Summary:

The response of the PRFPMI length degrees of freedom as measured in the LSC PDs was characterized. Two visualizations are in Attachment #1 and Attachment #2.

Details:

• The sensing matrix infrastructure in the c1cal model was used.
• The oscillator frequencies are set between 300 - 315 Hz.
• Notch filters at these frequencies were enabled in the CDS filter banks, to prevent actuation at these frequencies (except for CARM, in which case the loop gain is still non-negligible at ~300 Hz, this correction has not yet been applied).
• Mainly, I wanted to know what the DARM sensing response in AS55_Q is. 
  • The measurement yields 2.3e13 cts/m. This is a number that will be used in the noise budget to convert the measured DARM spectrum to units of m/rtHz.
  • We have to multiply this by 10/2^15 V/ct, undo the 6dB whitening gain on the AS55_Q channel, and undo the ~5x gain from V_RF to V_IF (see Attachment #4 of this), to get ~0.69 GV/m from the RFPD.
  • The RF transimpedance of AS55_Q is ~550 ohms, and accounting for the InGaAs responsivity, I get an optical gain of 1.8 MW/m. Need to check how this lines up with expectations from the light levels, but seems reasonable.
  • Note that T_SRM is 10%, we dump 70% of the output field into the unused OMC, and there is a 50/50 BS splitting the light between AS55 and AS110 PDs. Assuming 90% throughput from the rest of the chain, we are only sensing ~1.3 % of the output DARM field.
• Apart from this, I can also infer what the matrix elements / gains need to be for transitioning the PRMI control from 3f to 1f signals. To be done...
• I found these histograms in Attachment #2 to be a cute way of (i) visualizing the variance in the magnitude of the sensing element and (ii) visualizing the separation between the quadratures, which tells us if the (digital) demod phase needs to be modified.
  • The sensing lines were on for 5 minutes (=300 seconds) and the FFT segment length is 5 seconds, so these histograms are binning the 60 different values obtained for the value of the sensing element.
  • The black dashed lines are "kernel density estimates" of the underlying PDFs
  • I haven't done any rigorous statistical analysis on the appropriateness of using this technique for error estimation, so for now, they are just lines...