Department of Mathematics

The fundamental problem of optical wave propagation is the determination of the field at an observation point, given a disturbance specified over some finite aperture. In both vacuum and inhomogeneous media, the solution of this problem is given approximately by the superposition integral, which is a mathematical expression of the extended Huygens-Fresnel principle. In doing so, it is important to find the atmospheric impulse response (Green's function). Within a limited but useful region of validity, a satisfactory optical propagation theory for the earth's clear turbulent atmosphere could be developed by using Rytov's method to approximate the Helmholtz equation. In particular, we deal with two optical problems which are the time reversal and apodization problems. The background and consequences of these results for optical communication through the atmosphere are briefly discussed.