I wanted a quick first guess of new gains to use for the RF locking signals, so that we know roughly where to start when trying to lock DRMI, since the drive levels are slightly different with the new EOM. I'm using Koji's measured values from alog 41435. Note that the drive levels are slightly different now, since the EOM drivers have been moved to outside the PSL enclosure (alog 41852), but they're pretty similar. Our final gains will of course be set by measuring the loops, so this small discrepancy in the first round guess shouldn't really matter.
The amplitude of a PDH signal is proportional to J_0(Gamma)*J_1(Gamma), where J_n() is the Bessel function, and Gamma is the modulation depth in radians (see, for example, P1500001 appendix B for a derivation). The ratio that we will want to apply to the old gains will be:
ratio = ( J_0(Gamma_old) * J_1(Gamma_old) ) / ( J_0(Gamma_new) * J_1(Gamma_new) ).
For the 45 MHz channels (Gamma_old = 0.287, Gamma_new = 0.197), the ratio will be 1.43. For the 9 MHz channels (Gamma_old = 0.187, Gamma_new = 0.210) the ratio will be 0.89.
With the change out of the RF combiner for 45 MHz and 24 MHz (alog 41889), we now have a slighly higher modulation index for the 45 MHz signals. Now Gamma_45MHz is 0.259, rather than 0.197. This new value is much closer to the old EOM / RF driver combination from O2 of 0.287.
This means that the ratio defined in the above entry for 45 MHz is now 1.10.