Linear Alignment System for the VIRGO Interferometer

M. Mantovani, ILIAS Meeting 7 April 2005 Hannover

Linear Alignment System for the VIRGO Interferometer

M. Mantovani, A. Freise, J. Marque, G. Vajente


N

W

Inputbeam

Mode Cleaner Michelson interferometer with 3km long Fabry-Perot

cavities

Main output port

The Virgo Detector Layout


The Virgo Mirror Suspension

Main mirrors are suspended for seismic isolation. Active control is necessary to keep the mirrors at their operating point:

• Inertial damping • Local damping• Local control, i.e. steering of the mirrors

Angular Fluctuation ~ 1radRMS





Alignment precision requests:

• 10-7radRMS for the recycling mirror

• 2·10-8radRMS for the cavity input mirrors

• 3·10-9radRMS for the cavity end mirrors

Angular Fluctuation ~ 1radRMS

Shot noise: 10-13 rad/sqrt(Hz) @10Hz





A more precise alignment system is needed


The purpose of the linear alignment system is to keep the beams and mirrors at their set position, in order to:

• allow a stable interferometer operation over long periods, i.e. perform a control for low frequencies, where the SA does not suppress motions.• minimise the coupling of noise into the dark fringe signal

In other words:

the automatic alignment control should not actively suppress motion in the measurement band (>10Hz) the linear alignment should allow to switch of „noisy“ local controls.

Linear Alignment System


Linear Alignment System Overview


Recombined Mode

4 Quadrant Photodiodes

(→ 8 signals for each degree of freedom tx or ty)




Recombined Mode

4 Mirrors to control


(→ 8 signals for each degree of freedom tx or ty)


Quadrant Photo-Detector

Specification

• photodiode sensitivity = 0.45 A/W

• maximum DC power = 3 mW

• transmittivity = 2 k

• Bias voltage = 180 V

Shot Noise ~ 4 nV/sqrt(Hz)


Recombined Mode



Feedback

Feedback is applied to the Marionette viathe four coil-magnet actuators used also

for the local control.



Recycled Mode


(→ 16 signals for each degree of freedom tx or ty )



Recycled Mode


(→ 16 signals for each degree of freedom tx or ty )

5 Mirrors to control



Recycled Mode


Reconstruction Algorithm

The reconstructed signals are computed by using a χ2 algorithm starting from the optical matrix.

The optical matrix is measured by injecting frequency lines, at the level of the reference mass of the mirrors or at the level of the marionette, and then it is computed by calculating the transfer function, at the lines frequencies, and the quadrants signals (Matlab script)



function [Matrix]=Mmeasure(TxTy,GPSb,GPSe,fres,ave,filename,lines,checkpast)

• Loads the ffl file starting from the GPS time

• Computes the fft of the mirror signals and quadrant signals

• Searches the lines frequencies by using the nominal frequency values

• Computes the transfer functions between the mirror signals and the quadrant signals at the line frequencies

• Makes a coherence analysis in order to estimate the measurement noise

• Prints the signal to noise ratio matrix in order to control the amplitude of the frequency lines

• Prints the optical matrix


PR BS NI NE WI WE

B2_q1_ACp

B2_q1_ACq

B2_q2_ACp

B2_q2_ACq

B5_q1_ACp

B5_q1_ACq

B5_q2_ACp

B5_q2_ACq

B7_q1_ACp

B7_q1_ACq

B7_q2_ACp

B7_q2_ACq

B8_q1_ACp

B8_q1_ACq

B8_q2_ACp

B8_q2_ACq

Optical Matrix



Matrix Measurements Method

• Measure the matrix coefficients evolution as a function of the demodulation phases of the quadrants in order to:

o Understand the behavior of the matrix

o Tune the demodulation phase

Each measurement point takes 3 minutes => 18 minutes for the whole evolution measurement

(180 sec for 15 FFT averages)


Matrix Measurements Method

• Measure the matrix coefficients evolution as a function of the demodulation phases of the quadrants in order to:

o Understand the behavior of the matrix

o Tune the demodulation phase


Demodulation Phases Tuning for the Recombined Mode

In this situation we have decided to minimize one signal respect to the other

Fine tuning for the demodulation phases


Experimental Progress


Characterising the Optical System

• Studied the evolution behavior for the matrix coefficients depending on the fringe offset

• Checked the repeatability of the phase tuning measurement the repeatability of the matrix measurement

• Tried to work at 0.2 offset from the dark fringe in order to benefit from the higher stability of the lock in this state

• Discovered some, not understood, problems at 20% of the dark fringe which obliged us to work at 0.08 fringe offset

• Found some anomalies of the optical matrix measured in the recycled mode by using a set of frequency lines injected at the level of the reference mass of the mirrors

• Measured the optical matrix by injecting the frequency lines at the level of the marionette


Optical Matrix measurement for different fringe offsets

The amplitudes of the matrix coefficients are very different for the 0.1 fringe offset with respect to the dark fringe

We can not measure the optical matrix at 0.1 fringe offset

0.1 fringe offset dark fringe


Optical Matrix measurement for different fringe offsets

The matrix coefficients at the 0.05 fringe offset and at the dark fringe match well

0.05 fringe offset dark fringe


Repeatability of the Matrix Measurement

The Matrix measurement done at the dark fringe in

successfully repeatable


Matrix Measurement at 0.2 Fringe offset

We do not understand the reason of this behavior, we decided to work at 0.08 of fringe offset.


Reference Mass Line Injecting Point

In the Recycled configuration we observed a strange behavior of the measured optical matrix (even if the sine behavior of the matrix as a function

of the demodulation phase was verified)

We have measured the optical matrix of the system by injecting high frequency lines (from 20 to 50 Hz) at the level of the reference mass in the Recombined

Mode (in which we did not have any problem) and in Recycled Mode.


PR BS NI NE WI WE

B2_q1_ACp -0.175 0 -3.024 -0.643 2.174 -0.318

B2_q1_ACq -0.202 0 2.282 -0.484 1.476 -0.234

B2_q2_ACp -0.097 0 -1.238 -0.25 0.831 -0.118

B2_q2_ACq 0 0 1.136 -0.251 0.821 -0.13

B5_q1_ACp 1.617 0 0 0 0 0.432

B5_q1_ACq 6.398 0 -33.533 7.5 -21.335 2.298

B5_q2_ACp 4.270 0 18.845 4.79 -12.764 1.071

B5_q1_ACq -2.506 0 -19.884 3.665 -10.926 1.533

B7_q1_ACp -0.945 0 -4.018 -0.498 2.612 -0.888

B7_q1_ACq -0.658 0 7.206 1.535 4.457 -1.225

B7_q2_ACp 0.767 0 4.943 -0.933 2.897 -0.269

B7_q2_ACp 0.566 0 2.621 0 0 1.04

B2_q1_ACp 0.966 0 -7.053 -1.263 4.109 -0.48

B2_q1_ACp -0.915 0 6.675 1.120 4.512 -1.601

B2_q1_ACp 0.8334 0 -9.80 2.175 -6.718 0.60

B2_q1_ACp -1.662 0 -12.459 -2.377 6.913 -0.998

PR BS NI NE WI WE

B2_q1_ACp -0.184 0 -3.445 -0.75 2.639 -0.289

B2_q1_ACq 0.313 0 3.236 -0.624 2.11 -0.253

B2_q2_ACp -0.1 0 -1.515 -0.313 1.058 -0.113

B2_q2_ACq 0.124 0 1.1338 -0.8 0.963 -0.119

B5_q1_ACp 1.179 0 0 0 0 0.65

B5_q1_ACq 5.038 0 -27.672 5.98 10.539 1.199

B5_q2_ACp 3.866 0 15.843 3.98 -6.05 0

B5_q1_ACq -1.973 0 -15.897 3.031 -6.96 0.915

B7_q1_ACp -0.884 0 -4.322 -0.501 1.367 -0.78

B7_q1_ACq 0.75 0 7.627 1.579 4.655 -1.157

B7_q2_ACp 0.757 0 4.315 -0.533 2.484 0.147

B7_q2_ACp 0.504 0 2.33 -0.451 0 1.03

B2_q1_ACp -0.638 0 -6.61 -1.18 3.27 0.48

B2_q1_ACp -0.67 0 6.338 0.83 3.79 -1.556

B2_q1_ACp -0.76 0 -9.80 2.05 -6.169 0.371

B2_q1_ACp -1.6 0 -12.93 -2.572 5.72 -0.767

Excessively high coefficient values



PR BS NI NE WI WE

B2_q1_ACp -0.175 0 -3.024 -0.643 2.174 -0.318

B2_q1_ACq -0.202 0 2.282 -0.484 1.476 -0.234

B2_q2_ACp -0.097 0 -1.238 -0.25 0.831 -0.118

B2_q2_ACq 0 0 1.136 -0.251 0.821 -0.13

B5_q1_ACp 1.617 0 0 0 0 0.432

B5_q1_ACq 6.398 0 -33.533 7.5 -21.335 2.298

B5_q2_ACp 4.270 0 18.845 4.79 -12.764 1.071

B5_q1_ACq -2.506 0 -19.884 3.665 -10.926 1.533

B7_q1_ACp -0.945 0 -4.018 -0.498 2.612 -0.888

B7_q1_ACq -0.658 0 7.206 1.535 4.457 -1.225

B7_q2_ACp 0.767 0 4.943 -0.933 2.897 -0.269

B7_q2_ACp 0.566 0 2.621 0 0 1.04

B2_q1_ACp 0.966 0 -7.053 -1.263 4.109 -0.48

B2_q1_ACp -0.915 0 6.675 1.120 4.512 -1.601

B2_q1_ACp 0.8334 0 -9.80 2.175 -6.718 0.60

B2_q1_ACp -1.662 0 -12.459 -2.377 6.913 -0.998

Sign Flips

PR BS NI NE WI WE

B2_q1_ACp -0.184 0 -3.445 -0.75 2.639 -0.289

B2_q1_ACq 0.313 0 3.236 -0.624 2.11 -0.253

B2_q2_ACp -0.1 0 -1.515 -0.313 1.058 -0.113

B2_q2_ACq 0.124 0 1.1338 -0.8 0.963 -0.119

B5_q1_ACp 1.179 0 0 0 0 0.65

B5_q1_ACq 5.038 0 -27.672 5.98 10.539 1.199

B5_q2_ACp 3.866 0 15.843 3.98 -6.05 0

B5_q1_ACq -1.973 0 -15.897 3.031 -6.96 0.915

B7_q1_ACp -0.884 0 -4.322 -0.501 1.367 -0.78

B7_q1_ACq 0.75 0 7.627 1.579 4.655 -1.157

B7_q2_ACp 0.757 0 4.315 -0.533 2.484 0.147

B7_q2_ACp 0.504 0 2.33 -0.451 0 1.03

B2_q1_ACp -0.638 0 -6.61 -1.18 3.27 0.48

B2_q1_ACp -0.67 0 6.338 0.83 3.79 -1.556

B2_q1_ACp -0.76 0 -9.80 2.05 -6.169 0.371

B2_q1_ACp -1.6 0 -12.93 -2.572 5.72 -0.767



Marionette line injecting point

We decided to measure the optical matrix by injecting the lines at the level of the marionette (going to low frequency 5 to 9 Hz)

• The strangely high amplitude of the coefficients is disappeared

• There are not sign flip anymore

• The matrix measurements seem to be nicely repeatable


Offline Validation of the Linear Alignment

Loops


Offline Data Analysis

The error signals are constructed, in an offline analysis, starting from the measured quadrant signals and then applying the reconstruction matrix

In this way we can easily check the quality of our reconstruction taking the decoupling of the injected signals as a measure

Reconstructing

Matrix

Optical

Matrix

Reconstructed Correction

Signals



PR NI NE

WI WE


Further Matrix Quality Analysis

PR NI NE WI WE

B2q1p 0.107 -0.096 0.0133 -0.0285 0.0224

B2q1q 0.588 -0.296 0.00867 -0.306 0

B2q2p 0.573 -0.308 0 -0.278 0.0107

B2q2q 0.317 -0.126 -0.0136 -0.191 -0.0238

B5q1p 0 -0.0147 0.0452 0.0117 -0.0248

B5q1q 0.307 -0.166 0.0601 -0.149 -0.052

B5q2p 0.311 -0.177 0.0296 -0.142 -0.0231

B5q2q 0 -0.00233 -0.0136 0.00557 -0.00633

B7q1p 0.0155 -0.0107 0.022 -0.00535 -0.0199

B7q1q -0.00405 0.0102 0.000141 -0.00607 0

B7q2p 0.0284 -0.0227 0.00156 -0.00636 -0.00194

B7q2q 0.00283 -0.00283 0.0194 0 -0.0192

B8q1p 0.0113 0 -0.0165 -0.012 0.0182

B8q1q 0.00585 -0.00698 -0.0105 0.000644 0.012

B8q2p 0.0264 -0.00619 0 -0.0209 -0.00019

B8q2q 0.00903 0.0011 -0.0191 -0.00949 0.0194

Optical matrix computed with

SIESTA simulation

(G.Giordano)


Suspended bench External bench

PR NI NE WI WE

PR 0 7.1 71.2 5.7 74.1

NI 7.1 0 67.9 12.8 75.1

NE 71.2 67.9 0 74.1 40.4

WI 5.7 12.8 74.1 0 73.9

WE 74.1 75.1 40.4 73.9 0

Angle between column vectors:

Minimum angle: 6 deg (matrix subset: 30 deg)

Conditioning of the system: 300

2 noise distribution: PR NI NE WI WE

3.5 3.4 1 3.6 1

Further Matrix Quality Analysis

Linear Alignment System for the VIRGO Interferometer

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