Advances in Imaging and Electron Physics (eBook)

Cover 1
Contents 6
Contributors 8
Preface 10
Future Contributions 12
Phase Diversity: A Technique for Wave-Front Sensing and for Diffraction-Limited Imaging 18
Introduction and Problem Statement 20
Context 20
Image Formation 21
PSF of a Telescope 22
Origin of PSF Degradations: Intrinsic Aberrations 22
Origin of PSF Degradations: Atmospheric Turbulence 23
Astronomical observation from the ground 23
Earth observation from Space 24
Parameterization of the Phase 25
Discrete Image Model 27
Basics of Phase Diversity 28
Uniqueness of the Phase Estimate 28
Inverse Problems at Hand 28
Applications of Phase Diversity 29
Quasi-Static Aberration Correction of Optical Telescopes 30
Monolithic-Aperture Telescope Calibration 30
Space-based telescopes 30
Ground-based telescopes 30
Cophasing of Multiaperture Telescopes 31
Diffraction-Limited Imaging Through Turbulence 31
A posteriori Correction 32
Real-Time Wave-Front Correction 33
Phase Estimation Methods 33
Joint Estimator 34
Joint Criterion 34
Noise 35
Object prior probability distribution 35
Phase prior probability distribution 35
Criterion 36
Expression of o 37
Circulant Approximation and Expression in Fourier Domain 37
Tuning of the Hyperparameters 38
Noise 38
Aberrations 39
Object 39
Marginal Estimator 39
Expression of RI-1 40
Determinant of RI 40
Marginal Criterion 41
Relationship Between the Joint and the Marginal Criteria 41
Expression in the Fourier Domain 42
Unsupervised Estimation of the Hyperparameters 42
Extended Objects 43
Apodization 43
Guard Band 44
Joint estimator 44
Marginal estimator 44
Properties of the Phase Estimation Methods 45
Image Simulation 45
Asymptotic Properties of the Two Estimators for Known Hyperparameters 46
Joint Estimation: Influence of the Hyperparameters 49
Marginal Estimation: Unsupervised Estimation 51
Performance Comparison 52
Conclusion 53
Restoration of the Object 53
With the Joint Method 54
With the Marginal Method 55
Principle 55
Results 56
Influence of the Hyperparameters 56
With a "Hybrid'' Method 57
Principle 57
The Three Steps 57
Results 58
Conclusion 59
Optimization Methods 59
Projection-Based Methods 59
Line-Search Methods 61
Strategies of Search Direction 61
Step Size Rules 62
Trust-Region Methods 62
Application of Phase Diversity to an Operational System: Calibration of NAOS-CONICA 63
Practical Implementation of Phase Diversity 63
Choice of the Defocus Distance 63
Image Centering 64
Spectral Bandwidth 64
Calibration of NAOS and CONICA Static Aberrations 65
The Instrument 65
Calibration of CONICA Stand-Alone 66
Phase diversity setup 66
Example of CONICA aberration estimation 66
Calibration of the filters and objectives 67
Calibration of the NAOS Dichroics 68
Phase-diversity setup 68
Calibration of NAOS dichroic aberrations 68
Closed-Loop Compensation 69
Conclusion 70
Emerging Methods: Measurement of Large Aberrations 70
Problem Statement 70
Large Aberration Estimation Methods 72
Estimation of the Unwrapped Phase 72
Zernike polynomials 72
Delta functions 73
Estimation of the Wrapped Phase (Then Unwrapping) 73
Estimation of phi[2pi]: Construction of a regularized criterion 74
Phase-unwrapping 76
Simulation Results 76
Choice of an Error Metric 76
Results 76
Data generation 76
Point source 77
Extended object 77
Emerging Applications: Cophasing of Multiaperture Telescopes 80
Background 80
Experimental Results on an Extended Scene 82
Conclusion 85
References 85
Solving Problems with Incomplete Information: A Grey Systems Approach 94
Problems with Uncertainty 95
Stochastic Uncertainty 96
Grey Uncertainty 97
Uncertainty 97
Fuzzy Uncertainty 98
Rough Uncertainty 99
Soros Reflexive Uncertainty 100
Appearance of Grey Systems Research 100
The Fundamentals 101
Grey Numbers and Their Whitenizations 101
Grey Numbers with Only Lower Limits 101
Grey Numbers with Only Upper Limits 102
Interval Grey Numbers 102
Continuous Grey Numbers and Discrete Grey Numbers 102
Black and White Numbers 102
Essential Grey Numbers and Nonessential Grey Numbers 102
Arithmetic of Interval Grey Numbers 104
Degree and Information Content of Greyness 104
Methods for Sequences with Abnormal Behaviors 109
Sequences with Missing Entries 109
Sequences under Influence of Shock Waves 111
Calculus Generalized to Time Series 114
Incidence Analysis 118
Several Well-Employed Sequence Operators 119
Degrees of Grey Incidences 121
Analysis of Preferences 127
Clustering and Evaluations 131
Two Practical Situations 132
Methods of Clustering 134
Grey Statistics 140
Law of Exponentiality and Predictions 147
Model GM(1,1) 147
GM(1,N) and GM(0,N) 149
Time Series Predictions 152
Interval Predictions 152
Disaster Predictions 153
Seasonal Disaster Predictions 154
Stock Market-Like Predictions 155
Systems Predictions 156
A Test of Applications 158
Decision-Making Based on Incomplete Information 160
Decision-Making with Uncertain Targets 162
Decision-Making Employing Incidence Analysis 164
Decisions Based on Predicted Future 165
Collective Decision-Making 166
A Test of Applications 167
Programmings with Uncertain Parameters 169
Linear Models 170
Properties of Solutions of Grey Linear Models 172
Assignment Problems of Grey Prediction Type 174
Nonlinear Programming 176
Control of Not Completely Known Systems 178
Linear Control Systems 179
Transfer Functions 180
Other Kinds of Controls 183
A Test of Applications 184
References 186
Recent Developments in the Imaging of Magnetic Domains 192
Introduction 192
Experimental Techniques 197
SEM Type I Magnetic Contrast 200
Bitter Pattern Method 221
Magnetic Force Microscopy 241
Conclusions 257
References 261
Deconvolution Over Groups in Image Reconstruction 274
Introduction 275
Motivations 275
Organization 276
Convolution and Fourier Analysis on Groups 277
Convolution on Groups 277
Fourier Analysis on Groups 279
Group Stationary Processes 280
Wiener Filtering Over Groups 283
Remarks 284
Wideband Extended Range-Doppler Imaging 285
Fourier Theory of the Affine Group 288
Affine Group 288
Fourier Transform over the Affine Group 289
Target Reflectivity Estimation 290
Receiver Design 291
Waveform Design 292
Numerical Experiments 294
Radon and Exponential Radon Transforms 296
Fourier Transform over M(2) 299
Radon and Exponential Radon Transforms as Convolutions 302
Radon Transform 302
Exponential and Angle-Dependent Exponential Radon Transforms 303
Inversion Methods 304
Numerical Algorithms 306
Fourier Transform over M(2) 306
Reconstruction Algorithm 307
Numerical Simulations 307
Radon Transform 307
Exponential Radon Transform with Uniform Attenuation 309
Conclusion 309
Acknowledgments 309
Appendix A 310
Definitions 310
Definition A1.1 311
Definition A1.2 311
Definition A1.3 311
Appendix B 312
Distributions and Fourier Transform Over M(2) 312
References 313
Index 318