Inhomogeneous Random Media Research Articles

On the photon counting statistics of light passing through an inhomogeneous random medium

A quantum description of light passing through the turbulent atmosphere recently proposed by Tatarski is developed for arbitrary statistics of incident light, moments of arbitrary order are calculated and a modified photodetection equation is derived. Another description by Diament and Teich is shown to be also quantum but both the descriptions are valid under various conditions. A comparison of the Tatarski and Diament and Teich descriptions is performed and results for the monochromatic coherent state of a field are discussed as a special case.

Cherenkov and transient radiation of uniformly moving charge in random inhomogeneous medium

Radiation of a uniformly moving charged particle in a medium with weak, random inhomogeneities of dielectric permittivity is considered. The expression for the charge energy losses is obtained by the method of radiation reaction using the tensor of the effective permittivity. The limiting cases of small-and large-scale inhomogeneities are studied. Peculiarities of energy losses near the threshold of Cherenkov radiation are clarified.

Measurement of Spatial Coherence Using Speckle Patterns

A method is described for measuring the spatial coherence of light by means of speckle patterns produced by using ground glass as a random inhomogeneous medium. The theory of the method is developed and its verification is performed experimentally by using a laser and a mercury lamp as light sources. Characteristics of the present method for exploring the spatial coherence of light fields are discussed.

Equations for the correlation functions of a wave beam in a randomly-inhomogeneous medium

Equations for the correlation functions of a wave beam in a randomly-inhomogeneous medium

Detection Probabilities for Log-Normally Distributed Signals

The amplitude and power of a large family of radio signals are observed to have log-normal probability density functions. Among these are signals propagated through random inhomogeneous media, a notable example being low frequency atmospheric radio noise. Of greater importance are certain radar targets that have been observed to have essentially log-normal density functions. Both ships and space vehicles may fall into this category. Curves of probability of detection vs. signal-to-noise ratio for the case of log-normal signals in Gaussian noise have been computed and are presented in this paper. The curves apply for square-law detection with varying degrees of postdetection linear integration. Both fully correlated and completely uncorrelated fluctuating signals are considered. It is shown that for log-normal signal distributions having large variances, the probability of detection differs significantly from that obtained using curves based on an assumed Rayleigh signal distribution.

Validity of the Rytov Approximation in Optical Propagation Calculations*

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.

On Wave Propagation in a Random Inhomogeneous Medium

This paper examines the calculation of the coefficient of variation of intensity for acoustic transmission in a randomly inhomogeneous medium. An equation for this coefficient is derived which is valid over the range of frequencies between the wave limit and the ray limit previously reported by other authors.