I made plots of anti-symmetric power P_AS vs. power at reflected port of OMC P_OMC_REFL during the DARM offset step measurement on September 4th, (see LHO alog #86785 and 87629).
I had to use the Beckhoff reported power for this (H1:OMC-REFL_A_DC_POWER) as the front-end channel is calibrated wrongly (see LHO alog #87648).
I also plotted the P_OMC_REFL vs. P_DCPD, ie. reflected vs. transmitted power for the OMC.
The plots for our two measurements taken at different times during IFO thermalisation are below, both were taken when OM2 was hot.
I reran these plots as the axis limits of the P_REFL vs. P_DCPD plot were wrong and were cutting off end point, plus removed line that explained what the y-intercept was for each plot as different dependent on whether we plot P_REFL vs P_AS or P_REFL vs. P_DCPD.
I also switched the P_REFL channel being used in my code to H1:OMC-REFL_A_DC_POWER from H1:OMC-REFL_A_DC_POWERMON as this latter channel has a factor of 100 relative to the former that I don't really undestand. The DC_POWER channel seems to give a realistic reading for the OMC reflected power that is much less than the power into HAM6.
First link contains two plots when we were half-way thermalised:
First plot is power at the OMC reflected PD vs. power at the antisymmetric port (calibrated into the power into HAM6) for the case where we were 1Hr 25 mins into lock.
Second plot is power at the OMC reflected PD vs. power transmitted to the DCPDs for the case where we were 1Hr 25 mins into lock.
The second link contains two plots also when we were thermalised:
First plot is power at the OMC reflected PD vs. power at the antisymmetric port (calibrated into the power into HAM6) for the case where we were 3 hrs 59 mins into lock.
Second plot is power at the OMC reflected PD vs. power transmitted to the DCPDs for the case where we were 2 hrs 59 mins into lock.
We can write down an equation for P_REFL from the OMC in terms of P_DCPD, using our linear fit.
P_REFL = ( c*P_DCPD + d ) mW
We know the nominal setting for P_DCPD is 40mA, and we can take the responsivity of the DCPDs at 100 % efficiency to be
responsivity = e * lambda / (c * h)
From the squeezer budget (E2400269) we can get a number for the Q.E. of the PD that also includes OMC losses for the transmitted beam, transmissivity = 0.937
Therefore the power at the DCPDs at nominal DARM offset is 40mA/(responsivity*transmissivity) = 49.7 mW.
The reflectivity of the OMC breadboard is 2.75e-4 as calculated from parameters given in T1500060-v3.
The formula for the power measured at the reflected port of the OMC can also be expressed as:
P_REFL = R_cav [ P_00_arm + P_00_cd] + P_HOM_arm + P_sb + P_HOM_cd
where P_00_arm is the power in the fundamental carrier mode which changes with DARM offset, P_00_cd is the contrast defect light that is in the fundamental carrier mode, P_HOM_arm is light at higher order mode frequencies which also change with DARM offset, P_sb is power in the sidebands, P_HOM_cd is contrast defect light at higher order mode frequencies.
Whereas the formula for the power transmitted by the OMC can be described as:
P_DCPD = T_cav [ P_00_arm + P_00_cd]
As we assume that all HOM and sidebands are reflected by the OMC.
The mode-matching, MM, of the OMC to the differential arm mode is defined as:
P_00_arm / ( P_HOM_arm + P_00_arm )
This can be calculated using:
P_00_arm = (P_DCPD - d)/T_cav
P_HOM_arm = P_REFL - d - (R_cav*P_00_arm)
If we do this calculation for the half-way thermalised measurement we get
MM = 0.9975
For the fully thermalised case we get:
MM = 0.9978
The code to calculate this is in: Calculate_refl_power.py located at /ligo/home/jennifer.wright/git/2025/DARM_OFFSET/