On certain theories of multiple scattering in random media of discrete scatterers

Abstract

The paper presents new information on the accuracy of the heuristic approximations in two important theories of multiple scattering in random media of discrete scatterers: Twersky's “freespace” and “two‐space scatterer” formalisms. Two complementary approaches, based primarily on a one‐dimensional model and the one‐dimensional forms of the theories, are used. For scatterer distributions of low average density, the “heuristic” asymptotic forms for the coherent field and the incoherent intensity are compared with asymptotic forms derived from a systematic analysis of the multiple scattering processes. For distributions of higher density, both in the average number of scatterers per wavelength and in the degree of packing of finite‐size scatterers, the analysis is carried out “experimentally” by means of a Monte Carlo computer simulation. Approximate series expressions based on the systematic approach are numerically evaluated along with the heuristic expressions. The comparison (for both forward‐ and back‐scattered field moments) is made for the worst‐case conditions of strong multiple scattering for which the theories have not previously been evaluated. Several significant conclusions are drawn which have certain practical implications: (a) in application of the theories to describe some of the scattering phenomena which occur in the troposphere, and (b) in the further evaluation of the theories using experiments on physical models.

A review of theories of coherent radio wave propagation through precipitation media of randomly oriented scatterers, and the role of multiple scattering

“…Since the coefficient 2•rN(D)/ko decreases with frequency and f(n, D) becomes constant in the optical region, it is clear that this term is negligible at all frequencies. From the results of Olsen et al [1976], it is suggested that this term accounts at least approximately for the effect of the dominant backward multiple scattering processes. Other backward multiple scattering processes believed described by a multiplicativ½ term to the exponential in Twcrsky's free-space theory form for T' [see Rogers and Olsen, 1976] are higher order and have even less effect.…”

Remote sensing of layered random media using the radiative transfer theory

“…The current paper is devoted to the remote sensing applications. A discrete scatterer model is most appropriate and realistic for modeling real world problems [Mishchenko et al, 2006;Liang et al, 2005;Fung and Chen, 1981;Lam and Ishimaru, 1993;Ulaby et al, 1990;Olsen et al, 1976;Ito and Ogichi, 1987;Nghiem et al, 1993]. Notice that the analysis used in the discrete random media is quite different from the continuum case [Foldy, 1945;Lax, 1951;Twersky, 1964;Tsang et al, 1984;Lang, 1981].…”

Theoretical determination of the effects of multiple scattering by hydrometeors in monopulse systems at millimeter wavelengths

“…Among the sources of errors are noise, interference by extraneous signals, and self-interference caused by incoherent radiation; the assessment of the system accuracy in the presence of these error sources is a topic of great technical relevance which in the past received considerable attention. In particular, the self-interference by incoherent radiation was studied in connection to clear air turbulence [Valley, 1975;Knepp, 1976], but only recently, it has been recognized that at millimeter waves, the incoherent radiation arising from precipitation particles can also be a source of problems for radio systems owing to possible drawbacks such as extra noise, linear distortion, and &polarization [Ishimaru and Lin, 1972;Capsoni et al, 1976;Olsen et al, 1976;Capsoni and Paraboni, Copyright 1982 by the American Geophysical Union.…”