Interference Patterns; Comparison of Approximate Formulas with General Integrals and Measurements

Abstract

In Chapters 3 and 5 the exact general integrals for the electromagnetic field of vertical and horizontal electric dipoles near the plane boundary between electrically different half-spaces are expressed in terms of integrated formulas that are very good approximations within wide ranges of the variables and parameters. In order to determine the accuracy of the representations in a direct quantitative manner, it is appropriate to compare fields calculated from these formulas with corresponding ones obtained by the direct numerical evaluation of the integrals. Such comparisons are best made under critical conditions when even small differences are clearly delineated. Since E_1ρ(ρ, ø, z) is the most important and generally useful component, an extensive study of its properties over wide ranges of distances, frequencies, and material parameters is suggested. Less extensive comparisons for the other five components are also indicated.