When we leave z-correction loop open, if we send 1000 excitation at 0.1Hz to channel "END-len-ex2", we get 32.4 counts from PZT mon(1620counts from figure REF4, which is amplified by 50), which means 3240 counts are sent to main laser (PZT mon is 100 times smaller than the signal sent to main laser PZT). 3240/1000*0.31=1V. It corresponds to 2MHz of main laser frequency change. It corresponds to 2um change in cavity length.
When we leave z-correction loop closed, if we send 1000 excitation at 0.1Hz to channel "END-len-ex2", we get 1934 counts from z-correction loop correction signal. (there are still 10 counts sent to PZT, but since it is so small, we neglect it). Therefore, 1934 counts corresponds to 2 um length correction.
For correction signal sent to end mirror, the calibration factor is thus 1.034 um/kcount.
(the data of this calibration is saved in standalone desktop/detuning/20210628)
In the last calibration calculation, I didn't consider the loop gain. Therefore, the calibration factor must have some error.
Nevertheless, we can use another way to do this calibration without considering the loop gain.
0. Lock filter cavity.
1. Change slightly the temperature of main laser.
2. Read how much main laser frequency is changed.
3. Check how much length correction is sent to end mirror.
I did these procedures. The frequency change is read from the attached two figures. The correction signal change is in the attached figure three.
And get calibration factor (frequency difference)/(correction signal) = (248.6-235.2) [MHz]/ (5200) [counts] = 2.56 [MHz] / 1000 [counts]
Since 1pm = 1Hz, we can calibrate the factor above as 2.56 [um]/[kcounts].