Application and Optimisation of the Spatial Phase Shifting ...

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172 Improvements on SPS the heater was switched on, while for the cooling period ϕ O (x, y, t i ) was stored at an ambient temperature T 2 when the heater was switched off. 3.4 µm -0.4 µm -2.3 µm 1.3 µm Fig. 6.31: Displacement phases mod 2π (left) and corresponding "temperature" height maps as delivered by temporal unwrapping (right), for heating (top) and cooling period (bottom). Numerical values denote maximum and minimum displacements. While it would be very laborious to define and spatially unwrap all the regions separately, it is even impossible to determine their relative heights from the sawtooth images on the left. When such displacements are monitored with temporal unwrapping, the problems are overcome. Without the need to fit data from different sub-areas together, a complete profile of the surface changes is obtained. One can, and should, test its reliability by checking the obtained surface tilts for consistency with those following from the number of sawtooth fringes. On removing the abovementioned "slow" pixels, Φ(x, y) from temporal phase unwrapping did not deviate by more than 0.1 λ from Φ(x, y) as produced by spatial unwrapping of the corresponding sawtooth images, which also justifies some confidence in the absolute heights that are given in Fig. 6.31. According to the height maps from temporal unwrapping on the right, the deformations that developed in the heating period are almost reversed during cooling, apart from some remaining displacements and deformations that are clearly emphasised by an addition of the height data from the two states, as demonstrated in Fig. 6.32 on the right. Most of the remaining displacement is presumably caused by an ambient temperature at the end of the cooling period that differed from T 1 .
6.7 Extensions of SPS by temporal unwrapping 173 Fig. 6.32: Overall displacement after heating and cooling. Residual tilts are visible in the sawtooth image (left); rigid-body displacements are revealed in the "temperature" height map (right). Arrows mark locations of possible misinterpretations of the sawtooth image. On the other hand, the sum of the sawtooth images lacks important information. At the black arrow, a substantial piston-type displacement is not discernible from the sawtooth image, while at the white arrow, the nearly matching fringe positions almost conceal the step of 0.3 µm (1 fringe) that has actually remained. On the contrary, the results based on the height maps from the temporally unwrapped data are unambiguous. They need no interpretation and thus allow an easier assessment of object changes.
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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 124 and 125: 122 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:
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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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