I'm reading the book Polarimetric Radar Imaging: From Basics to Applications, on chapter 6 it is said that:

  1. The s-matrix for a dihedral corner reflector has the form: $$S=\begin{bmatrix}e^{2j\gamma_H}R_{TH}R_{GH} & 0 \\ 0 & e^{2j\gamma_V}R_{TV}R_{GV}\end{bmatrix}$$
    Assuming that the reflector surfaces can be made of different dielectric materials. The vertical (trunk) surface has Fresnel reflection coefficients $R_{TH}$ and $R_{TV}$ for vertical and horizontal polarizations, respectively. And the horizontal (ground) surface has Fresnel reflection coefficients $R_{GH}$ and $R_{GV}$ for vertical and horizontal polarizations, respectively. Assuming that the complex coefficients $\gamma_H$ and $\gamma_V$ represent any propagation attenuation and phase change effects.
  2. The s-matrix for first-order bragg surface scattering has the form:
    $$S=\begin{bmatrix}R_H & 0 \\ 0 & R_V\end{bmatrix}$$ where:
    $$R_H=\frac{\cos\theta-\sqrt{\varepsilon_r-\sin^2\theta}}{\cos\theta+\sqrt{\varepsilon_r-\sin^2\theta}}$$ $$R_V=\frac{(\varepsilon_r-1)\{\sin^2\theta-\varepsilon_r(1+\sin^2\theta)\}}{\left(\varepsilon_r\cos\theta+\sqrt{\varepsilon_r-\sin^2\theta}\right)^2}$$
    are the bragg surface reflection coefficients for vertically and horizontally polarized waves in which $\theta$ is the local incidence angle and $\varepsilon_r$ is the relative dielectric constant of the surface.

I'm looking for the book, paper, etc in which the above expressions are proven or are mentioned for the first time.
It seems that the two expressions do work for the whole electromagnetic spectrum not only the microwave or radar part of the spectrum so maybe this reference is very old? I don't know!
I have the proof for Fresnel reflection coefficients from lecture 13 in Dr. Tim Noe's lecture note for ELEC262: Introduction to Waves and Photonics course for Electrical and Computer Engineering Faculty of Rice University but I want to understand why the s-matrix takes the given forms especially in the dihedral case?


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  • 1
    $\begingroup$ Is it important that it is for the first time? $\endgroup$ – Qmechanic Apr 24 '17 at 8:22
  • $\begingroup$ @Qmechanic no, as I said somewhere that it is proved or mentioned for the first time. Maybe my poor English has caused this misunderstanding. I'm just searching for a reference that can be cited officially and also something to convince myself like a proof or reason why these expressions are established? $\endgroup$ – Sepideh Abadpour Apr 24 '17 at 9:11

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