## Abstract

Some of the advantages and limitations of Moliere’s high-energy solution of the Schrödinger scattering equation are discussed in connection with the study of wave propagation in a turbulent medium. Certain inconsistencies in the conventional Born and Rytov methods are shown to be closely related to an unwarranted extension of the Moliere solution to higher order in the stationary-phase approximation. The error associated with the extended solution is shown to increase as the penetration distance decreases; its estimated magnitude may be restricted to be relatively small by adoption of a lower range limit for the validity of the Born–Rytov approximation. This restriction, when combined with the standard upper limit associated with the first-order refractive-index approximation, defines a range interval, bounded from above and below, outside of which the Born–Rytov approximation is inconsistent. For optical propagation in the atmosphere, the lower limit exceeds the upper limit, and the Born–Rytov approximation is nowhere consistent.

© 1971 Optical Society of America

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