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A numerical study of the Kirchhoff approximation in horizontally polarized backscattering from a random surface
Author(s) -
Chan H. L.,
Fung A. K.
Publication year - 1978
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs013i005p00811
Subject(s) - range (aeronautics) , gaussian , gaussian quadrature , surface (topology) , mathematics , computation , optics , born approximation , scattering , mathematical analysis , physics , computational physics , wavelength , integral equation , geometry , nyström method , materials science , quantum mechanics , algorithm , composite material
The backscattering characteristics of a computer‐generated known one‐dimensional random surface are studied by computing first the exact surface current distribution over the illuminated area (using four or more points per wavelength) by the moment methods and then calculating the backscattered field by the gaussian quadrature technique. These computations are repeated 40 to 65 times (depending on the incident frequency) over different surface segments to obtain enough scattered field samples to estimate the average scattered power. If the surface current distribution over the surface segment is estimated by the Kirchhoff approximation, the above calculations may be repeated to obtain the average scattered power under the Kirchhoff approximation. By comparing these two average scattered powers at different frequencies, it was found that (1) the two averaged powers can agree to within 2 dB over a range of frequencies in the incident angular range 0° ≤ θ ≤ 40°; (2) within the range of agreement specified in (1), the average backscattered power need not be proportional to the slope distribution of the random surface; and (3) further study is needed to establish the range of validity of the Kirchhoff approximation. Comparisons were also made between existing approximations to the Kirchhoff integral representing the average backscattered power and the numerically computed backscattered power under the Kirchhoff approximation. It was found that the choice of approximations depends upon the incident frequency and the shape of the surface correlation function.