Application and Optimisation of the Spatial Phase Shifting ...

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162 Improvements on SPS To obtain performance data for our approach, we use the σ d values from a simple out-of-plane tilt. The test object is a white painted metal plate that scatters with strong depolarisation (ρ = 0.78 ± 0.01). The light scattered off the object is imaged with a lens L2 onto the target of the CCD camera, with 1024×768 pixels. A polariser PF in front of the camera target selects either the vertical or horizontal SOP of the scattered light. The measured correlation coefficient for the corresponding speckle fields S vi (x,y) and S hi (x,y) is c = 0.02 ± 0.005 which is in acceptable agreement with the value of c = 0.03 ± 0.003 expected for the measured depolarisation coefficient. Since S v /S h 0.78, the plane of polarisation of the reference wave is set to 48° instead of 45° by the POC to obtain P vb (x,y)P hb (x,y), this is, we intend to replace some 50% of ϕ O,vi (x,y) (ϕ O,vf (x,y)) by entries from ϕ O,hi (x,y) (ϕ O,hf (x,y)), whereby the best utilisation of both speckle patterns is assured. The reference wave's fibre end is placed in the aperture plane A of the imaging system and positioned to yield α x = 120°/column on the CCD sensor. The phase stabilisation works as follows: part of the object light is reflected by the small mirror M1 mounted on the object. It passes through the lens L2 and is then reflected by another small mirror M2, close beside the CCD chip, towards the plane S. On the opposite side of the CCD sensor, a small beamsplitter BS reflects a part of the reference wave towards S. By proper adjustment of M1, M2 and BS, both waves can interfere in S, forming an interference pattern of concentric fringes as shown in Fig. 6.21. This is far easier to achieve than broad fringes of stable shape. D2 D1 Fig. 6.21: Interference pattern in the plane S of the PID unit; the white squares indicate the locations and areas of the photodiodes. The circular boundary of the pattern is due to the imaging aperture. A photodiode D1 is placed in the centre of this pattern where a broad fringe occurs. Another one, D2, is placed outside the centre, integrating the intensity distribution over some 12 fringes. Thus, the output of D2 is insensitive to phase variations and tracks the intensity fluctuations of the laser instead. Whenever phase changes occur between the object and the reference wave, the intensity in the centre of the fringe system changes. This variation is detected by D1, while intensity fluctuations of the laser are detected by
6.6 Use of depolarisation to eliminate invalid pixels 163 D2 and D1. The difference signal of the detectors D1 and D2 is processed by a PID controller and then fed into a high voltage amplifier HV. The amplifier drives a piezo electric cylinder PZ (Ferroperm PZ 27), onto which some turns of the reference fibre are wound and which works as a phase shifter [Dav74]. By this closed-loop control system, the phase difference between O and R is stabilised with respect to that point of the object surface where M1 is mounted. The achieved cut-off frequency of the phase compensating unit of about 1.4 kHz is found to be adequate for the desired purpose. Also, the long-term stability of this arrangement was found to be satisfactory [Sag98]. At the beginning of the measurement, B 10 and d s 3 d p were adjusted. Unfortunately, we have to use an average for R, and hence for the beam ratio, here: as can be seen in Fig. 6.20, the reference wave was directed so as to illuminate BS sufficiently. The maximum of its intensity profile lay beside the CCD array, which caused the local intensity of R to vary between 2R and R/3 from edge to edge of the sensor. Hence, 3
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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
Page 114 and 115: 112 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 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
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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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Application and Optimisation of the Spatial Phase Shifting ...

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