Research On Problems Related To The Electromagnetic Scattering And Inverse Scattering From Random Rough Surfaces

The study of electromagnetic wave scattering from random rough surfaces has been the subject of intensive investigation for its application in a number of important research areas, such as the remote sensing, radar imaging, ocean engineering, wireless communications, surface optics, as well as the semiconductor physics. This dissertation presents theoretical studies of electromagnetic scattering and inverse scattering from random rough surfaces. The first topic in this dissertation mainly focuses on the scattering of time harmonic wave and ultra-wide-band (UWB) pulse wave by one-dimensional (1-D) random rough surfaces. The 1-D model is then extended to the two-dimensional (2-D) model. Moreover, the characteristics of scattering by non-Gaussian distributed rough surfaces are examined. Finally, emphasis is also put on studying the inverse scattering from random rough surfaces, including the reconstruction of surface profile and the retrieval of statistical parameters. The main works and results are as follows:1. The Kirchhoff single-scattering model for 1-D rough surfaces is extended to the Kirchhoff double-scattering model. Numerical simulations and theoretical analysis lead to the conclusion that the backscattering enhancement is caused by multiple scattering paths.2. A Chebyshev canonical-grid (CCG) method is proposed by expanding the Green's function in the series of Chebyshev polynomials, and it is proved to be more convenient than the conventional Sparse-Matrix canonical-grid (SMCG) method. The multiplication in the CCG method can be readily calculated by the FFT. The numerical results are compared with those obtained by the moment method, and it demonstrates that the CCG method has high efficiency in numerical simulations.3. An analytic method is constructed for the scattering problem of 1-D rough surfaces, which are illuminated by a UWB pulse quasi-beam. The analytic expression of the electromagnetic scattered field in the time domain is derived combining with the Kirchhoff scattering theory, the decomposition and synthesis of the incident quasi-beam, as well as the paraxial far zone approximation. The scattered electric field from the surface of dry sand is calculated with the fourth-order Rayleigh pulse illuminating. The precision of analytic method is also examined by comparing with the results obtained by time domain moment method.4. A new method is proposed to calculate the multiple scattering from 2-D rough surfaces with large surface root-mean-square (RMS) slope. The dependency of bistatic scattering coefficients on azimuth angles and the backscattering coefficients on RMS slope is discussed. The theoretical model is applied to the calculation of the millimeter wave scattering from nickel coated surfaces, the numerical results are also compared with the experimental data from University of Washington, and the validity of the model is tested.5. The analytic method of the UWB pulse quasi-beam constructed for the scattering problem of 1-D rough surfaces (Chap. 3 in this dissertation) is then extended to the 2-D rough surface model. The analytic expression for the scattered electric filed of the UWB pulse quasi-beam in the time domain by 2-D rough surfaces is presented. The characteristics of propagation and attenuation of the second-order Rayleigh pulse scattered by 2-D bare soil surfaces are analyzed.6. As an extension of Gaussian distributed surface model, the electromagnetic scattering model on Alpha-stable non-Gaussian distributed surfaces is developed. The magnetic field integral equation (MFIE) is formulated to study the electromagnetic scattering from Alpha-stable non-Gaussian metallic material surface with a time harmonic wave and a UWB pulse wave incidence. Numerical simulations show that the scattered field from metallic material surfaces is affected significantly by the probability distribution of the surfaces.7. Based on the spatial reconstruction of total field, the algorithm is proposed to solve the inverse scattering of a time harmonic wave and a UWB pulse wave from rough surfaces, respectively. Reconstructions of sinusoidal surfaces, non-sinusoidal surfaces, Gaussian correlated random rough surfaces and Alpha-stable non-Gaussian distributed surfaces are performed using this technique. Good agreements of these results demonstrate that the inverse scattering method is reliable.8. The Gaussian beam scattering model is developed to analyze the scattering from Fractional Brownian Motion (FBM) rough surfaces. A multi-frequency inverse algorithm is set up to estimate the fractal dimension of the FBM surfaces with the least-square method. In addition, a new fully theoretical framework for the retrieval of the statistical parameters of Gaussian correlated rough surfaces is proposed, and the suggested scheme is to retrieve the RMS height and the correlation length with the use of the specular coherent scattering intensity and incoherent scattering intensity, respectively.