At today's meeting, it was suspected that these noise levels were far too low. (ELOG 9660)
I've attached the math I did to get the conversions, as well as the dark noise SQRTINV spectra at various imitated transmission values and the python script that does the converting.
I've gone over my calculations, and think they're self-consistent. However, a potential source of misestimation is the treatment of the Lorentzian profile simply existing with the coupled arm line width (38pm). The conversion to m/rtHz is directly proportional to the line width of the transmission peak, so if it is much broader in practice (because of imperfect PRC buildup or something), the noise will be that much worse.
I'm open to any other feedback about what I may have done wrong!
#! /usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt
data = np.loadtxt('./SQRTINVspectra.dat')
# Coupled arm linewidth
w = 38e-12
# Lorentzian value at full resonance
I0 = 700