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# Accession Number:

## AD0641100

# Title:

## THE METHOD OF SPHERICAL REPRESENTATION FOR TREATING ELECTROMAGNETIC SCATTERING.

# Descriptive Note:

## Final rept., 15 Apr 65-14 Apr 66,

# Corporate Author:

## LOCKHEED MISSILES AND SPACE CO SUNNYVALE CALIF

# Report Date:

## 1966-04-14

# Pagination or Media Count:

##
69.0

# Abstract:

## Since the distant scattered radiation is best represented as spherical waves, and generalized spherical functions may be used to establish a system of components for field vectors, each of which transforms independently on rotation, a spherical representation can be achieved with a geometry in which the surface of the scatterer is transformed into a sphere. At large distances, this geometry is chosen congruent with that of ordinary space. The generalized spherical functions are then taken to be functions of the angles in the spherical polar coordinate system in the transformed space, whose metric is non-Euclidean. Relevant properties of generalized spherical functions and means for computing them are described, and also the recurrence relations, derived from group theory, used to compute coupling integrals. The representation of spherical waves by generalized spherical functions, the transformation of Maxwells equations, and the representation of an arbitrarily polarized electromagnetic wave arbitrarily directed with respect to the polar axis of the spherical representation is developed. Geometrical and electromagnetic representation for an axially symmetric scatterer is treated in detail, and the derivation of coordinate systems from electrostatic field distributions is presented as a general method. The procedure for finding the scattered field, backscattering cross section, and radar scattering matrix for a perfectly conducting prolate spheroid is elaborated. Scattering by limiting prolate and oblate spheroids is discussed with advantage in terms of the spherical representation. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#