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Message ID: 821     Entry time: Sun Feb 12 19:40:50 2012
Author: Frank 
Type: DailyProgress 
Category: Seismic 
Subject: re-measuring seismic coupling to cavities 

trying again to measure the coupling from seismic to cavity length for the individual cavities. Measuring the coupling to differential length (beat signal) is not a problem at all, but to the individual length.

The problem arises from the small coupling coefficient from vertical acceleration to changes in length. to not measure any effect from the filtering from the stack we have to measure at low frequencies. The first mechanical resonances occur at around 6Hz, the stack itself has it's first resonance at 16Hz. So we have to measure below 5Hz. The coupling to changes in length is small, about 1e-9 * Length of the cavity  [units: m/(m/s2)], so about 2e-10 m/(m/s2). The signal from shaking the table around 1Hz is estimated to be a few hundreds of Hz/rtHz with maximum modulation. However the laser frequency noise is 10kHz/rtHz @1Hz, so we have to integrate very long to get a reasonable SNR. We cant use anything on the table to pre-stabilize the laser to reduce it's noise as this would be shaked as well and we don't really know which one we actually measure.

For the first cavity we have to look at the feedback to the laser pzt as this tells us how much the laser frequency has to be corrected. We assume that shaking the table at 1Hz does not mechanically modulate the laser frequency in any other way. For the second cavity we can't simply lock it the usual way as we would have two coupled cavities (that's what we measure using the beat signal already). So we have to lock the laser to the second cavity instead without using the FSS path by feeding back to the laser (fast actuator) instead of the VCO.

A first measurement showed that we have an additional mechanical resonance around 6Hz which we currently don't have in our current stack model (and actually don't know exactly where it's coming from).
We measured the Eigenmodes of the stack some time ago and have two candidates for it (see here)

  1. beam line, translational motion, f = 6.96 Hz, Q = 21.5 
  2. horizontal transverse motion, f = 6.35Hz, Q = 25.9.

So i will re-measure the TF below 10Hz to clearly identify which one it is.


resonance frequencies of the stack : 16.1Hz and 55.6Hz
other resonance frequency: 6.5Hz

coupling to cavity length: COMSOL model: 53 kHz / (m/s2)
~100 kHz / (m/s2)

All data and plots on the svn in /measurements/2012_02_12.


Notes for calibration:

TF to beat signal:

  • accelerometer sensitivity: 1023mV/g
  • range of PLL VCO: 10kHz -> 7kHz/V

TF to fast actuator:

  • accelerometer sensitivity: 1023mV/g
  • FAST MON output:  3.07 MHz/V


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