Scattering and Transmission of Waves in Multiple Random Rough Surfaces: Energy Conservation Studies With the Second Order Small Perturbation Method

Abstract

Abstract-Energy conservation is an important consideration in wave scattering and transmission from random rough surfaces and is particularly important in passive microwave remote sensing. In this paper, we study energy conservation in scattering from layered random rough surfaces using the second order small perturbation method (SPM2). SPM2 includes both first order incoherent scattering and a second order correction to the coherent fields. They are combined to compute the total reflected and transmitted powers, as a sum of integrations over wavenumber k x , in which each integration includes the surface power spectra of a rough interface weighted by an emission kernel function (assuming the roughness of each interface is uncorrelated). We calculate the corresponding kernel functions which are the power spectral densities for one-dimensional (1D) surfaces in 2D scattering problems and examine numerical results for the cases of 2 rough interfaces and 51 rough interfaces. Because it is known that the SPM when evaluated to second order conserves energy, and it can be applied to second order for arbitrary surface power spectra, energy conservation can be shown to be satisfied for each value of k x in the kernel functions. The numerical examples show that energy conservation is obeyed for any dielectric contrast, any layer configuration and interface, and arbitrary roughness spectra. The values of reflected or transmitted powers predicted, however, are accurate only to second order in small surface roughness.

Electromagnetic Scattering of Rough Ground Surface Covered by Multilayers Vegetation

“…By adding the average deviation of leaf angle distribution to accurately estimate the backscattering coefficients with the angular effect of scattering particles in a vegetation canopy, the water-cloud model is modified, and the results agree with the radar measurements of vegetation fields at C-and X-bands [15]. The energy conservation in scattering from layered random rough surfaces is studied with the second-order small perturbation method (SPM2), which includes both first-order incoherent scattering and a second-order correction to the coherent fields [16]. The coherent branching model of soybean shows that HH scattering has a significant difference up to 3 dB from that of the independent scattering [17].…”

Modeling of Multilayered Media Green’s Functions With Rough Interfaces

“…In contrast to single rough layer EM models, literature on EM models for multilayered media with multiple rough interfaces remains sparse [30], and only a few models dealing with more than two rough interfaces have been developed. To the best of our knowledge, only classical asymptotic models exist, and are only valid for slightly rough interfaces [31]- [40]. The proposed solutions are generally based on the SPM.…”

“…However, if only the first-order of the SPM is used, the coherent scattered intensity reduces to that of flat surfaces. Therefore, it is necessary to use at least the second-order SPM [40] or the SSA [38]. For the SSA, the solution proposed in [38] is restricted to Gaussian height distributions and correlation functions.…”

“…For the SSA, the solution proposed in [38] is restricted to Gaussian height distributions and correlation functions. Regarding the SPM, an expression of the second-order coherent normalized radar cross section (NRCS) has been derived recently [40], but only for two-dimensional problems.…”

Electromagnetic Scattering From One Dimensional Random Rough Surfaces of Dielectric Layered Media With Waveguide Modes Using Second Order Small Perturbation Method

“…The small perturbation method has been studied for random rough surface scattering extensively [1][2][3][4][5][6][7][8][9][10][11][12]. Recently, the method has been studied for multi-layered random rough surfaces [2,5,7] as an analytical method which has advantages over numerical methods for multiple rough interfaces.…”