Application and Optimisation of the Spatial Phase Shifting ...

Table of Contents 1
1 INTRODUCTION 3
2 STATISTICAL PROPERTIES OF SPECKLE PATTERNS 7
2.1 Experimental set-up 7
2.2 First-order speckle statistics 10
2.2.1 Basic probability-density function 10
2.2.2 Intensity and phase 11
2.2.3 Gradients in one dimension 12
2.2.4 Gradients in two dimensions 21
2.2.5 Zero-intensity minima 26
2.3 Second-order speckle statistics 33
2.3.1 Intensity autocorrelation 33
2.3.2 Phase autocorrelation 35
2.3.3 Second-order probability densities 37
3 ELECTRONIC OR DIGITAL SPECKLE PATTERN INTERFEROMETRY 47
3.1 Subtraction-mode ESPI 49
3.2 Phase-shifting ESPI 51
3.2.1 Calculation of phase changes in ESPI 54
3.2.2 Spectral transfer properties of few-sample phase shifting formulae 61
3.3 Temporal phase shifting 75
3.3.1 Speckle "size" in interferograms 76
3.4 Spatial phase shifting 79
3.4.1 Geometrical description of spatial phase shift 81
3.4.2 Evaluation of SPS interferograms 83
3.4.3 Relation of speckle size and magnification 85
3.4.4 Spatial phase shifting on speckle fields 86
3.4.5 Spectral side-effects of spatial phase calculation 88
3.4.6 Distorted phase distributions due to miscalibrated phase shift 94
4 QUANTIFICATION OF DISPLACEMENT-MEASUREMENT ERRORS 99
4.1 Previous methods 99
4.1.1 Processing of correlation fringes 99
4.1.2 Processing of sawtooth fringes 101
4.2 Noise quantification in this work 106