Sheila, Craig

The other day Craig changed the modulation depth of both 9 and 45 MHz a few hours into a lock, so that we can estimate the fraction of the power at different ports from different fields. 

In the attached screenshot you can see that the normalized POP18+POP90 channels, after the gain is adjusted to compensate for the change in modulation depth, still change slightly when the modulation depths are changed.  This probably means that there is an alignment offset that changes based on the modulation depth, and that we are not operating at the best possible vertex alignment in terms of sideband build ups (when the 9MHz is increased, POP18 increases and POP90 decreases).  This will make some error on these estimate of power ratios.

We can write an expression for the total power at a port in terms of 3 scale factors for carrier power, 45MHz power and 9 MHz power and bessel functions of the modulation depths. Combining the three measurements (nominal mod depth, increased 45, increased 9) we can solve a matrix equation for the power on each diode from the carrier, 9 and 45.  Assuming that the modulation depths at the nominal settings are those listed in 48513, we get the following result for percentage of power at each port:

The DC diodes used are the sum of the two OMC QPDs for AS, the sum of the two POP QPDs, the sum of LSC REFL A+REFL B, and the sum of the two arm circulating power measurements, which are each based on the average of the two transmission QPDs.  A matlab script is attached.  We can compare this to a similar result for the AS port here: 46490 

We could also attempt to estimate the modulation depths from the change in arm power for the change in modulation depth, this results in an inferred modulation depth of 0.176 for 45 MHz, and 0.125 for 9 MHz.  These numbers could be confused by a change in recycling gain because of the alignment offset that seems to change when we change the modulation depth.