Summary:

I've been playing around with Evan's NB code trying to put together a noise budget for the data collected during the DRMI locks last week. Here is what I have so far.

Attachment #1: Sensing matrix measurement.

• This is basically to show that the MICH error signal is mostly in AS55Q.
• The whitening gain used was 0dB, and the demod phase was -82 degrees.
• The MICH sensing response was 5.31*10^8 V/m, where V is the demod board output. The 40m wiki RFPD page for AS55 says the RF transimpedance is ~550ohms, and I measured the Demod Board puts out 5.1V of IF signal (measured at after the Preamp, which is what goes to the ADC) for 1V of RF signal at the PD input. Using these numbers, and assuming a PD responsivity of 0.8 A/W at 1064nm, the sensing response is 2.37*10^5 W/m. I don't have a feeling yet for whether this is a reasonable number, but it would be a number to compare to what my Finesse model tells me to expect, for example.
• Actuator calibration used to arrive at these numbers was taken from this elog. 

Attachment #2: MICH OLTF measurement vs model

• In order to build the MICH OLTF model, I used MATLAB to put together the following transfer functions:
  • BS pendulum
  • Digital servo filters from LSC_MICH
  • Violin mode filters 
  • Analog/Digital AA and AI filters. For the digital AA/AI filters, I took the coefficients from /opt/rtcds/rtscore/release/src/fe/controller.c
• The loop measurement was taken with digital filter modules FM1, FM2, FM3, FM7, FM9 engaged. 
• In order to fit the model to the measurement, I tried finding the best-fit values for an overall loop gain and delay. 
• The agreement between model and measurement isn't stellar, but I decided to push ahead for a first attempt. This loop TF was used to convert various noises into displacement noise for plotting.

Attachment #3: Noise budget

• It took me a while to get Evan's code going, the main changes I made were to use nds2 to grab data instead of GWPy, and also to replace reading in .txt files with importing .mat files. This is a work in progress.
• Noises plotted:
  • Measured - I took the in loop error signal and estimated the free-running displacement noise with the model OLTF, and calibrated it into metres using the sensing response measurement. This looks consistent with what was measured back in Dec 2015.
  • Shot noise - I used the measured DC power incident on the PD, 13mW, RF transimpedance of 550 V/A, and the V/m calibration factor mentioned above, to calculate this (labelled "Quantum Noise").
  • Dark noise - measured with PSL shutter closed.
  • Seismic noise, thermal noise, gas noise - calculated with GWINC

I think I did the various conversions/calibrations/loop algebra correctly, but I may have overlooked something. Now that the framework for doing this is somewhat set up, I will try and put together analogous NBs for PRCL and SRCL. 

GV 22 August 2017: Attachment #4 is the summary of my demod board efficiency investigations, useful for converting sensing measurement numbers from cts/m to W/m.