Validity of the Rytov Approximation in Optical Propagation Calculations*

Abstract

The applicability of the Rytov approximation to the calculation of the characteristics of optical propagation in a weakly inhomogeneous random medium is investigated. The condition that the mean square value of the second term in the associated perturbation expansion be smaller than that of the first is adopted as a criterion for the validity of the Rytov approximation. It is shown that there is a very severe range limitation on the validity of the Rytov approximation for optical propagation in the lower portions of the earth’s atmosphere. Furthermore, comparison of the limiting form for large x/kl² of the validity condition derived in this paper with the condition on the validity of the Born approximation obtained independently by Mintzer, and by Kay and Silverman reveals that the Rytov and Born approximations have the same domain of validity in this limiting case. The equivalence of the validity conditions for the Rytov and Born approximations contradicts the statements of Tatarski and Chernov who contend that the Rytov approximation is superior to the Born approximation. It is conjectured that the Rytov and Born approximations have the same domain of validity for all x/kl².