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Entry  Fri Sep 18 10:47:48 2020, gautam, Update, BHD, Sensing scheme for homodyne phase fieldQuads.pdfPMAMratio.pdf
    Reply  Tue Sep 22 22:38:11 2020, gautam, Update, BHD, Sensing scheme for homodyne phase - some analytic calcs simpleMich.pdf.zip
Message ID: 15596     Entry time: Tue Sep 22 22:38:11 2020     In reply to: 15579
Author: gautam 
Type: Update 
Category: BHD 
Subject: Sensing scheme for homodyne phase - some analytic calcs 

I got some feedback from Koji who pointed out that the phase tracker is not required here. This situation is similar to the phase locking of two lasers together, which we frequently do, except in that case, we usually we offset the absolute frequencies of the two lasers by some RF frequency, and we demodulate the resulting RF beatnote to use as an error signal. We can usually acquire the lock by simply engaging an integrator (ignoring the fact that if we actuate on the laser PZT, which is a frequency actuator, just a proportional feedback will be sufficient because of the phase->frequency conversion), the idea being that the error signal is frequently going through a zero-crossing (around which the sinusoidal error signal is approximately linear) and we can just "catch" one of these zero crossings, provided we don't run of actuation range.

So the question here becomes, is the RF44 signal a suitable error signal such that we can close a feedback loop in a similar way? To try and get more insight, I tried to work out the situation analytically. I've attached my thinking as a PDF note. I get some pretty messy complicated expressions for the RF44 signal contributions, so it's likely I've made a mistake (though Mathematica did most of the heavy lifting), it'll benefit from a second set of eyes. 

Anyways, I definitely think there is some additional complications than my simple field cartoon from the preceeding elog would imply - the relative phases of the sidebands seem to have an effect, and I still think the lack of the PRC/SRC make the situation different from what Hang/Teng et. al. outlined for the A+ homodyne phase control analysis. Before the HEPA failed, I had tried closing the feedback loop using one quadrature of the demodulated RF44 signal, but had no success with even a simple integrator as the loop (which the experience with the PLL locking says should be sufficient, and pretty easily closed once we see a sinusoidally oscillating demodulated error signal). But maybe I'm overlooking something basic conceptually?

Quote:

eSummary:

I don't think the proposed scheme for sensing and controlling the homodyne phase will work without some re-thinking of the scheme. I'll try and explain my thinking here and someone can correct me if I've made a fatal flaw in the reasoning somewhere.

Attachment 1: simpleMich.pdf.zip  249 kB  Uploaded Tue Sep 22 23:50:03 2020
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