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An Expansion of the Helmholtz Integral and Its Evaluation
Author(s) -
Dougherty H. T.
Publication year - 1969
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs004i011p00991
Subject(s) - helmholtz free energy , class (philosophy) , scattering , mathematical analysis , reflection (computer programming) , helmholtz equation , terrain , integral equation , mathematics , aperture (computer memory) , surface integral , physics , optics , boundary value problem , computer science , acoustics , quantum mechanics , ecology , artificial intelligence , biology , programming language
The Helmholtz integral theorem for the scattering or radiation of radio waves from surfaces is examined to obtain a more general approximation of the observed field distribution. The resulting new integral expansion is particularly responsive to evaluation by the method of stationary phases, yielding a quantitative solution applicable to a more general class of surfaces and aperture boundaries than was previously feasible. The problem of reflection from finite irregular surfaces, such as terrain or atmospheric layers, is evaluated formally. The result indicates a source of significant reflections not generally treated by ray theory.