Some time ago, I had done an actuator calibration of ITMX. This suspension hasn't been victim to the recent spate of suspension problems, so I can believe that the results of those measurement are still valid. So I decided to calibrate the in-loop error signal of the EX green PDH loop, which is recorded via an SR560, G=10, by driving a line in ITMY position (thereby modulating the X arm cavity length) while the EX green frequency was locked to the arm cavity length. Knowing the amount I'm modulating the cavity length by (500 cts amplitude sine wave at 33.14159 Hz using awggui, translating to ~17.2 kHz amplitude in green frequency), I demodulated the response in C1:ALS-X_ERR_MON_OUT_DQ channel. At this frequency of ~33 Hz, the servo gain should be large, and so the green laser frequency should track the cavity length nearly perfectly (with transfer function 1/(1+L), where L is the OLG).

The response had amplitude 5.68 +/- 0.10 cts, see Attachment #1. There was a sneaky gain of 0.86 in the filter module, which I saw no reason to keep at this strange value, and so updated to 1, correcting the demodulated response to 6.6 cts. After accounting for this adjustment, the x10 gain of the SR560, and the loop suppression, I put a "cts2Hz" filter in (Attachment #2). I had to guess a value for the OLG at 33 Hz in order to account for the in-loop suppression. So I measured the OLTF using the usual IN1/IN2 method (Attachment #3), and then used a LISO model of the electronics, along with guesses of the cavity pole (18.5 kHz), low-pass filter poles (4x real poles at 70 kHz), PZT actuator gain (1.7 MHz/V) and PDH discriminant (40 uV/Hz, see this elog) to construct a model OLTF. Then I fudged the overall gain to get the model to line up with the measurement between 1-10kHz. Per this model, I should have ~75dB of gain at ~33Hz, so the tracking error to my cavity length modulation should be ~3.05 Hz. Lines up pretty well with the measured value of 4.7 Hz considering the number of guessed parameters. The measured OLG tapers off towards low frequency probably because the increased loop suppression drives one of the measured inputs on the SR785 into the instrument noise floor.

The final calibration number is 7.1 Hz/ct, though the error on this number is large ~30%. Note that these "Hertz" are green frequency changes - so the change to the IR frequency will be half.

Attachment #4 shows the error signal in various conditions, labelled in the legend. Interpretations to follow.