On April 10, 2023 I ran another mod depth test during a long 78 W input power lock.
I've been doing this to estimate the total IFO carrier reflection, and from that estimate the total IFO losses and arm power.

Recently we've been wondering about what the 9 MHz is doing, since it seems to be decaying rapidly as we power up, similar to O3 but way less bad (alog 68531).
Worse, the PRG and PRCL gain are anticorrelated which makes very little sense.  

This alog is meant to provide a measure of the 9 MHz PRG and reflection.  We can later use these estimates to estimate loss, and how it is changing with thermalization (if we run a mod depth test early in a power-up, or at 2 W).

Results
Power-recycling gains for sidebands and carrier

9 MHz PRG = 55.0
45 MHz PRG = 21.5
Carrier PRG = 43.1

Reflection ratios for sidebands and carrier

9 MHz reflection ratio = 0.194
45 MHz reflection ratio = 0.363
Carrier reflection ratio = 0.060

Thermal state at the time of measurement (1365174767-1365175057)
Input power
PSL requested input power       H1:IMC-PWR_IN_OUT16            : 77.596 W    
Input power incident on PRM     H1:IMC-IM4_TRANS_NSUM_OUT16    : 73.923 W    

PRG
Power recycling gain            H1:LSC-PR_GAIN_OUT16           : 42.903 W/W  

Reflected power
LSC REFL A DC power             H1:LSC-REFL_A_LF_OUT16         : 8.195 mW   
LSC REFL B DC power             H1:LSC-REFL_B_LF_OUT16         : 8.230 mW

Ring Heaters
ETMX ring heater upper power    H1:TCS-ETMX_RH_UPPERPOWER      : 1.365 W    
ITMX ring heater upper power    H1:TCS-ITMX_RH_UPPERPOWER      : 0.720 W    
ETMY ring heater upper power    H1:TCS-ETMY_RH_UPPERPOWER      : 1.368 W    
ITMY ring heater upper power    H1:TCS-ITMY_RH_UPPERPOWER      : 0.000 W    

CO2s
CO2X power monitor              H1:TCS-ITMX_CO2_LSRPWR_MTR_OUT16 : 1.686 W    
CO2Y power monitor              H1:TCS-ITMY_CO2_LSRPWR_MTR_OUT16 : 1.698 W  

Method
Very briefly, by changing the mod depths you can get the RF power to total DC power ratio incident on a PD.
Then, by estimating the LSC POP and REFL diode path efficiency you can estimate how much power was in the IFO at a time, e.g.

RF_9_PRG = 9 PRC power / 9 input power = (ratio 9 RF POP diode * total DC power on POP diode / efficiency of PRC to POP path) / (ratio 9 RF input power * total DC input power)


I tried using the POP path efficiency from alog 63154, updated for the HAM1 vent changes to be TransPR2 * Trans_M12 = 1.236e-5, but it gave me PRGs that were way too low.
So instead I estimated what the the POP path efficiency was by assuming our normal PRG = Total DC PRC / Total DC Input = 42.9 W/W was correct, which set the POP path efficiency to be 1.05e-5.  
This value was then used to estimate the PRGs for sidebands and carrier.
In all, the POP path efficiency was not that far away from what we might have expected.
This PRG-based POP path efficiency agrees better with what Peter calculated at 40W full power (alog 62936).



analysis code
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/ligo/gitcommon/labutils/mod_depth_up_down_test/code/mod_depth_analysis.py

alogs
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1. HAM1 measurements: alog 63510
2. REFL path efficiency calc (from HAM1): alog 66432
3. POP path efficiency single bounce (from before vent): alog 63154
4. M12 replacement during HAM1 vent (trans 54% of what it used to be): alog 63523
5. Keita's summary of replaced HAM1 vent optics: alog 63625
6. Peter's POP path efficiency at full power: alog 62936