Preface ..................................................... xiii
Acknowledgments ................................................ xv
List of Contributors ......................................... xvii
1. Introduction ................................................. 1
1.1. Scope ................................................... 1
1.2. Perspective on the Field ................................ 2
1.3. Structure of the Book ................................... 4
References ................................................... 5
2. Review of Radiometry ......................................... 7
2.1 Radiometric Terms ........................................ 7
2.1.1. Definition of terms ............................... 7
2.1.2. Blackbody radiators .............................. 17
References .................................................. 20
3. The Wave Nature of EM Energy and an Introduction of the
Polarization Ellipse ........................................ 21
3.1. Wave Nature of EM Energy ............................... 21
3.2. The Polarization Ellipse ............................... 27
3.3. Special (Degenerate) Forms of the Polarization
Ellipse ................................................ 31
3.3.1. Linear polarization ............................. 31
3.3.2. Unrotated ellipse ............................... 31
References .................................................. 32
4. Representation of the Polarimetric State of a Beam .......... 33
4.1. The Stokes Parameters .................................. 33
4.2. Stokes Vector Representation ........................... 34
4.3. Methods to Characterize and Interpret Stokes
Vectors ................................................ 38
4.4. Parameters of the Polarization Ellipse and the
Poincare Sphere ........................................ 44
References .................................................. 49
5. Polarimetric Interactions: Reflection and Transmission ...... 51
5.1. Fresnel Specular Reflection ............................ 51
5.2. Polarized Transmission and Polarizing Materials ........ 54
5.3. The Mueller Matrix: Polarimetric Energy-Matter
Interactions ........................................... 57
References .................................................. 61
6. Polarimetric Bidirectional Reflectance Distribution
Functions (pBRDF) ........................................... 63
6.1. Bidirectional Reflectance Distribution Functions ....... 63
6.1.1 Ways to characterize reflectance ................. 63
6.2. Polarimetric Bidirectional Reflectance Distribution
Functions (pBRDF) ...................................... 67
6.2.1. Specular reflectors ............................. 67
6.2.2. Optical scatter from surfaces ................... 71
6.3. Reflectance Variability or Texture ..................... 76
6.4. BRDF Measurement ....................................... 77
6.4.1. Conventional laboratory measurements ............ 78
6.4.2. Camera-based measurements ....................... 79
6.4.3. Field measurements .............................. 82
6.4.3.1 Overhead BRDF measurement ...................... 84
6.4.4. Polarimetric BRDF measurement ................... 85
6.5. BRDF Models ............................................ 88
6.5.1. Torrance-Sparrow model .......................... 88
6.5.2. Maxwell-Beard model ............................. 89
6.5.3. Polarimetric BRDF models ........................ 94
6.5.3.1. Target material pBRDF models ........... 94
6.5.3.2. Background material pBRDF models ....... 95
6.6. Summary of pBRDF Concepts .............................. 96
References ................................................. 101
7. Polarized Form of the Governing Equation Including
Atmospheric Scattering Terms ............................... 107
7.1. Governing Polarized Radiance Equation ................. 107
7.1.1. Scalar representation of the governing
equation ....................................... 107
7.1.2. Governing equation—Stokes representation ....... 109
7.2. Atmospheric Scattering and the Polarized State of
the Terms in the Governing Equation ................... 112
7.2.1. Characterization of the polarized state of
the incident radiative field ................... 113
7.2.1.1. Rayleigh scatter ...................... 114
7.2.1.2. Aerosol and nonselective scatter ...... 116
7.2.2. Estimation of the atmospheric terms in the
polarized governing equation ................... 116
7.2.2.1. Use of radiative transfer codes
to estimate polarimetric
atmospheric terms ..................... 117
7.2.2.2. Visualization of sky polarization
and validation of the DIRSIG
implementation of MODTRAN-P ........... 122
7.3. Predicting the Polarimetric Radiance at the Sensor .... 128
References ................................................. 132
Color Plate Section
8. Sensors for Measuring the Polarized State of a Beam ........ 135
8.1. Sensing of Polarization Contrast ...................... 135
8.2. Generalized Stokes Vector Polarimeters ................ 138
8.3. Polarimetric Imaging Sensors .......................... 144
8.4. Issues Related to Polarimetric Imaging Sensors ........ 149
References ................................................. 151
9. Processing and Display Algorithms .......................... 153
9.1. Display of Polarimetric Images ........................ 153
9.2. Data Processing and Analysis .......................... 160
References ................................................. 162
10.Measurements and Modeling of the pBRDF of Materials ........ 165
10.1.Polarimetric BRDF Measurement Approach ................ 165
10.1.1.Measurement approach ........................... 165
10.1.2.BRDF probability distribution (BRVF)
calculation .................................... 169
10.1.3.Imaging system description and
characterization ............................... 170
10.1.4.Example measurement results .................... 172
10.2.Incorporation of pBRDF Models in Synthetic Scene
Generation Models ..................................... 175
10.2.1.Introduction to DIRSIG ......................... 175
10.2.2.Surface radiometry solvers ..................... 176
10.2.3.Supported polarimetric BRDF models ............. 177
10.2.3.1.Generalized microfacet-based
target model .......................... 177
10.2.3.2.Polarized Roujean background model ... 178
10.2.3.3.Priest-Germer BRDF .................... 179
10.2.3.4.Torrance-Sparrow BRDF ................. 179
10.2.3.5.Stokes vector orientation
considerations ........................ 179
10.3.End-to-End Passive Polarimetric Scene Simulation ...... 180
10.3.1.Polarized atmosphere ........................... 180
10.3.2.Polarized manmade sources ...................... 181
10.3.3.Surface leaving radiance ....................... 181
10.3.4.Platform and sensor modeling ................... 182
10.3.5.Simulation examples ............................ 182
References ................................................. 187
11.Longwave Infrared pBRDF Principles ......................... 191
11.1.Background on Polarimetric Remote Sensing in the
Thermal Infrared ...................................... 191
11.2.Applications of Polarimetric Infrared Imaging ......... 195
11.3.Polarized BRDF and Emissivity Model ................... 199
11.3.1.Polarized specular reflection component of
the pBRDF model ................................ 200
11.3.2.Unpolarized reflection component ............... 202
11.4.Polarized Emissivity .................................. 202
References ................................................. 208
12.LWIR pBRDF Measurements and Modeling ....................... 211
12.1.Measurement of Polarized Emissivity and pBRDF
Estimation ............................................ 211
12.1.1.Measurement approach ........................... 211
12.1.2.Image data collection .......................... 217
12.1.3.Emissivity model parameter fitting ............. 222
12.2.Thermal Infrared Polarimetric Scene Simulation ........ 227
12.3.Closing Thoughts ...................................... 239
References ................................................. 239
Index ......................................................... 241
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