Derivation of Uniform PO Diffraction Coefficients Based on
Field Equivalence Principle
Ken-ichi Sakina, Suomin Cui, and Makoto Ando
Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, Tok yo, 152-8552 Japan
SUMMARY
A novel approach for asymptotic reduction of physi-
cal optics (PO) integration is proposed for two-dimensional
line source diffraction from a half-sheet. The field equiva-
lence principle provides alternative integration surfaces not
on the original half-sheet but on the geometrical shadow
(SB) and reflection (RB) boundaries, where analytical in-
tegration leads to the well-known Fresnel-type uniform PO
diffraction coefficient of UTD type. The superiority of the
uniform diffraction coefficient to those of other types is
explained in terms of the location of the integration surfaces
and is demonstrated numerically. © 2001 Scripta Technica,
Electron Comm Jpn Pt 2, 84(2): 5462, 2001
Key words: PO; PO diffraction coefficient; field
equivalence principle.
1. Introduction
Physical optics (PO) [1] is a high-frequency tech-
nique in which the total induced currents J are approxi-
mated in the sense of geometrical optics (GO). The PO
currents J
PO
thus defined are then integrated over the sur-
face to give finite fields everywhere, including geometrical
boundaries and caustics in focusing systems. PO has been
widely applied to the pattern analysis of reflector antennas.
In PO, the scattering fields are obtained by evaluating
the surface radiation integrals of J
PO
, which is performed
numerically in general. The asymptotic evaluation of these
surface integrals [2, 3] leads us to line integral repre-
sentations or closed-form expressions of fields, which
greatly contributes not only to reducing the computation
time but also to mechanism extraction of PO [4]. In general,
the asymptotic reductions of PO surface integrals such as
the geometrical theory of diffraction (GTD) become infi-
nite at geometrical boundaries and caustics. To eliminate
these difficulties, several uniform expressions have been
proposed. In Ufimtsevs physical theory of diffraction
(PTD) [57], PO currents are improved by adding another
component called fringe wave currents J
FW
. Many works
about the evaluation of surface integrals for diffraction from
a half-sheet are developed in the spectral domain [811].
Efforts to achieve surface to line integral reduction
have included both an exact approach based on the Helm-
holtzHuygheng principle [1215] and asymptotic ap-
proaches such as the high-frequency approximation
[1621]. The asymptotic and local expressions are quite
different from the exact and global ones and sometimes
have the advantage that the former is applicable to a much
wider class of scatterers based on local features of the
diffraction phenomena.
In two-dimensional (2D) problems of half-sheet dif-
fraction illuminated by a line source, the edge contribution
of the PO integral is asymptotically expressed in terms of
PO diffraction coefficients. PO diffraction coefficients of
the classical Keller type are nonuniform at geometrical
boundaries, such as shadow and reflection boundaries
(SB/RB) [1618]. Two types of uniform expressions to
cope with these difficulties are available. The coefficients
of the first kind were derived by directly applying the
uniform asymptotic evaluation to integration on a half-sheet
© 2001 Scripta Technica
Electronics and Communications in Japan, Part 2, Vol. 84, No. 2, 2001
Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J83-C, No. 2, February 2000, pp. 118127
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