Electrical and Computer Engineering ETDs

Publication Date

5-31-1968

Abstract

Significant errors may be introduced into the theoretical calculation of scattered fields from a roughened sphere by the use of erroneously derived shadowing probabilities. These shadowing probabilities, of recent appearance in the literature, had been derived using an infinite plane as the mean surface. This paper undertakes the derivation of shadowing probabilities using a spherical mean surface. Although closed form expressions could not be obtained, computer evaluation of a "correction factor" showed that the errors incurred through use of the infinite plane probabilities (rather than the spherical surface) are insignificant. The class of rough surfaces considered was with a gaussian distribution of heights with respect to the mean sphere. To insure isotropy, a correlation function dependent only on the separation distance between points was postulated. With the Stratton-Chu integral formulation, and the tangent-plane approximation to obtain total fields at the surface, integral expressions were derived for the squared-magnitudes of the right- and left-circularly polarized components of the scattered electric field intensity. This was done for the general bistatic case assuming a right-circularly polarized plane-wave incident on the scatterer. Shadowing formulation was accomplished by introducing a random functional, S, of unity or zero value, into the integrands of the scattered field expressions. This essentially results in zero total fields at the surface in the shadow regions. Stochastic averages of the integrands containing S are expressed approximately as averages of random functions, one of which is the random probability that S=1 at a point on the surface, given the random height and slopes at the point. For the bistatic case, it is concluded that S=1 only if the point is both illuminated by the source and visible to the observer. Approximate expressions for total, as well as conditional, probabilities that S=1 are derived, and compared with those derived on the infinite plane basis. These differed by a factor which departed from unity value only in the neighborhood of grazing (to the mean sphere) incidence.

Sponsors

The University of New Mexico, the National Aeronautics and Space Administration NASA Grant NsG 129-61

Document Type

Dissertation

Language

English

Degree Name

Electrical Engineering

Level of Degree

Doctoral

Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

Ahmed Erteza

Second Committee Member

William Jackson Byatt

Third Committee Member

Shlomo Karni

Fourth Committee Member

Julius Rubin Blum

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