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Spie Press Book

Fundamentals of Polarimetric Remote Sensing
Author(s): John R. Schott
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Book Description

This text is for those who need an introduction to polarimetric signals to begin working in the field of polarimetric remote sensing, particularly where the contrast between manmade objects and natural backgrounds are the subjects of interest. The book takes a systems approach to the physical processes involved with formation, collection, and analysis of polarimetric remote sensing data in the visible through longwave infrared.

Beginning with a brief review of the polarized nature of electromagnetic energy and radiometry, Dr. Schott then introduces ways to characterize a beam of polarized energy (Stokes vectors) and polarized energy matter interactions (Mueller matrices). The polarized bidirectional reflectance distribution function (pBRDF) is then introduced as a way to characterize the reflective and emissive polarimetric behavior of materials.

With Dr. Schott's text, you will gain an introduction to polarimetric remote sensing, an appreciation of its issues, and the tools to begin to work in the field.


Book Details

Date Published: 30 March 2009
Pages: 268
ISBN: 9780819475343
Volume: TT81

Table of Contents
SHOW Table of Contents | HIDE Table of Contents
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
4.3 Methods to Characterize and Interpret Stokes Vectors 38
4.4 Parameters of the Polarization Ellipse and the Poincaré 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 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 Target material pBRDF models 94 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 112 Rayleigh scatter 114 Aerosol and nonselective scatter 116
    7.2.2 Estimation of the atmospheric terms in the polarized governing equation 116 Use of radiative transfer codes to estimate polarimetric atmospheric terms 117 Visualization of sky polarization and validation of the DIRSIG implementation of MODTRAN-P 121
7.3 Predicting the Polarimetric Radiance at the Sensor 128
References 132
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 Generalized microfacet-based target model 177 Polarized Roujean background model 178 Priest-Germer BRDF 179 Torrance-Sparrow BRDF 179 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


This book was motivated by a short course on polarimetric remote sensing that I taught for industry about a year ago. I had supervised three doctoral students on thesis topics involving this subject and when I was asked to teach the course I thought it would be relatively easy to pull the course material together. In the months leading up to the course I discovered two things. First, as is so often the case, in preparing to teach the topic I found I knew far less than I thought I knew and dramatically less than I needed to know to teach a course. Second, I found that while there is a good treatment of polarization principles in the electro-optics literature, the treatment from the remote sensing perspective was quite scarce. In particular, while there were many journal and conference papers on specific topics, there was nowhere to send a student to get a good start on the fundamentals that they would need to prepare to delve into the more specific topics in the journals. So, to make a long story short, with considerable effort, I pulled together a variety of material and taught the course.

Afterwards, I realized I had the foundation for an introductory book that might save others getting started in this field from a similar effort. As a result, I spent the last year fleshing out the initial material, with a good deal of help from dedicated colleagues. The final book focuses on passive electro-optical polarimetric remote sensing in the visible through the thermal infrared (0.4-14 mm).

Polarimetric remote sensing is a relatively new field. It has champions who tout that polarimetric measurements are uncorrelated with traditional measurements of the magnitude and spectral content of the electromagnetic signal and should therefore add significant information. Likewise, it has detractors who point out that often the sought for contrasts between targets and backgrounds or between phenomena are not observed or are not as dramatic as they might be using some other sensing approach. I believe the jury is still out regarding how much utility we will eventually find in passive polarimetric remote sensing and what its role should be relative to other sensing approaches (e.g., multispectral). One of the main reasons for this is that polarimetric signatures are a rather involved function of source, target, and sensor geometry. Potential users must develop a more thorough knowledge of the relevant source-target-propagation-sensor physics to determine the true utility of this modality for their application. Once we understand and apply the relevant physics, we can develop tools to make it easier for other users to guide collection, processing, and analysis to improve signature contrast and determine the true utility of polarimetric remote sensing. It is for these students of the relevant physics (myself included) that I have written this book. I hope you find it a useful starting point for exploring this largely unexplored field.

As I listen today to the waves crashing on the beach, drowned out periodically by the thunder rumbling across the sky and watch the bay lit up by lightning, I can't help but be reminded how rich and complex nature is and how rewarding its study can be.

John R. Schott, Ph.D.
Wyldewood Beach
Port Colborne, Ontario
February 2009

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