Hartmann Wavefront Sensors for Advanced Gravitational Wave Interferometers Aidan F. Brooks

252 Pages·2007·9.3 MB·English

Hartmann Wavefront Sensors for
Advanced Gravitational Wave
Interferometers
by
Aidan F. Brooks
Thesis submitted for the degree of
Doctor of Philosophy
in
The University of Adelaide
Department of Physics
School of Chemistry and Physics
July, 2007
2
For my parents
2
Contents
Abstract vii
Statement of Originality ix
Acknowledgements xi
List of Symbols xiii
List of Figures xv
List of Tables xix
1 Gravitational wave astronomy 1
1.1 A better understanding of the Universe . . . . . . . . . . . . . 1
1.1.1 Gravitational waves . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Sources of GW and potential new science . . . . . . . . 2
1.2 The challenge of GW interferometry . . . . . . . . . . . . . . . 3
1.2.1 First generation GW interferometry . . . . . . . . . . . 3
1.2.2 Advanced GWI enabling gravitational astronomy . . . 6
1.2.3 Higher stored power leads to wavefront distortion . . . 9
1.2.4 Adv. GWI: thermally-induced performance reduction . 11
1.3 Active compensation of WD . . . . . . . . . . . . . . . . . . . 12
1.3.1 Thermal compensation techniques . . . . . . . . . . . . 12
1.3.2 Wavefront sensor requirements for thermal compensation 14
1.4 Wavefront sensors for TCS . . . . . . . . . . . . . . . . . . . . 14
1.5 This thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
i
ii CONTENTS
2 Interferometric test of H-V theory 19
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Design and choice of test optic . . . . . . . . . . . . . . . . . . 20
2.3.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 Choice of material . . . . . . . . . . . . . . . . . . . . 21
2.3.3 Induced WD vs. H-V predicition . . . . . . . . . . . . 22
2.4 Measurement and analysis of WD . . . . . . . . . . . . . . . . 25
2.4.1 Multiple heating beam sizes . . . . . . . . . . . . . . . 26
2.4.2 Experiment design . . . . . . . . . . . . . . . . . . . . 26
2.4.3 Measurement procedure . . . . . . . . . . . . . . . . . 29
2.4.4 Analysis of MZ interference patterns . . . . . . . . . . 30
2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.1 Background noise . . . . . . . . . . . . . . . . . . . . . 36
2.5.2 Temporal development of measured wavefront distortion 36
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3 Hartmann sensor development 43
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Hartmann sensor basics . . . . . . . . . . . . . . . . . . . . . . 44
3.2.1 Applications of the Hartmann sensor . . . . . . . . . . 44
3.2.2 Overview of Hartmann sensor . . . . . . . . . . . . . . 46
3.2.2.1 Absolute or differential operation . . . . . . . 50
3.2.3 Hartmann plate - CCD configurations . . . . . . . . . . 52
3.2.4 Variants of the traditional Hartmann sensor . . . . . . 54
3.2.4.1 Shack-Hartmann . . . . . . . . . . . . . . . . 54
3.2.4.2 Other variations . . . . . . . . . . . . . . . . 57
3.2.5 Temperature dependence of Hartmann sensors . . . . . 59
3.3 Hartmann sensor for advanced GWI . . . . . . . . . . . . . . . 60
3.3.1 Light source - coherent versus incoherent . . . . . . . 60
3.3.2 Optimization of Hartmann plate design . . . . . . . . . 63
3.3.2.1 Modelling . . . . . . . . . . . . . . . . . . . . 64
3.3.2.2 Simulations of cross-talk . . . . . . . . . . . . 70
3.3.2.3 HWS construction . . . . . . . . . . . . . . . 74
CONTENTS iii
3.3.2.4 Estimatedtemperaturedependentdefocuser-
ror . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3.3 CCD camera . . . . . . . . . . . . . . . . . . . . . . . 75
3.3.3.1 Expected noise in CCD . . . . . . . . . . . . 77
3.3.3.2 CCD: Measurement of noise . . . . . . . . . . 78
3.3.3.3 Pixel size measurement . . . . . . . . . . . . 79
3.3.4 Centroiding algorithms . . . . . . . . . . . . . . . . . . 80
3.3.4.1 Weighted center of gravity (WCoG) . . . . . . 82
3.3.4.2 Fractional pixel centroiding (FPC) . . . . . . 83
3.3.4.3 Comparison of algorithms . . . . . . . . . . . 85
3.3.5 Wavefront reconstruction algorithm . . . . . . . . . . . 87
3.3.5.1 Modal wavefront reconstruction . . . . . . . . 87
3.3.5.2 Zonal wavefront reconstruction . . . . . . . . 88
3.3.5.3 Error propagation - From gradient to wavefront 91
3.3.6 Summary of noise sources . . . . . . . . . . . . . . . . 92
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4 Testing the sensor 95
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2 Lever arm calibration . . . . . . . . . . . . . . . . . . . . . . . 96
4.2.1 Discounting other solutions due to pattern degeneracy 98
4.3 Incoherent vs. coherent sources . . . . . . . . . . . . . . . . . 100
4.4 Temperature dependence of HWS . . . . . . . . . . . . . . . . 106
4.5 Noise floor of the Hartmann sensor . . . . . . . . . . . . . . . 108
4.6 Accuracy test using known wavefront change . . . . . . . . . . 111
4.6.1 Analytic form of known wavefront change . . . . . . . 111
4.6.2 Experiment design . . . . . . . . . . . . . . . . . . . . 113
4.6.3 Calibration of the origin for z . . . . . . . . . . . . . . 115
0
4.6.4 Mitigating cyclic temperature fluctuations . . . . . . . 118
4.6.5 Experiment procedure . . . . . . . . . . . . . . . . . . 118
4.6.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
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5 HOPTF WD measurement 127
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3 Description of measurement system . . . . . . . . . . . . . . . 128
5.3.1 The high-optical-power cavity at HOPTF . . . . . . . . 128
5.3.2 Installation of the HWS at HOPTF . . . . . . . . . . . 130
5.3.3 Reduction of environmental noise coupling into HWS . 132
5.4 Measurement procedure and analysis . . . . . . . . . . . . . . 135
5.4.1 Measurement procedure . . . . . . . . . . . . . . . . . 135
5.4.2 Analysis of wavefront distortion . . . . . . . . . . . . . 138
5.4.2.1 Off-axis WD to on-axis WD . . . . . . . . . . 138
5.4.2.2 On-axis WD to cavity-mode WD . . . . . . . 141
5.4.2.3 Defocus of cavity-mode WD . . . . . . . . . . 143
5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.5.1 Measured off-axis wavefront distortion . . . . . . . . . 145
5.5.2 Temporal development of cavity defocus . . . . . . . . 145
5.5.3 Measured distortion and stored power correlation . . . 148
5.5.4 Measured distortion and cavity mode size correlation . 150
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6 Off axis measurement of distortion 155
6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
6.3 Analysis of off-axis WD. . . . . . . . . . . . . . . . . . . . . . 156
6.3.1 A zonal representation of T(r,z) . . . . . . . . . . . . . 158
6.4 Numerical simulation of voxel analysis . . . . . . . . . . . . . 161
6.4.1 Simulation procedure . . . . . . . . . . . . . . . . . . . 161
6.4.2 Simulation results . . . . . . . . . . . . . . . . . . . . . 163
6.5 Proof-of-principle of off-axis analysis . . . . . . . . . . . . . . 165
6.5.1 System layout . . . . . . . . . . . . . . . . . . . . . . . 165
6.5.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
CONTENTS v
7 Conclusion 171
7.1 Review of aims . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.2 Summary of results . . . . . . . . . . . . . . . . . . . . . . . . 172
7.3 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . 173
A Additional derivations 175
A.1 Analytic form of Hello-Vinet solution . . . . . . . . . . . . . . 175
A.2 Variance of a digitized value . . . . . . . . . . . . . . . . . . . 177
A.3 ABCD cavity calculation . . . . . . . . . . . . . . . . . . . . . 178
B Computer code 181
B.1 Hartmann plate optimization code . . . . . . . . . . . . . . . . 181
B.2 Cross-talk analysis: diffraction propagation . . . . . . . . . . . 189
B.3 FEM of ITM and CP thermal lens at the HOPTF . . . . . . . 192
C Relevant papers 203
C.1 Gen. Relativ. Gravit. 37, 1575-1580 (2005) . . . . . . . . . . . 203
C.2 Opt. Express 15 (16), 10370-10375 (2007) . . . . . . . . . . . 210
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