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Entry  Mon Mar 10 21:12:30 2014, Koji, Summary, LSC, Composite Error Signal for ARms (1) composite_linear_signal.nb.zip
    Reply  Tue Mar 11 15:14:34 2014, den, Summary, LSC, Composite Error Signal for ARms (1) 
       Reply  Tue Mar 11 15:21:08 2014, Koji, Summary, LSC, Composite Error Signal for ARms (1) 
Message ID: 9708     Entry time: Mon Mar 10 21:12:30 2014     Reply to this: 9715
Author: Koji 
Type: Summary 
Category: LSC 
Subject: Composite Error Signal for ARms (1) 

The ALS error (i.e. phase tracker output) is linear everywhere, but noisy.
The 1/sqrt(TR) is linear and less noisy but is not linear at around the resonance and has no sign.
The PDH signal is linear and further less noisy but the linear range is limited.

Why don't we combine all of these to produce a composite error signal that is linear everywhere and less-noisy at the redsonance?

This concept was confirmed by a simple mathematica calculation:

The following plot shows the raw signals with arbitorary normalizations

1) ALS: (Blue)
2) 1/SQRT(TR): (Purple)
3) PDH: (Yellow)
4) Transmission (Green)

The following plot shows the preprocessed signals for composition

1) ALS: no preprocess (Blue)
2) 1/SQRT(TR): multiply sign(PDH) (Purple)
3) PDH: linarization with the transmission (If TR<0.1, use 0.1 for the normalization). (Yellow)
4) Transmittion (Green)

The composite error signal

1) Use ALS at TR<0.03. Use 1/SQRT(TR)*sign(PDH)*(1-TR) + PDH*TR at TR>0.03
2) Transmittion (Purple)
 

Attachment 1: composite_linear_signal.nb.zip  345 kB  Uploaded Tue Mar 11 09:30:40 2014
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