Abstract
The various factors in the saddle point approximation to the path integrals of wave hop theory are identified with their geometrical optical equivalents more completely than heretofore. In the process, one 'diffractive correction' to the convergence coefficient of geometrical optics is shown to be invalid in the shadow region. The range of validity of the approximations is quantified, and the saddle point approximation and classical geometrical optics results are compared numerically. Height-gain functions are introduced in the equation for the path integrals. Finally, the saddle point approximation for the general case of an elevated transmitter and (or) receiver is derived. In this case, there are four saddle points corresponding to the four possible wave paths.
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