This is the transfer function between the phase-frequency discriminator and the FET IQ demodulator while the cavity is locked. The blue trace is "initial" conditions, i.e., with a well-aligned cavity and standard modulation sidebands. The green "sb shift" trace was taken with the RF modulation sideband frequency tuned 200 Hz higher than its initial value. The red "alignment shift" trace was taken with the ITM yaw misaligned.
The FSR is 37.512 kHz, with a higher-order FSR peak at 75.018 kHz. Given this FSR, the cavity length is 3995.95 m.
The peaks due to the RF modulation sidebands are at 54.432 kHz and 58.098 kHz in the initial trace. These peaks shift 200 Hz in the green trace.
Additional structure is observed at 46.301 kHz, 55.325 kHz, 57.252 kHz, and 66.229 kHz. The peaks at 46.301 kHz and 66.229 kHz increase for the case of yaw misalignment and are thus likely to be (1,0) modes.
The separations between these peaks are:
75.018 - 66.229 = 8.789 kHz
66.229 - 57.252 = 8.977 kHz
46.301 - 37.512 = 8.784 kHz
55.325 - 46.301 = 9.024 kHz
The mean modal spacing is 8.8935 kHz.
From this modal spacing, the g-factor is 0.540532, corresponding to approximate mirror radius of curvature of 2302.86 m.
The FWHM of the FSR peak is approximately 94 Hz. Finesse is thus 37512/94 = 399.064. This would occur for a reflectivity of about 99.2%.
There's a follow-up of this in the works for characterizing cavity properties during ring heater use.
The RF frequency is 24.515730 MHz and was shifted to 24.515930 MHz for the second measurement. Making the ansatz f_SB = (N - 1) * f_FSR + f_mease with f_FSR ~ 37.51kHz, N an integer, and f_meas = 58.098 kHz, we determine N = 653 Now, we can go back and recalculate f_FSR = 37511.71 Hz with a few ppm precision. This then yields L_arm = 3995.985m.