[Louis, Elenna, with input from Sheila, Daniel, others] 

Elenna and I measured the PRC Gouy phase using the inertial kick technique used by Stefan et al in the past. Some relevant links to past PRC inertial kick measurements are 52504, 66215. Elenna's alog from a few days ago describing the SRC gouy results is also very relevant: 92136. 

We measure the single pass Gouy phase in the PRC to be 17.78° +/- 0.02°.

This differs from the most recent measurements in 2022 (66215, 20.66° +/- 0.17°) by about 2.88° and from the 2019 measurements (52504, 23.23° +/- 0.17°) by about 4.45°. 

Ring heaters were set to 0W during this test (92075).

Procedure

We followed the 'Measurement2' procedure from 52504. It took a few tries to get it right. We used H1:LSC-PRCL2_OUT as a trigger channel. We used an offset of -1e6 and used the engagement of said offset as the data start time. We got 5 kick measurements, ranging from 5 - 13 FSRs (page 1 of prc_gouy_sept_2026.pdf). 

The diaggui templates we used live as ~elenna.capote/inertial_gouy/PRC_gouy_kick<1-5>.xml. Those templates have a lot of channels. The primary channel used in my analysis is H1:LSC-POPAIR_B_LF_OUT. Unfortunately I did not get the corresponding IOP fast channel for that channel. It's not necessary but would have been nice to have to get more samples across each of the resonances. I did record the fast channel POPX segment data for future followup. 

I have a few thoughts on how we can get a better measurement next time there's an opportunity to repeat this. I'll state some brief comments here to remind future me to expand on this more clearly: 1.) it would be great to *not* feed REFL to PRCL during the measurement, 2.) we should revisit trying to hold MICH on a dark fringe instead of continuing to let it actuate during the swing, 3.) we should use the trigger method we used for SRC to get a more deterministic measurement, 4.) do we really need full PRMI to get this measurement?

Data Extraction 

I exported the trigger (LSC-PRCL2_OUT) and readback (LSC-POPAIR_B_LF_OUT) channel data to txt files stored at ~elenna.capote/inertial_gouy/prc_data/. There is a short description of what each txt file is in notes.txt. The processing script is at analyze.py in the same directory. It is also on gitlab.

Comments on Results

Before I started writing alog entry, I was quite concerned with the result of ~18° mostly because it seems like such a large deviation from the ~23° measurement from 2019. I didn't appreciate that the more recent 2022 measurement is much closer at 20.66°. As a sanity check for myself, I used my analysis script to process a subset of one of the preceding gouy measurements to make sure that I get a similar answer. I processed one of the 2019 measurements from 52504 and uploaded the resultant plot to prc_gouy_52504_sanity_check.pdf. My result is within 0.1° of what's reported in that entry. 

I don't yet have a good explanation for why the gouy phase has changed this much. The most 'obvious' thing to point at is the new bigger beam splitter. Sophie and I are planning to run some tests with Finesse this week to figure out what amount of lensing (presumably at the BBS) would account for the delta in gouy phase we're seeing in the PRC and SRC. 

In the attached prc_gouy_sept_2026.pdf I have several diagnostic plots: 

- Page 1: time series of each of the 5 measurements. vertical counts is from POPAIR_B_LF_OUT.
- Pages 2-6: overlays in time and fractional FSR spacing for each measurement set. both subplots are aligned so the 00 peaks lay at the horizontal origin. The temporal overlays indicate that the PRM was accelerating throughout the measurement. The changing velocity had to be accounted for. The FSR overlay shows the 01+10, 02+20 modes line up pretty well after using a cubic spline on the velocity. I believe the bump at 0.5 FSR could be the sidebands. 
- Page 7: the speed of the PRM through each measurement set (kick). The speed is evaluated at the mid point between each set of successive 00 peaks. 
- Page 8: displacement of the PRM across each measurement set (kick) as a function of time elapsed since the first 00 peak.
- Page 9: measured single pass gouy phases for each measurement set. The black horizontal line is the mean of the means and the gray shaded region spans mean +/- std mean error. The kick2 and kick3 measurements both contain outliers that deviate from the rest by more than their errorbars. This kind of thing can likely be tightened up by 1.) carefully retaking the measurement in a more deterministic configuration and/or 2.) being more careful of how I'm handing the changing velocity & identifying the peak centers through each swing. The contributed biases due to these outliers is nowhere near large enough to account for the change in phase being measured (~3-5°).

Some relevant links: 

- Stefan's 2019 measurement (52504) 
- Stefan's 2022 measurement (66215) 
- Our SRC gouy measurement from last week (92136) .