Yohei,
This is a log on 2024/2/7.
I measured the thermal actuation response of the main laser.
Schematics can be found here.
The signal modulation is injected between the slow filter F_thr and thermal actuator A_thr. By measuring the voltage right before and after the injection point and take its ratio, one can obtain the ration of A_thr*F_thr and A_pzt*F_pzt.
Each filter is constructed by a PID controller (see the log 3426 to calcurate the transfer function). The filter shapes can be checked here.
| Path | P | I (freq. gain) | D (freq. gain) |
| Fast (PZT) | -30 dB | 19.09 kHz, 53. dB | - |
| Slow (temp.) | - | 124.1 mHz, 1.0 dB | 4.522 Hz, 1.0 dB |
The measurement is separated to two frequency regions, 10 Hz - 600 mHz and 600 mHz to 100 mHz. The sweeping voltages are 25 mVpp and 60 mVpp, respectively.
The raw data and inferred A_thr are plotted here.
Given the open loop gain of the fast path is large enough and the PZT response is flat around the frequency region, one can infer the shape of A_thr using the following formulas:
G = - (A_thr*F_thr) / (A_pzt*F_pzt.) -> A_thr \propto G*F_pzt/F_thr.
Accoring to Akutsu's PhD thesis, A_thr is fitted by the following function:
A_thr(f) = -3e6/(1+1j*f/0.22)/(1+1j*f/0.46+(1j*f/1.07)**2)
In our measurement, A_thr can be fitted by this function. The fitted data is plotted here.
Also, from the raw data, one can know the stability of the system. The unity-gain frequency of this measurement means the point that the thremal actuation and PZT actuation get crossed.
In our measurement, the phase margin is ~30 degrees at UGF ~2.3 Hz, which is sufficient to make the system stable when locking the cavity by two actuation paths.