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Entry  Wed Jul 23 22:34:07 2008, Yoichi, Update, LSC, Arm cavity g-factor measurement 
    Reply  Thu Jul 24 01:27:00 2008, Koji, Update, LSC, Arm cavity g-factor measurement 
       Reply  Thu Jul 24 02:57:26 2008, rob, Update, LSC, Arm cavity g-factor measurement 
          Reply  Thu Jul 24 08:09:26 2008, Yoichi, Update, LSC, Arm cavity g-factor measurement 
Message ID: 730     Entry time: Thu Jul 24 01:27:00 2008     In reply to: 728     Reply to this: 731
Author: Koji 
Type: Update 
Category: LSC 
Subject: Arm cavity g-factor measurement 

I locked the Y-arm and mis-aligned the end mirror in Yaw until the transmission power gets half.
Then I injected a 30Hz sinusoid into the error point of the Y-arm servo to shake the ETMY.
I observed AS166_I and AS166_Q as I changed the 166MHz frequency.

A-ha! Do you always expect the 30Hz signal, don't you?
Because this is the PDH technique.

You have a carrier and phase modulation sidebands at 166MHz this time.
Inject them into a cavity. Detect the reflection by a photo detector.
Demodulate the photocurrent at 166MHz.

This is the PDH technique.

A 30Hz sinusoid was injected to the error point of the cavity lock.
This means that the cavity length was fluctuated at 30Hz.

We should see the 30Hz signal at the error signal of the 166MHz demodulation, regardless of the tuning of the modulation frequency!
In other words, the 30Hz signal in the demod signal at the 166MHz is also understandable as the beating between the 30Hz sidebands and the 166MHz sidebands.


So, now I feel that the method for the TEM01 quest should be reconsidered.

If we have any unbalanced resonance for the phase modulation sidebands, the offset of the error signal is to be observed even with the carrier exactly at the resonance. We don't need to shake or move the cavity mirrors.

Presence of the MC makes the things more complicated. Changing the frequency of the modulation that should go throgh the MC is a bit tricky as the detuning produces FM-AM conversion. i.e. The beam incident on the arm cavity may be not only phase modulated but also amplitude modulated. This makes the measurement of the offset described above difficult.

The setup of the abs length measurement (FSR measurement) will be easily used for the measurement of the transverse mode spacings. But it needs some more time to be realized.
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