# The Scope of This Book

This book is intended to provide the basic principles of radar polarimetry and its utilization using illustrations and figures as much as possible. The readers are assumed to know a little bit about electromagnetic waves. The mathematical expressions are frequently used for complete understandings. The contents are briefly categorized into the basics of polarization and its applications. Figure 1.9 shows the constitution of this book.

The basic principle of radar polarimetry and polarization matrices are defined from Chapter 1 to 4. Based on the scattering matrix in the coherent scattering, a 3 x 3 covariance or coherency matrix is used for data analyses in most of the incoherent scattering scenarios. Since these two matrices are positive semi-definite mathematically, they are convenient for various applications. We used coherency matrix formulation from Chapter 5 to 15, from the physical scattering point of view and from simple mathematical operations.

Chapter 2: Starting from Maxwell’s equations, the solution of the Helmholtz wave equation is reviewed. The plane wave, which is the most fundamental solution of the wave equation, is described in detail to understand the property of the electromagnetic wave propagation. The expression of a polarized wave is represented in the form of the Jones vector, geometrical parameters (ellipticity angle and tilt angles), Stokes vector, and on the Poincare sphere plot.

Chapter 3: The polarization state of the scattered wave from an object is different from that of the transmitted wave. The vector nature of wave scattering is defined by a 2 x 2 scattering matrix. The scattered wave is received by a radar antenna. This phenomenon is formulated in receiving antenna voltage and receiving power in the polarimetric radar channel. Taking into account the polarimetric characteristics, the basic principles of radar polarimetry are established. The polarization signatures of various objects are presented to show how the polarimetric response changes and how important it is for identifying objects. Polarimetric enhancement of a desired target against an undesired target can be achieved by polarimetric filtering. This chapter deals with scattering waves and receiving power in polarimetric radar channels.

Chapter 4: Once the scattering matrix is obtained, just like a snapshot in the coherent scattering case, there are five independent parameters in a relative scattering matrix form. For incoherent scattering, scattering matrix data are ensemble averaged to obtain the polarimetric information. There are nine independent parameters in the covariance matrix, coherency matrix, Kennaugh matrix, Mueller matrix, etc., in the form of the second-order statistics. This chapter introduces these matrices and their relations and indicates four important parameters in these polarization matrices.

Chapter 5: The H/A/alpha-bar method is the most frequently used decomposition method, developed by S. Cloude and E. Pottier. This method is based on the rigorous eigenvalue/eigenvector

FIGURE 1.9 Book chapters.

expansion of the coherency matrix. Since the principle has been described in detail [19,20], only a brief review is provided.

Chapter 6: Any kind of scattering matrix can be created by a combination of dipoles aligned in the range direction. If dipoles with different orientation and appropriate spacing are used as a scatterer aligned in a radar range resolution, various kinds of scattering matrices can be generated. This is called a compound scattering matrix. These phenomena have been confirmed by finite difference time domain (FDTD) simulations and polarimetric measurements in a well-controlled anechoic chamber.

Chapter 7: Followed by the compound scattering matrix, scattering mechanisms and the modeling of coherency matrix elements are given. There are nine real-valued and independent parameters in a coherency matrix. For each parameter, an appropriate coherency matrix is derived based on the corresponding feasible compound scattering matrix. Scattering mechanisms and modeling with physically realizable situations are summarized.

Chapter 8: Using scattering models in Chapter 7, several scattering power decomposition schemes are presented. The measured coherency matrix is expanded as a sum of scattering models based on scattering mechanisms. The decomposition procedure and its algorithm, as well as the decomposition image of San Francisco, are displayed and compared. Starting from the original three-component decomposition by Freeman and Durden, the updated four-component decomposition (Y40, Y4R, S4R, G4U), the six-component decomposition (6SD), and up to seven-component decompositions are described in a unified manner.

Chapter 9: Correlation is one of the most important concepts in radar signal processing. This chapter deals with the correlation coefficient in various polarization bases and it shows the effectiveness of the circular polarization basis. Using the correlation coefficient in the circular polarization basis, a polar plot is used to classify target categories. A modified version of the correlation coefficient and the scattering power decomposition combination complementarily yielded excellent classification results. Furthermore, a similarity parameter is updated and redefined in order to make full use of nine polarimetric information more effectively. This new similarity parameter is used to extract the desired scattering objects successfully.

Chapter 10: In order to understand radar images, it is important to understand how the image is created. The range resolution as well as the azimuth resolution are the key parameters of radar images. This chapter explains the principle of SAR processing and image formulation using an example of frequency modulated and continuous wave (FMCW) radar. SAR is expanded to the PolSAR system with two transmitting antennas and two receiving antennas. Some applications of handmade FMCW PolSAR are explained with measured data. As an advanced application, the polarimetric Holo-SAR system is introduced to show its 3D imaging capability from 360° viewing angles. Concrete building models and trees are imaged by a polarimetric Holo-SAR system.

Chapter 11: The physical scattering nature from objects is determined by the boundary condition of electromagnetic waves on the object surface. The object has its own shape, orientation, and dielectric materials. This chapter summarizes the material constant of objects, that is, relative permittivity of various materials, using a well-known Debye model.

Chapter 12: When dealing with SAR and PolSAR images, we often encounter basic questions, such as foreshortening, layover, the effect of incidence angle, and resolution. Some notes on the interpretation of these questions on SAR images are presented for reference.

Chapter 13: Scattering power decompositions to PolSAR data sets yields the surface-scattering power P„ the double-bounce scattering power Pd, and the volume-scattering power Pv, among other powers. This chapter shows the applications of the surface-scattering power Ps. Through the decomposition of ALOS/ALOS2 data sets, it is found that the surface-scattering power increases after disaster events, such as by mud, soil, landslide, and flooding. The power magnitude is also dependent on snow depth and volcano ashes, which might be effective for environmental monitoring.

Chapter 14: Right-angle structure induces the double-bounce scattering phenomenon. This scattering can be seen in man-made structures such as building walls, road surfaces, or tall tree/ vegetation sterns on the ground surface. The scattering model is reviewed again, and some scattering measurement results on the incidence angle and squint angle characteristics are described. The applications to monitor tidal height, ship detection, and flooding are shown.

Chapter 15: Since the cross-polarized HV component is mainly generated from vegetation, this component can be a good indicator of the forest. This chapter is mainly devoted to monitoring forest, trees, and vegetation and seeks a possibility of classifying tree types using high-frequency and high-resolution PolSAR. In other applications, a reduction of the volumescattering power Pr is successfully applied to detect a landslide area caused by an earthquake on a woody mountain area.

In addition, scattering power decomposition images are posted on the following websites:

https://gsrt.airc.aist.go.jp/landbrowser/index.html (Global ALOS quad pol images and data) https://landbrowser.airc.aist.go.jp/polsar/index.html (Partial ALOS2 quad pol images) http://www.wave.ie.niigata-u.ac.jp (which includes ALOS. AL0S2, PiSAR-L2, PiSAR-X2 data) http://www.csre.iitb.ac.in/gulab/index.html (which includes ALOS2 data)

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