NUMERICAL INVESTIGATION OF ELECTROMAGNETIC SCATTERING AND DIFFRACTION BY CONVEX OBJECTS
Abstract
The solutions D(x,y,y sub o,q) of the partial differential equation D sub yy + iDx + yD = O are employed as a mathematical model for the fields reflected from and diffracted around an opaque convex surface. This solution involves the Airy function w sub 1(t) which is a solution of w' sub 1(t) tw sub 1 (t) = O. FORTRAN computer programs and tables are given for the appropriate Airy functions. Representations for the roots of the equation w' sub 1(ts) - qw sub 1 (ts) = O which play a fundamental role in the theory are discussed. As a function of q, these roots satisfy the Riccati equation (t - q squared) (dt/dq) = 1. The Riccati equation is used to develop several representations for these roots. FORTRAN programs are presented for the evaluation of these constants. Tables of the roots are given for certain cases which have been shown to be of practical significance. Asymptotic expansions are developed for the height gain function F(y) which is a solution of F'(y) + (k squared f(y) - lambda s)F(y) = O. The theory of representing functions by a series of Chebyshev polynomials is reviewed and a discussion is given of the significance of these expansions for future work in diffraction theory.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1965
- Accession Number
- AD0634070
Entities
People
- Nelson A. Logan
Organizations
- Lockheed Martin Missiles and Space