Bom Son Lee

Full wave solutions for rough-surface bistatic radar cross sections : comparison with small perturbation, physical optics, numerical, and experimental results

In this paper, full wave solutions are derived for the like- and cross-polarized electromagnetic fields diffusely scattered by two-dimensional rough surfaces. These expressions for the diffuse scattered fields are used to obtain the random rough-surface cross sections. The rough surface is characterized by a Gaussian joint probability density function for the surface heights and slopes at two points. These full wave results are compared with the associated small-perturbation results and physical optics results. They are also compared with experimental and numerical results (based on Monte Carlo simulations). The earlier assumption that the surface height and slopes can be considered to be uncorrelated is examined. The impact of using the large-radii curvature assumption and including self-shadow is also considered.

Radar scatter cross sections for two-dimensional random rough surfaces – full wave solutions and comparisons with experiments

Abstract In this paper, the full wave expressions for the radar scattering cross sections for two-dimensional random rough surfaces are obtained. The rough-surface height/slope correlations are accounted for in this analysis. Analytical and numerical comparisons of the full wave solution with the small perturbation and physical optics solutions are made for isotropic, homogeneous random rough surfaces with Gaussian probability density function. The full wave results are also compared with experimental results.

Transmission scatter cross sections across two-dimensional random rough surfaces – full wave solutions and comparison with numerical results

Abstract In this paper, the full wave expressions for the bistatic transmission scattering cross sections across two-dimensional random rough surfaces are obtained. The full wave analysis accounts for the surface height/slope correlations. Analytical and numerical comparisons of the full wave solutions with the small perturbation and physical optics solutions are made for isotropic random rough surfaces. The full wave results are also compared with the numerical results based on Monte Carlo simulations of one-dimensional random rough surfaces. Detailed consideration is given to illustrating the relationship between these full wave solutions and the original full wave solutions including the impact of accounting for the height/slope correlations in this analysis.

Like‐ and cross‐polarized transmission scatter cross sections for random rough surfaces: Full wave solutions

The full wave expressions for the transmission scatter cross sections for two-dimensional random rough surfaces are obtained using the full wave approach. The solutions are compared with published numerical results based on Monte Carlo simulations of rough surfaces.

Full wave scatter cross sections for two-dimensional random rough surfaces using joint conditional surface height characteristic functions

The bistatic radar scatter cross sections for two-dimensional random rough surfaces are obtained using the full wave approach. The formal solution is expressed as a 10-dimensional integral over the random surface heights h/sub 1/, h/sub 2/ and slopes h(x1), h/sub x2/, h/sub z1/, h/sub z2/ and the surface variables x/sub s1/, x/sub x2/, z/sub s1/, z/sub z2/. On averaging over the surface heights, the joint conditional surface height joint characteristic functions /spl chi/(a,blh(x1), h/sub x2/, h/sub z1/, h/sub z2/) are introduced and the l0-dimensional integral reduces to an 8-dimensional integral. For homogeneous isotropic rough surfaces, /spl chi/ is a function of r/sub d/=/spl radic/(x/sub d//sup 2/+z/sub d//sup 2/) where x/sub d//spl equiv/x/sub s1/-x/sub s2/ and z/sub d//spl equiv/z/sub x1/-z/sub x2/ and the solution reduces to a 5-dimensional integral over h(x1), h/sub x2/, h/sub z1/, h/sub z2/ and r/sub d/. If the radius of the curvature of the surface is large compared to the wavelength of the incident wave, the surface slopes at two neighboring points are approximately equal. Thus the 5-dimensional integral can be expressed as a 3-dimensional integral. These full wave results can be further simplified if the mean square surface slopes are small (/spl Lt/0.15), in which case it can be assumed that the surface height and slopes are uncorrelated and the above 3-dimensional integral reduces to the product of a 2 and a 1-dimensional integral. In the low frequency limit when the surface height and slopes are of the same order of smallness, the full wave solution reduces to the small perturbation solution. For high frequencies, the 3-dimensional integral reduces to the 1-dimensional physical optics integral. In the high frequency limit, it reduces to the geometrical optics solution since in this case the Fourier transform of /spl chi/(a,.<<ETX>>

Electromagnetic scattering and depolarization across rough surfaces: Full wave analysis

Full wave solutions are derived for vertically and horizontally polarized waves diffusely scattered across an interface that is two-dimensionally rough separating two different propagating media. Since the normal to the rough surface is not restricted to the reference plane of incidence, the waves are depolarized upon scattering; and the single scattered radiation fields are expressed as integrals of a surface element transmission scattering matrix that also accounts for coupling between the vertically and horizontally polarized waves. The integrations are over the rough surface area as well as the complete two-dimensional wave spectra of the radiation fields. The full wave solutions satisfy the duality and reciprocity relationships in electromagnetic theory, and the surface element scattering matrix is invariant to coordinate transformations. It is shown that in the high-frequency limit the full wave solutions reduce to the physical optics solutions, while in the low-frequency limit (for small mean square heights and slopes) the full wave solutions reduce to Rices (1951) small perturbation solutions. Thus, the full wave solution accounts for specular point scattering as well as diffuse, Bragg-type scattering in a unified, self-consistent manner. It is therefore not necessary to use hybrid, perturbation and physical optics approaches (based on two-scale models of composite surfaces with large and small roughness scales) to determine the like- and cross-polarized fields scattered across the rough surface.

Scatter cross sections for two-dimensional random rough surfaces-full wave analysis

The full wave solutions for the fields diffusely scattered from two-dimensional random rough surfaces are used to evaluate the scatter cross sections. Unlike the original full wave solution, E. Bahar et al. (1979), this full wave solution accounts for rough surface height and slope correlations and can, therefore, be used for a wide range of surface roughness scales, E. Bahar et al. (1994). The computation time is relatively short compared to the numerical results based on Monte Carlo simulations (even for one-dimensional random rough surfaces). The full wave scatter cross sections for the two-dimensional random rough surfaces are shown to reduce to the small perturbation and physical optics solutions in their appropriate regions of validity. It is also shown that there is good agreement between the full wave results and experimental data or numerical results based on Monte Carlo simulations.

Mueller matrix associated with diffuse scattering from two-dimensional random rough surfaces-full wave analysis

In earlier work, it was shown that there is good agreement between the full wave results and experimental data or numerical results based on Monte Carlo simulations for one dimensionally random rough surfaces [Bahar and Lee 1994, 1995]. In this work, the full wave solutions for the diffusely scattered fields from two-dimensional random rough surfaces [Bahar and Lee, 1994] are used to evaluate elements of the 4/spl times/4 Mueller matrix. The modified Mueller matrix elements are related to the like and cross polarized radar cross sections as well as to the relative phase of the vertically and horizontally polarized waves. The 4/spl times/4 Mueller matrix elements completely characterize electromagnetic scattering from targets (rough surfaces, in this case). The full wave solution presented here can be applied to surfaces with a wide range of roughness scales. Computation time for the full wave Mueller matrix elements is significantly less than the numerical results based on the Monte Carlo simulations even for one-dimensional random rough surfaces.

Transmission scatter cross sections for random rough surfaces-full wave solutions

The full wave expressions for the transmission scatter cross sections for two-dimensional random rough surfaces are obtained using the full wave approach. The solutions are compared with published numerical results based on Monte Carlo simulations of rough surfaces.

Full wave transmission scatter cross sections for random rough surfaces-comparisons with numerical solutions

The full wave expressions for the transmission scatter cross sections for 2-dimensional random rough surfaces are obtained and the solutions are compared with the numerical results based on Monte Carlo simulations of the rough surfaces.