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Library of Congress Cataloging-in-Publication Data

Jin, Ya-Qiu.

Polarimetric scattering and SAR information retrieval / Ya-Qiu Jin and Feng Xu.

pages cm.

Includes bibliographical references and index.

ISBN 978-1-118-18813-2 (cloth)

1. Synthetic aperture radar. 2. Electromagnetic waves–Scattering. I. Title.

TK6592.S95J56 2013

621.3848′5–dc23

2012038931

ISBN: 978-1-118-18813-2

Preface

Polarimetric imagery of synthetic aperture radar (POL-SAR) technology has been one of the most important advances in spaceborne microwave remote sensing during recent decades. Remote sensing data and images have resulted from complex interactions of electromagnetic (EM) waves with natural media, that is, terrain surface, atmosphere, ocean, and so on. The great amount of remote sensing data/images presents rich sources for quantitative description and monitoring of our Earth's environments. However, information retrieval from POL-SAR remote sensing images requires a full understanding of the polarimetric scattering mechanism and SAR imaging principles. The study of EM wave scattering for remote sensing applications, especially for POL-SAR technology, has become an active and interdisciplinary area.

This book presents an account of some of the progress made in research on both the theoretical and numerical aspects of POL-SAR information retrieval.

We begin in Chapter 1 with some basics of polarimetric scattering, for example, the concepts of the scattering matrix, the polarization vector, the four Stokes parameters, and the Mueller matrix solutions for volumetric and surface scattering.

In Chapter 2, the vector radiative transfer (VRT) theory of natural media is presented. The VRT takes account of multiple scattering, emission, and propagation of random scattering media. Its analytical solution provides insights into the underlying mechanism of EM wave–terrain surface interaction. The components of VRT, that is, the scattering, absorption, and extinction coefficients, and the phase matrix of non-spherical scatterers, are introduced. The first-order Mueller matrix solution of VRT for a vegetation canopy model is derived. Polarization indices, eigen-analysis, and entropy are presented. The statistics of multi-look SAR images and the covariance matrix are also investigated.

Chapter 3 first introduces some fundamentals for POL-SAR technology. Based on POL-SAR imaging technology, a new approach to SAR imaging simulation for comprehensive scenarios is developed. It is called MPA (mapping and projection algorithm). In the MPA, scattering contributions from scatterers are cumulatively summed on the slant range plane (the mapping plane), while their extinction and shadowing effects are cumulatively multiplied on the ground range plane (the projection plane). Some parameterized models of random non-spherical scattering media, for example, buildings, the vegetation canopy, rough and tilted surfaces, and so on, are incorporated into the MPA simulation scheme. It finally constructs simulated POL-SAR images of a comprehensive terrain scene. The MPA presents a complete SAR raw data simulation chain, based on scattering models of natural and artificial media and a time-domain raw-data generator.

Chapter 4 deals with the simulation of bistatic POL-SAR images as well as bistatic polarimetry and signal processing. Bistatic SAR (BISAR) with separated transmitter and receiver flying on different platforms has become of great interest. Most BISAR research is focused on hardware engineering realization and signal processing algorithms, with a little on land-based bistatic experiments or theoretical modeling of bistatic scattering. The BI-MPA is developed as a fast and efficient tool for monostatic and bistatic imaging simulations. It involves the physical scattering process of multiple terrain objects. Based on simulated BISAR images, bistatic polarimetry and the unified bistatic polarization bases are discussed. Finally, raw data processing of stripmap BISAR is explored.

Chapter 5 first presents some basic concepts of radar polarimetry and target decomposition, and then develops deorientation theory for surface classification of POL-SAR images. The novel “deorientation” concept is introduced to reduce the influence of randomly fluctuating orientation and reveal the generic characteristics of the targets for better classification. The parameterized model of a random non-spherical scattering medium and its Mueller matrix solution for deorientation validation are developed. A new set of parameters of polarimetric scattering targets is defined to describe target orientation, orderly or random, and scattering surface classification.

Chapter 6 presents some inversion applications using POL-SAR images. It can be found that, as the surface is tilted, the orientation angle at the maximum of co-pol or cross-pol signature can shift from . This shift can be applied to convert the surface slopes. Making use of the Mueller matrix solution and morphological processing, the digital elevation mapping of the Earth's surface is inverted from single-pass polarimetric SAR image data. Using the deorientation theory of Chapter 5, the imaging positions of first-, second-, and third-order scattering of a bridge body can be located. Using the thinning, clustering algorithm, and Hough transform, the lines indicating different orders of scattering are used to invert the bridge height.

Chapter 7 deals with automatic reconstruction of building objects from multi-aspect SAR images. This approach is called as AMAR (automatic multi-aspect reconstruction). Reconstruction of three-dimensional objects from SAR images has become a key issue for target information retrieval. It has been noted that scattering from man-made objects produces bright spots at submeter resolution, or presents strip/block images at meter resolution. The linear profile of a building object is regarded as the most prominent characteristic. The POL-CFAR detector, Hough transform, probabilistic description of the detected façade images, and the maximum-likelihood estimation of building objects from multi-aspect observed façade images are discussed. Eventually, in association with a hybrid priority rule of inversion reliability, an automatic algorithm is designed to match multi-aspect façade images and reconstruct the building objects.

Chapter 8 discusses the Faraday rotation (FR) on a POL-SAR image at UHF/VHF bands. As the polarized electromagnetic wave propagates through the Earth's ionosphere, the polarization vectors are rotated as a result of the anisotropic ionosphere and the action of the geomagnetic field. This rotation is called the FR effect. The FR may decrease the difference between co-polarized backscattering, enhance cross-polarized echoes, and mix different polarized terms. Since the FR is proportional to the square power of the wavelength, it has an especially serious impact on SAR observations operating at a frequency lower than L band. For example, the FR angle at P band can reach dozens of degrees. In this chapter, the Mueller matrix with FR is derived, and recovered from FR. The algorithm of phase unwrapping is also studied.

Chapter 9 presents an algorithm for change detection. Multi-temporal SAR observations provide fast and practicable technical means for surveying and assessing terrain surface changes. How to detect and automatically analyze information on change in terrain surfaces is a key issue in remote sensing. In this chapter, two-threshold expectation maximum (EM) and Markov random field (MRF) algorithms (2EM-MRF) are developed to detect the change direction of backscattering enhanced, reduced, and unchanged regimes from the SAR difference image. As examples, this approach is applied to change detection of urban areas and earthquake regions.

Chapter 10 presents the temporal Mueller matrix solution for polarimetric scattering and radiative transfer as a pulse wave incident upon an inhomogeneous random medium. The Mueller matrix solution for seven scattering mechanisms describes temporal polarimetric scattering and propagation through inhomogeneous scattering media, and, as examples, is applied to image simulation of pulse echoes from the lunar regolith layer, and for monitoring debris flows and landslides.

Chapter 11 introduces a novel numerical approach, that is, the bidirectional analytic ray tracing (BART) method. The basic idea is to launch ray tubes from both the source and observation, trace among the facets, and then record the illumination areas of rays shooting on facets and edges. For each pair of forward and backward rays illuminating the same facet/edge, a scattering path from source to observation is constructed by linking the forward and backward rays, and the corresponding scattering contributions are added up to give the total scattering. This fast computation is applied to the simulation of composite scattering from an electrically large target over a randomly rough surface.

Finally, Chapter 12 deals with a numerical train of simulated polarized scattering–imaging–reconstruction for a complex-shaped electrically large object above a dielectric rough surface. Target detection and reconstruction have been of great interest in both civilian and defense applications. The step-frequency (SF) radar technique is employed to 3D SAR imaging using the downward-looking spotlight mode to alleviate the sheltering and layover effect. The BART of Chapter 11 is employed to calculate the scattering matrix of a 3D target over a rough surface. Some simulation examples of 3D imaging and reconstruction of perfectly electrically conducting targets, that is, a square frustum, and a tank-like target over a rough surface, as well as discussions on the accuracy and computational efficiency, are presented.

This book is based on research progress in our laboratories over the past decade. It is assumed that readers are familiar with material normally covered in undergraduate courses on electromagnetics and some basis of radar remote sensing. However, in each chapter, some fundamentals of these topics are given whenever needed.

This book is intended as a textbook for a graduate course on advanced topics in electromagnetic scattering and SAR remote sensing, and is also a useful reference for researchers working on electromagnetic scattering and POL-SAR microwave remote sensing with various applications. New advances on POL-SAR, such as POL-INSAR, tomography SAR, inverse SAR, counter-SAR, and so on, remain for further study.

This work was partly supported by several projects of the National Science Foundation of China.

Ya-Qiu Jin and Feng Xu
Shanghai and Rockville
October 2012

1

Basics of Polarimetric Scattering

1.1 Polarized Electromagnetic Wave

1.1.1 Jones Vector and Scattering Matrix

Radar transmits an electromagnetic (EM) wave and receives the scattered wave from the target. The polarization of an EM wave is defined as the time–space variation of the electric field vector in the plane perpendicular to its propagation direction. As depicted in Figure 1.1, let us first define a coordinate system (), where denotes the propagation direction, and denote the directions of vertical and horizontal linear polarizations, respectively. (In this book, unless otherwise specified, vectors are denoted as bold letters, for example, , and matrices are bold letters with a bar, for example, . A letter with a hat (e.g., ) denotes a unit vector.) A completely polarized monochromatic EM wave can be represented by two orthogonal components along (Kong, 2005)

Figure 1.1 (a) Polarized EM wave and polarization vector. (b) Coordinate system of the polarization vector

(1.1) equation

where are the corresponding vertical and horizontal components of the electric field, k is the wavenumber and is the angular frequency. In addition, we have the following relationships, which can be readily derived:

(1.2) equation

In spherical coordinates, where the source is located at the origin, we have .

Imagine when an EM wave passes a certain position in space; the tip of the electric field vector will form a certain trajectory. The shape of such a trajectory is determined by the amplitude ratio and phase difference between the two orthogonal components, that is, the polarization ratio,

(1.3) equation

The polarization of an EM wave is named after the shape of such a trajectory, that is, linear polarization (when ), circular polarization (when , and ) or elliptical polarization (in general). The trajectories of different polarizations are depicted accordingly in the plane as in Figure 1.2a. In fact, any polarization trajectory can be expressed using the following ellipse equation:

(1.4) equation

Figure 1.2 (a) Plane of polarization ratio. (b) Parameters of elliptical polarization

There are three geometric parameters of such an elliptical trajectory: amplitude , elliptical angle , and orientation , as illustrated in Figure 1.2b, that is

(1.5) equation

where the sign of indicates the rotation direction, that is, counter-clockwise (+) or clockwise (−), the elliptical angle determines the shape, and indicates orientation.

We can write Equation 1.1 in the form of a complex vector,

(1.6) equation

which is often referred to as the Jones vector. It can be found from Equation 1.3 that the polarization ratio is in fact the ratio of these two elements

(1.7) equation

The Jones vector can also be expressed using the elliptical parameters,

(1.8) equation

where is the absolute phase. It can be seen from Equation 1.8 that transformation of the Jones vector would correspondingly modify polarization characteristics. This is important in radar polarimetry, as will be discussed later in Chapter 5.

A completely polarized wave incident upon a point target or deterministic simple target would produce a completely polarized scattered wave, which is often called coherent scattering. As a polarized wave incident on a scatterer of volume and dielectric constant , the wave equation can be written as (Jin, 1994)

(1.9) equation

where the time-harmonic factor is () and is the distance from the scattering point to the observation point. Solving Equation 1.9 under the far-field approximation yields the scattering wave

(1.10) equation

Here, the scattering field is now expressed by a 2 × 2 (dimensional) complex matrix, that is, the scattering matrix, . Each element of the scattering matrix , represents the complex scattering coefficient under q-polarization incidence and p-polarization scattering.

For a single scattering, its scattering matrix has to be obtained by first calculating the internal field in Equation 1.10 and then performing the integration. Explicit solutions exist for many canonical problems. For example, a small scatterer with its size a far smaller than the wavelength, that is, , can be solved by Rayleigh approximation. A non-spherical particle such as an ellipsoid, a needle- or a disk-like particle with its smallest dimension d far smaller than the wavelength, that is, , can be solved using the Rayleigh–Gans approximation (Ishimaru, 1978, 19911978, 1991). A scatterer of perfectly spherical geometry can be solved using Mie theory. Explicit expressions for also exist for symmetric geometries such as cylinders, spheroids, and so on. Analytic calculations of the scattering matrix for these examples under the Rayleigh–Gans approximation are given later in this chapter. For a more complete derivation, readers are referred to the literature focusing on EM theory (e.g., Jin, 1994).

For a large scattering body with complicated geometry, we have to resort to numerical methods such as the method of momentss (MoM), finite element method (FEM), and finite difference time difference (FDTD), or high-frequency methods such as geometrical optics and physical optics. Chapter 11 will introduce a high-frequency method for calculation of scattering from very complex targets in natural environments.

In practice, fully polarimetric radar measures the entire scattering matrix , while single-polarization radar (single-pol) or dual-polarization radar (dual-pol) can only measure one or two elements of the scattering matrix. Conventionally, co-pol refers to scattering with the same polarization for incidence and scattering, while cross-pol refers to different polarization for incidence and scattering.

Another important concept is the scattering coefficient or radar cross-section (RCS). It is defined as the power ratio of scattering versus incidence as if the scattered field were uniform in all directions:

(1.11) equation

The RCS is more useful for single-polarization radar where phase information is not critical.

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