Abstract
As the preparation of the paramter updates on the front-end calibration of IMC, I started to check the MC parameters in klog#29194.
Model function with latest parameters seems to match with the latest measurements same extent as the past estimation in klog#16718
Mismatch between the model and measured TF is 1-2dB around the cross over frequency of PZT and EOM.
This mismatch might be explained by more precise investigation such as a change of the optical gain in time for each measurement.
Details
In order to confirm that OLTF model with the latest estimation of actuator efficiencies in klog#29194 can explain the latest OLTF measured in klog#29073, I made a comparison plot (Fig.1) of measured and model transfer functions. Used parameters (see also klog#29194) are as follows.
- PZT: 4.5MHz
- EOM: 0.34rad/V
- Optical gain: 17.9V/MHz
- Cavity pole: 5.74kHz
Because there is no measurement about resonant frequency and Q-value of PZT, I assumed them as f=150kHz and Q=1.3 which are the eye-fit. Catalog spec of resonant frequency is ~100kHz and PZT loop gain around 100kHz is ~10 times less than the EOM loop gain. So even if eye-fit is not so correct, this effect should be less than ~10%. According to the residual plot of measurements and model (see Fig.2), there is ~2dB mismatch around the cross over frequency. Because residual value depends on the frequency, mismatch seems to come from the bias of the actuator efficiency ratio of PZT and EOM not an overall gain.
Other measurements in klog#29073, and klog#29194 which represent ratio of local loop gains are also modelized and shown in Fig.3. Mismatch on blue and cyan curves above 100kHz seems to come from ignorant about PZT resonance. One on red and pink curves around 30-40kHz seems to come from the bias of the actuator efficiency ratio same as OLTF plot. Mismatch on green curves in phase which has existed also in the past estimation in klog#16718 probably comes from ignorant about thermal pole.
For the calibration on the digital system (below 8kHz), PZT gain (i.e. bias on the ratio of PZT and EOM gains) is an important factor. A possible cause of such a bias is a change in optical gain between measurements. So I checked some EPICS channels at the time of measuring OLTF (Fig.4) and of measuring BFs in Fig.3 (Fig.5). We can see the IN1 gain is 1dB different between two screenshots. IN1 gain is decided during the lock acquisition to keep open loop gain in my remember and it should depends on the alignment situation before starting lock acquisition. On the other hand, current IMC lock finally reaches same alignment (same optical gain) by ASC. This fact mean that final open loop gain (after calming down ASC control) may be different as the difference of IN1 gain. Though I'm not sure that measurement time for all TF measurement are recorded (especially for measurement by Moku-lab), I'll try to check the gain situation for each measurements.
