40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop | ||||||||||

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## Measurement of Schnupp asymmetryThis was done by measuring the relative phase between the sidebands reflected from the two arms while the arm cavities are locked. ## Description:As a phase reference we use the zero crossing of the response function for the out-of-phase control signal for the single arm cavity lock [0]. The difference in the RD rotation phase of the response zero crossings indicates the phase difference in the sideband signals reflected from the arms. Assuming the asymmetry is less than half the RF modulation wavelength [1], the asymmetry is given by the following formula: \Delta \phi c 1 L_sa = ----------- ----- - 360 f_RSB 2 We use a LSC digital lock-in to measure the response of the arm cavity at a single-frequency drive of it's end mirror. [0] The locations of the zero crossings in the out-of-phase components of the response can be determined to higher precision than the maxima of the in-phase components. [1] f ## Procedure:- Lock/tune the Y arm only.
- We use AS55_I to lock the arms.
- Engage the LSC lock-in.
- Tune the lock-in parameters:
- Set as input to the lock-in the out-of-phase quadrature from the control RFPD. In this case AS55_Q->LOCKIN.
- Drive the arm cavity end mirror by setting the LOCKIN->Y_arm element in the control matrix.
- Note the "RD Rotation" phase between the demodulated signals from the control PD (AS55)
- For some reasonable distribution of phases around the nominal "RD Rotation" value, measure the amplitude of the lock-in I output.
- Assuming the Q output is nearly zero, it can be neglected. In this case the Q amplitude was more than a factor of 10 less than the I amplitude.
- Here we take 5 measurements, each separated by one over the measurement bandwidth (as determined by the lock-in low pass filter), in this case 10 seconds. The figure above plots the mean of these measurements, and the error bars indicate the standard deviation.
lock-in freq: 103.1313 Hz I/Q filters: 0.1 Hz low-pass phase: 0 degrees The data and python data-taking and plotting scripts are attached. ## Error Analysis:To to determine the parameters of the response (which we know to be linear) we use a weighted linear least-squares fit to the data: ## References:Valera's LLO measurement | ||||||||||

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#!/usr/bin/env python import sys import os import subprocess import time import pickle from numpy import * import nds import matplotlib ... 229 more lines ... | ||||||||||

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#!/usr/bin/env python import pickle from numpy import * import matplotlib #matplotlib.use('AGG') from matplotlib.pyplot import * ################################################## ... 137 more lines ... | ||||||||||

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(dp0 S'I' p1 (dp2 cnumpy.core.multiarray scalar p3 (cnumpy dtype p4 ... 341 more lines ... | ||||||||||

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(dp0 S'I' p1 (dp2 cnumpy.core.multiarray scalar p3 (cnumpy dtype p4 ... 341 more lines ... |