Application and Optimisation of the Spatial Phase Shifting ...

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175 7 Summary This thesis work has presented a detailed investigation of various aspects that concern the application of spatial phase shifting (SPS) in ESPI. The objective was to broaden the previously somewhat sparse knowledge of what happens in spatial phase sampling on speckle fields, and to utilise the findings to introduce some improvements of SPS. The ground on which to base such an investigation is, first of all, an extensive study of the nature of speckle fields. Fortunately, speckle statistics have been an important topic in optical research for some 40 years, so that many useful results could be collected and grouped. The theoretical studies were accompanied by experimental validations of some results. With respect to SPS, the one-dimensional intensity and phase gradients deserve particular interest, and it was found that the speckle intensity is correlated with the intensity gradient and anticorrelated with the phase gradient. This simple rule of thumb provided valuable guidance as to the assistance of speckle statistics in improving SPS. The speckle intensity field, showing more spatial structure than the phase field, hardly allows reasonable assumptions to be modelled in the phase calculation, but is directly accessible in the experiment. This extra information can be used to counteract the disadvantageous influence of speckle intensity fluctuations on the interferogram. The speckle phase field was seen to be co-operative for interferometry: the phase gradients are low where the speckle field is bright, and those regions of the field where the phase "leaps" or is even undefined, were seen to be rather dark anyway. Since constant speckle phase gradients can be envisaged as linear phase-shift miscalibrations, the use of phase-calculation formulae that are tolerant of this type of error seemed to be the most sensible decision for effectively reducing measurement errors. After getting familiar with the properties of the speckled object wavefront, it was necessary to turn towards optimisation of the way to process speckle interferograms. For this purpose, digital speckle interferometry and the phase-sampling process have been reviewed. It was found that it is always better, in SPS and TPS, to subtract speckle phase maps than to work with correlation fringes; this has been confirmed by experimental results. The aspects of speckle interferometry that pertain especially to SPS have been discussed in detail. The spatial phase shift was seen to be geometrically quasi-constant to a very high degree of accuracy; however the spatial frequency content of speckle interferograms supersedes this theoretical result, and the subjects of speckle size and phase-shift setting have been addressed from the viewpoint of spatial frequencies. Since speckle phase gradients cause significant distortions in the carrier fringe pattern, its spatial frequency spectrum will be considerably broadened. It is therefore worthwhile to examine the effect in the spatial frequency domain. Consequently, the well-established and powerful Fourier description of phaseshifting formulae has been used. It interprets phase extraction as a digital signal filtering process in the spectral domain, with characteristic spectral amplitude and phase transfer functions. When using this
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Application and Optimisation of the
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Table of Contents 1 1 INTRODUCTION
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3 1 Introduction The present era of
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Introduction 5 retrieval can help t
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7 2 Statistical Properties of Speck
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2.1 Experimental set-up 9 Gaussian
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2.2 First-order speckle statistics
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2.3 Second-order speckle statistics
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47 3 Electronic or Digital Speckle
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3.1 Subtraction-mode ESPI 49 some 4
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3.2 Phase-shifting ESPI 51 filled u
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3.2 Phase-shifting ESPI 53 known si
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3.2 Phase-shifting ESPI 55 α n =α
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3.2 Phase-shifting ESPI 57 But reme
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3.2 Phase-shifting ESPI 59 ϕ ϕ O,
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3.2 Phase-shifting ESPI 61 These fo
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3.2 Phase-shifting ESPI 63 ∞ ~ ~
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3.2 Phase-shifting ESPI 65 ∞ N
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3.2 Phase-shifting ESPI 67 The spec
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3.2 Phase-shifting ESPI 69 − 0. 2
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3.2 Phase-shifting ESPI 71 ν x 0 i
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3.2 Phase-shifting ESPI 73 to think
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3.3 Temporal phase shifting 75 Agai
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3.3 Temporal phase shifting 77 addi
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3.4 Spatial phase shifting 79 which
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3.4 Spatial phase shifting 81 3.4.1
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3.4 Spatial phase shifting 83 cross
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3.4 Spatial phase shifting 85 Fig.
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3.4 Spatial phase shifting 87 arran
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3.4 Spatial phase shifting 89 infor
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3.4 Spatial phase shifting 91 frequ
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3.4 Spatial phase shifting 93 altho
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3.4 Spatial phase shifting 95 error
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3.4 Spatial phase shifting 97 Since
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100 Quantification of displacement-
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110
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112 Comparison of noise in phase ma
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Page 126 and 127: 124 Comparison of noise in phase ma
Page 136 and 137: 134 Improvements on SPS intensity o
Page 138 and 139: 136 Improvements on SPS 0.14 σ d /
Page 140 and 141: 138 Improvements on SPS we are conc
Page 142 and 143: 140 Improvements on SPS 6.2 Modifie
Page 146 and 147: 144 Improvements on SPS Fig. 6.7 te
Page 148 and 149: 146 Improvements on SPS Finally, bo
Page 150 and 151: 148 Improvements on SPS To use the
Page 152 and 153: 150 Improvements on SPS The improve
Page 154 and 155: 152 Improvements on SPS On the whol
Page 156 and 157: 154 Improvements on SPS In classica
Page 158 and 159: 156 Improvements on SPS generally n
Page 162 and 163: 160 Improvements on SPS uncertain,
Page 164 and 165: 162 Improvements on SPS To obtain p
Page 166 and 167: 164 Improvements on SPS Fig. 6.22:
Page 168 and 169: 166 Improvements on SPS This proced
Page 170 and 171: 168 Improvements on SPS 6.7.2 Long-
Page 172 and 173: 170 Improvements on SPS Fig. 6.28:
Page 174 and 175: 172 Improvements on SPS the heater
Page 178 and 179: 176 Summary method to search for a
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Page 182 and 183: 180 References [Bot97] [Bra87] [Bro
Page 184 and 185: 182 References [Ett97] [Fac93] [Far
Page 186 and 187: 184 References [Har94] [Her96] [Het
Page 188 and 189: 186 References [Kuj89] [Kuj91a] [Ku
Page 190 and 191: 188 References [McLa86] [Mer83] J.
Page 192 and 193: 190 References [Rav99] I. Raveh, E.
Page 194 and 195: 192 References [Sur98b] [Sur98c] [S
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Page 198 and 199: 196 Appendix A: Counting events and
Page 200 and 201: 198 Appendix B: Real-time phase cal
Page 202 and 203: 200 Appendix C: Derivation of inten
Page 204 and 205: I 1 a r g ( S ~ ( ) ) 202 Appendix
Page 206 and 207: 204 Appendix D: Alternative error-c
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Page 212 and 213: 210 The author List of publications
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