Validity of Image Theorems under Spherical Geometry

TL;DR

This paper evaluates the accuracy of classical image theorems in spherical geometry by comparing approximate and exact electromagnetic fields, using two analytical methods, with applications in mirror design and large object scattering.

Contribution

It introduces a quantitative analysis of image theorem deviations in spherical geometry using vector potential and Green's function methods.

Findings

Quantifies deviation of image theorems in spherical geometry

Uses two analytical methods for comparison

Provides insights for mirror design and scattering applications

Abstract

This paper deals with different image theorems, i.e., Love's equivalence principle, the induction equivalence principle and the physical optics equivalence principle, in the spherical geometry. The deviation of image theorem approximation is quantified by comparing the modal expansion coefficients between the electromagnetic field obtained from the image approximation and the exact electromagnetic field for the spherical geometry. Two different methods, i.e., the vector potential method through the spherical addition theorem and the dyadic Green's function method, are used to do the analysis. Applications of the spherical imaging theorems include metal mirror design and other electrically-large object scattering.