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Entry  Fri Feb 21 12:45:57 2014, ericq, Update, LSC, Equivalent Displacement Noise from QPD Dark Noise in SQRTINV SQRTINVspectra.pdfSQRTINV_DarkNoise.pdf
    Reply  Wed Mar 5 18:04:36 2014, ericq, Update, LSC, Equivalent Displacement Noise from QPD Dark Noise in SQRTINV calc1.jpgcalc2.jpgSQRTINVspectra.dat.zipdarkTransmonSpec.py
Message ID: 9660     Entry time: Fri Feb 21 12:45:57 2014     Reply to this: 9693
Author: ericq 
Type: Update 
Category: LSC 
Subject: Equivalent Displacement Noise from QPD Dark Noise in SQRTINV 

EQ UPDATE: Measured it wrong the first time, fixed now.

I measured the spectra of the SQRTINV channels from dark QPDs, with offsets adjusted to imitate various transmission levels. (While the dark noise stays constant in terms of, say, TRX counts, 1/sqrt(TRX) isn't linear, and so the noise coupling depends on the TRX offset). 

SQRTINVspectra.pdf

I did some calculations to turn this into the equivalent displacement noise when using SQRTINV as an error signal. This depends on where on the fringe you are locking, since the slope of SQRTINV vs. position is not constant, and can only really be treated as linear down to about 1/3 of a line width away from full resonance. In my calculations, I assumed a coupled arm line width of 38pm, and a full transmission of 700 counts in TRX/Y. 

The QPD dark noise RMS when two line widths away (TR = 40) is about 5fm, and only goes down from there. 

SQRTINV_DarkNoise.pdf

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