410