Inequalities for quantitative estimation of the limits of applicability of the physical optics method

Alexander A. Popov

doi:10.1117/12.323281

1 October 1998 Inequalities for quantitative estimation of the limits of applicability of the physical optics method

Alexander A. Popov

Author Affiliations +

Proceedings Volume 3453, Mathematical Methods in Geophysical Imaging V; (1998) https://doi.org/10.1117/12.323281
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

In this paper a simple approach to the quantitative estimate of the limits of applicability of the physical optics method is proposed. In the case of non-absorbing body, the local and integral characteristics of scattered field are compared, i.e. cross-section of extinction and cross-section of scattering which are obtained by means of the physical optics method. It is shown that for arbitrary dimensions of a scatterer cross-section these characteristics are not equal, as it takes place in the case of a rigorous method, but are connected by an inequality. A relative difference of characteristics of extinction and scattering is assigned to a relative error of the physical optics method, within the scope of which they are obtained. For the relative error of the physical optics method the bounding inequalities are derived. It is shown that the relative error for the scatterers of round or square cross-section is equal to 1/p, where p equals ka is the diffraction parameter, a is the radius of a round cross-section or a halfwidth of square cross- section side. The relative error for the scatterers of rectangular cross-section is expressed via the combination of Bessel's functions.

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Alexander A. Popov "Inequalities for quantitative estimation of the limits of applicability of the physical optics method", Proc. SPIE 3453, Mathematical Methods in Geophysical Imaging V, (1 October 1998); https://doi.org/10.1117/12.323281

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