This is a report on the measurement we did on 03/07.

We measured the open-loop transfer function of the cavity by injecting a swept-sine disturbance signal between plant H and actuator A and taking the ratio of measurement data from directly before and directly after signal injection. Goal of this measurement was to assess lock stability by means of the phase margin. The lock of the main laser is achieved by a fast actuation with a piezo with servo transfer function F_pzt*A_pzt combined with slow thermal actuation with servo F_th*A_th, both actuations performed on the laser itself. While F_pzt, A_pzt and A_th are basically fixed , we can influence the stability of the lock by adjusting the servo F_th with the MokuLab. Based on trial and error, we designed the thermal servo to have the following parameters:

Integrator gain (saturation limit) and UGF: g_i = 43.6 dB, f_i = 160 Hz

Differentiator gain (saturation limit) and UGF: g_d = -45.5 dB, f_d = 315.6 kHz

With the above information and the knowledge of F_pzt, A_pzt and A_th, the optical gain can be inferred and found to be constant. UGF lies around 100 Hz and the phase margin amounts to around 85 deg. The lock seems reasonably stable, at least, enough for our purposes, so we will continue. A plot of the described analysis can be found here.