ENGINEERING SCIENCES ; t rical Bngi.net

IMAGING WITH SYNTHETIC APERTURE

RADAR Didier Massonnet & Jean-Claude Souyris

EPFL P r e s s A Swiss academic publisher distributed by CRC Press

Table of Contents

Acknowledgements v

Preface vii

A THEORETICAL EMERGENCY KIT FOR SAR IMAGERY 1

1.1 The propagation and polarization of electromagnetic waves 1

1.1.1 Maxwell's Equations 1

1.1.2 The polarization of electromagnetic waves . . . . 4

1.1.3 Partially polarized waves . . 11

1.1.4 In passing: the elegant algebra of the SU(2)-0+(3) homomorphism 17

1.2 The electromagnetic radiation of microwave antennas . . 19

1.2.1 Introduction 19

1.2.2 The electromagnetic radiation equation 19

1.2.3 Resolving the electromagnetic radiation equation 20

1.2.4 Antenna pattern, directivity and gain 20

1.2.5 The radiation of planar antennas 21

1.2.6 Array antennas 24

1.2.7 SAR antenna technology 26

1.3 Interaction between waves and natural surfaces 26

1.3.1 Introduction 26

1.3.2 Surface scattering 27

1.3.3 Volume scattering 35

1.3.4 Penetration properties of electromagnetic waves . 36

1.3.5 The effects of slope on radiometry 39

1.4 Elements of signal processing 40

1.4.1 Introduction 40

1.4.2 Fourier series of real periodic functions 40

1.4.3 Fourier transform 40

X IMAGING WITH SYNTHETIC APERTURE RADAR

1.4.4 Properties of the Fourier transform (FT) 41

1.4.5 Fourier transforms of standard functions 42

1.4.6 Sampling real signals 45

1.4.7 Sampling theorem (Shannon's theorem) 46

1.4.8 The Fast Fourier transform (FFT) algorithm . . . 48

1.4.9 The two-dimensional Fourier transform 50

CHAPTER 2 SAR PROCESSING: AT THE HEART OF THE SAR

TECHNIQUE 53

2.1 Introduction 53

2.2 General principles of Synthetic Aperture Radar 54

2.2.1 A different way of observing the Earth 54

2.2.2 Range vision 55

2.2.3 The three fundamental radar frequencies 56 2.2.4 An intuitive geometrical approach to synthetic

aperture 59

2.2.5 Synthetic aperture, an analytic geometry formulation 64

2.3 Frequency representation 69

2.3.1 Phase distribution expressed in the frequency domain 70

2.3.2 Non-Zero Mean Doppler 71

2.3.3 Doppler locking 73

2.3.4 Mean Doppler (or Doppler centroid) estimation . 74

2.3.5 Mean reduced Doppler estimation (integer part) . 76

2.3.6 Range migration 78

2.3.7 Range processing 80

2.3.8 Saturation effects 81

2.3.9 Interference effects 82

2.3.10 Motionless radar approximation 83

2.4 SAR Synthesis algorithms 84

2.4.1 A common preliminary step, range compression . 84

2.4.2 Time or 'naive' processing 85

2.4.3 Range-azimuth or 'classic' processing 86

2.4.4 An alternative technique, the Clk processor . . . . 87

2.4.5 Subtle distortion, chirp scaling 87

2.4.6 PRISME architecture, a multistage processing technique 88

2.4.7 Unfocussed processing, a special case 90

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2.4.8 A practical example of the unfocussed processing technique 90

2.4.9 Another special case, deramping processing . . . 91

2.4.10 A radar processing technique without approximations 93

2.5 System constraints 94

2.5.1 Radar system design 94

2.5.2 Timing constraints 95

2.5.3 The different types of radar data 96

2.5.4 Tricks for cheating nature 97

2.6 Geometry characteristics 101

2.6.1 A practical example of the effect of range

on images 101

2.6.2 Equations for geometric positioning 104

2.6.3 Perpendicular radargrammetry 107

2.6.4 Radargrammetry and interferometry 108

2.6.5 Oblique radargrammetry 109

2.6.6 Radar clinometry 109

2.7 An introduction to super-resolution 110

2.8 Radar processing and geometric specificity of bistatic data 112

2.8.1 Direct echo 115

2.8.2 Triangular resolution 115

CHAPTER 3 FROM SAR DESIGN TO IMAGE QUALITY 117

3.1 Introduction 117

3.2 Radar equation, Radar Cross Section (RCS) of

a point target 118

3.2.1 Loss terms 120

3.3 Radar signature for extended targets - the backscatter . . 122 3.4 Signal to noise ratio (SNR) of the radar-target link before

SAR synthesis 123

3.5 Modifying the SNR during SAR synthesis 123

3.5.1 Point targets 124

3.5.2 Extended targets 130

3.6 Instrument Noise Equivalent cr°(NEcx0mst) 133

3.6.1 Energy cost for improving resolution 133

3.7 Impact of image ambiguities on the NEa°'nst - total . . . 133

3.7.1 Range ambiguities 134

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3.7.2 Azimuth ambiguities 136

3.7.3 Combined processing of range and azimuth ambiguities 137

3.7.4 Total NEa°(NEcr0"") 137

3.8 Volume of data generated onboard 139

3.9 Telemetry data rate 140

3.9.1 Source coding 141

3.10 Calibration and corresponding image quality requirements 143

3.10.1 Internal calibration 144

3.10.2 External calibration 144

3.10.3 Calibration requirements and expected scientific results 145

3.11 Speckle noise and image statistics 146

3.11.1 Physical origin 146

3.11.2 Statistics of fully developed speckle 148

3.11.3 Speckle noise: multiplicative nature and modeling 149

3.11.4 Texture effect 150

3.11.5 Speckle noise in multi-look images 151

3.11.6 Speckle reduction filters 154

3.12 The impulse response (IR) 158

3.12.1 Range impulse response (RIR) 159

3.12.2 Azimuth impulse response (AIR) 160

3.12.3 Complex image spectrum, ISLR, PSLR,

weighting effect 161

3.13 Radiometric elements of Image Quality 162

3.13.1 Estimating and analysing NEaotot 162

3.13.2 Estimating the ambiguity level 162

3.13.3 Radiometric resolution: 164

3.14 Geometric elements of image quality 165

3.14.1 Spatial resolution and pixel size . 165

3.14.2 Geometric distortion 166

3.14.3 The image location 167

3.15 Radar image interpretation 169

3.15.1 Description of data 169

3.15.2 Assessment of the Doppler spectrum 172

3.15.3 Platform position 173

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3.15.4 Saturation effects 173 3.15.5 Directional effects 174 3.15.6 Is it possible to fully characterize a radar instru­

ment only from an image? 175 CHAPTER 4 SAR INTERFEROMETRY: TOWARDS THE ULTIMATE

RANGING ACCURACY 177 4.1 Principles and limitations of radar interferometry 177

4.1.1 A specific use for radar 177 4.1.2 A brief history of interferometry 179 4.1.3 Interferometry and the physical properties of radar

images 179 4.1.4 Phase difference between radar images 180 4.1.5 Robustness of the phase signal in interferometry . 181 4.1.6 Limitations due to geometric and surface changes 181 4.1.7 Eliminating systematic contributions 184

4.2 Implementing interferometry processing 184 4.2.1 Radar image co-registration 186 4.2.2 Calculating phase differences between images . . 186 4.2.3 Finishing tasks 189

4.3 Application for topography 190 4.3.1 Set of equations and error budget 190 4.3.2 Eliminating measurement ambiguity 192

4.4 Application for displacement measurement 193 4.4.1 Set of equations and error budget 193 4.4.2 Examples of use 194

4.5 How slope effects limit interferometry 198 4.5.1 Frequency interpretation of the slope effect . . . . 201

4.6 Interpreting the results 202 4.6.1 Typical signatures of different contributions . . . 202 4.6.2 Methods for improving interpretation 202 4.6.3 Interferometry interpretation in practice 205

4.7 Availability and mission perspectives 211 4.7.1 Availability of archived radar data 211 4.7.2 Availability of processing resources 212 4.7.3 Principles of data selection 213 4.7.4 Possibilities for future dedicated space missions . 213

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4.8 Comparison of interferometry with other methods . . . . 221

4.8.1 Comparison with optical stereoscopy for topographic measurement 221

4.8.2 Comparison with GPS for measuring displacement 222

4.9 Robustness of coherent processing when faced with ambiguities 224

4.10 Permanent reflectors 226

CHAPTER 5 SAR POLARIMETRY: TOWARDS THE ULTIMATE

CHARACTERIZATION OF TARGETS 229

5.1 Introduction 229

5.2 Radar polarimetry: operating principle 230

5.2.1 Timing analysis - impact on system design . . . . 231

5.3 The scattering matrix 232 5.3.1 The monostatic singularity - the backscattering

matrix 233

5.3.2 Target vector 233

5.4 Standard forms of backscatter 234

5.4.1 Odd-bounce (single, triple) scattering 234

5.4.2 Even-bounce (double) scattering 236

5.4.3 Diffraction or dipole mechanisms 237

5.5 Polarization synthesis 238

5.5.1 Polarimetrie signatures 239

5.6 Characteristic polarization and Euler parameters 240

5.6.1 The Huynen fork 241

5.7 Coherent decomposition of the Polarimetrie measurement 241

5.7.1 Decomposition into standard mechanisms - the group of Pauli matrices 241

5.7.2 Algebraic decomposition: the Cameron approach 243

5.8 Taking depolarization into account 247

5.8.1 Stokes formalism and Mueller matrix 247

5.9 Covariance matrix - coherence matrix 250

5.9.1 Covariance matrix 251

5.9.2 Coherence matrix 253

5.10 Incoherent decomposition of Polarimetrie measurements . 254

5.10.1 Decomposition into polarization states: the Huynen approach 254

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5.10.2 Decomposition into standard mechanisms - the Freeman approach 255

5.10.3 Algebraic decomposition - The (H, a) approach . 257

5.11 Practical cases of Polarimetrie analysis 262

5.11.1 Radiometric analysis 262

5.11.2 Entropy analysis 264

5.11.3 Average backscattering mechanism 265

5.12 Synoptic representation of Polarimetrie information . . . 265

5.13 Future compact Polarimetrie systems 266

5.13.1 Another idea: compact polarimetry and the JT/4

mode 268

5.14 Merging polarimetry and interferometry: PolInSAR . . . 269

5.14.1 Interferometric coherence optimization . . . . . . 270

5.14.2 Application to the inversion of vegetation height . 271

5.14.3 PolInSAR extensions 272

5.15 Conclusion 273

Index 277