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KA Analytical Solution of Dielectric Rough Surface with Arbitrary Power Spectrum

It is well known that Small Perturbation Method (SPM) method gives analytical expressions of electromagnetic scattering from arbitrary power spectrum rough surface. However, KA method only gives explicit analytical expressions for Gauss spectrum rough surface. This paper attempts to derive the analytical expression of KA scattering from rough surfaces with arbitrary spectrum fluctuations. It is divided into three main parts. Firstly, the paper derives the formula of traditional Kirchhoff Approximation (KA) method. Then, based on the basic spectrum, such as Gaussian Spectrum and Exponential Spectrum, the paper invents two ways Fourier Transform Method (KAF) and Convolutional Method (KAC) to solve EM scattering from complex spectrum rough surface. The numerical results show that KAC is more accurate but needs more computation and memory than KAF.