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Entry  Tue Mar 13 19:14:40 2012, kiwamu, Update, LSC, Noise estimatino in the REFL33Q as a MICH sensor NB_REFL33.png
    Reply  Wed Mar 14 13:16:50 2012, kiwamu, Update, LSC, A correction on Noise estimatino in the REFL33Q 
Message ID: 6407     Entry time: Tue Mar 13 19:14:40 2012     Reply to this: 6414
Author: kiwamu 
Type: Update 
Category: LSC 
Subject: Noise estimatino in the REFL33Q as a MICH sensor 

A feasibility study of the REFL33Q as a MICH sensor was coarsely performed from the point view of the noise performance.

The answer is that :

  the REFL33Q can be BARELY used as a MICH sensor in the PRMI configuration, but the noise level will be at only sub-nano meter level.

  Tonight I will try to use the REFL33Q to control the MICH DOF to see what happens.



  I neeeeeeeed a 3f signal which is sensitive enough to hold the Michelson in the PRMI configuration so that I can test the single arm + PRMI configuration.
Based on the data I got in the sensing matrix measurement (#6403) I wanted to see how noises in the REFL33Q look like.

(Noise analysis)

  I did a coarse noise analysis for the REFL33Q signal as shown in the attached plot below while making some assumptions as follows.

  •  Optical gain for MICH = 0.8  W/m (#6403)
    • In the plot below, I plotted a unsuppressed MICH motion which had been measured the other day with a different sensor. This is for a comparison.
  •  Shot noise due to DC light on the REFL33 photo diode
    •  With a power of 5.0 mW (#6355)
    • Assume that the responsivity is 0.75 A/W, this DC light creates the shot noise in the photo current at a level of 35 pA/sqrtHz.
    • Then I estimated the contribution of this shot noise in terms of the MICH displacement by calibrating the number with the optical gain and responsivity.
    • It is estimated to be at 60 pm/sqrtHz
  • Dark current
    • I assumed that the dark current is 0.52 mA. (see the wiki)
    • In the same manner as that for the shot noise, the dark current is estimated to be at 20 pm/sqrtHz in terms of the displacement
  • Whitening filter input referred noise
    • I assumed that it is flat with a level of 54 nV/sqrtHz based on a rough measurement by looking at the spectrum of the LSC input signals.
    • The contribution was estimated by applying some gain corrections from the conversion efficiency of the demod board, transimpedance gain, responsivity and the optical gain.
    • This noise is currently the limiting factor over a frequency range from DC to 1 kHz.
  • ADC noise
    • I did the same thing as that for the whitening filter noise.
    • I assumed the noise level is at 6 uV/sqrtHz and it is flat (I know this not true particularly at mHz region the noise becomes bigger by some factors)
    • Then I applied the transfer function of the whitening filter to roll off the noise above 15 Hz.


(Some thoughts)

  •   Obviously the limiting noises are that of ADC and the whitening filter.
    • These noise can be easily mitigated by installing an RF amplifier to amplify the RF signals from the REFL33Q RFPD.
    • Therefore this is not the real issue
  • The real issue is that the shot noise is already at a level of 60 pm/sqrtHz, and we can't suppress the MICH motion less than that.
    • In order to decrease it, one possibility is to increase the modulation depth. But it is already at the maximum.
    • If the REFL165 RFPD is healthy, it is supposed to give us a bigger MICH signal. But it didn't look healthy ... (#6403)
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