Abstract:

I tried cavity scan again and obtained the optical gain as (1.6 +/- 1.1)e-6 V/Hz.
In addition, I calculated the optical gain from the fitting of OLTF and obtained 8.5e-7 V/Hz, which is consistent with the value measured by cavity scan.

Detail:

I remeasured the optical gain of PMC with 10 times higher scan speed (I changed K1:IMC-SERVO_NPRO_TEMP_BIAS_OFFSET by 0.2 with 60 seconds ramptime).
In addition, I used the peak around the center of the scan time to use the data when the scan speed is stable as much as possible.
Furthermore, I calculated the optical gain by using both forward and backwrd scan data to evaluate the systematic error.

Figure 1 shows the data during forward scan.
I used two peaks overlapped with T cursors to calculate the scan speed and the peak between T cursor to calculate the slope of PDH signals.
According to fig1, 2FSR is corresponding to 3.903 seconds, so the scan speed is 7.61e7 Hz/s.
Figure 2 shows the enlarged view of the peak between the T cursors in fig1.
The slope of the PDH signals are 203.3 V/s, so the optical gain can be estimated as 2.67e-6 V/Hz.

Figure 3 and 4 show the similar ndscope screem in fig1 and fig2 during backward scan.
The scan speed and slope of PDH signals are 7.60e7 Hz/V and 42.96 V/s, which is corresponding to the optical gain of 5.65e-7 V/Hz.

Since the optical gain of PMC should be between these two values, the optical gain can be estimated as (1.6 +/- 1.1)e-6 V/Hz.
I also calculated the optical gain from the fitting of the measured OLTF between 500 Hz to 10 kHz and obtained 0.85e-6 V/Hz, which is consistent with the above measurement.
Figure 5 shows the overplot of measured OLTF and OLTF model with the optical gain of 0.85e-6 V/Hz.

Note:

The main problem of the cavity scan measurement is thermal expansion of PMC, which causes large difference between forward and backward measurement, so the effect can be mitigated if we measure with low power.
Since TF of electrical circuit and PZT actuator should not be changed, we would evaluate the PMC optical gain from the OLTF measurement if we will once characterize them with low power.