Mark J. Beran

Two-scale solution for atmospheric scintillation

We demonstrate that a recently derived approximate solution to the fourth-moment equation that was thought to be Valid only for strong scattering is in fact valid for all values of the scattering parameter. We use a modified Kolmogorov spectrum for the index-of-refraction fluctuations and present results in two dimensions for comparison with numerical solutions. We also present results in three dimensions that should represent a quantitatively accurate, theoretical description of the atmospheric-scintillation problem.

Two-scale solutions for intensity fluctuations in strong scattering

An exact integrodifferential equation is derived for a certain transform of the four-point coherence function by using a two-scale embedding procedure. The solution is expanded in an asymptotic series in the inverse strong-scattering parameter, the terms of which are solutions of a hierarchy of simple first-order partial differential equations. Further approximations simplify the retransformation and display the four-point coherence in a useful, numerically convenient form. Results compare favorably with existing numerical computations of the scintillation index and the covariance in two-dimensional plane-wave propagation. Results for three-dimensional plane-wave propagation are also presented.

A neural network approach to source localization

The use of neural network techniques to localize an acoustic point source in a homogeneous medium is demonstrated. The input data are the cosines of the phase difference measurements at an array with N detectors. Only the most fundamental types of neural network systems will be considered. Use will be made of linear and sigmoid‐type neurons in a single‐layer network. The performance of the single‐layer network is very satisfactory for a wide range of configuration parameters if the resolution and sampling conditions are satisfied. Once the parameters of the neural network are determined, the computational effort to determine a new source location is minimal. However, when a source/detector configuration is considered that does not satisfy the resolution and sampling conditions, the single‐layer network will not consistently perform well.

Two-scale solution for atmospheric scintillation from a point source

In a previous paper [ J. Opt. Soc. Am. A2, 2133 ( 1985)] we presented three-dimensional numerical solutions for the scintillation index versus the range for a plane wave propagating in the atmosphere, based on the two-scale approximate solution to the fourth-moment equation. In that paper the refraction-index fluctuations were represented by a modified Kolmogorov spectrum, which included an inner scale. In the present paper we present the equivalent results for a point source. The spectrum here is modeled by a function that is somewhat different from that used in the previous paper, and we discuss the relation between the two. The results of the present paper are of interest because they can be compared with recent experimental data.

PROPAGATION IN RANDOM STRATIFIED WAVEGUIDES : A MODAL-SPECTRAL TREATMENT

The statistics of a forward-propagating wave is considered in a random, anisotropic, stratified three-dimensional waveguide, where modal analysis offers unique advantages. After extracting the vertical dependence in the usual way, the equations are formulated which govern the range evolution of the transverse horizontal spectra of the modal field coefficients (MTWS). A short-range perturbation solution is used to derive the difference equations governing the long-range behavior of the two lowest moments of the field spectra. The conditions under which these difference equations can be approximated as differential equations are given. These equations are not limited by the parabolic approximation, and are amenable to numerical treatment by marching techniques. They are used here to study the effect of scattering on the spectral redistribution of the modal power, and the related problem of the coherence of plane and cylindrical waves. It is shown that, as a result of scattering in the transverse horizontal ...

Volume scattering in a shallow channel

Using a generalization of the modal coherence equations previously developed by Sutton and McCoy [J. Math. Phys. 18, 1052 (1977)], the effect of volume scattering in a shallow channel is treated. The difference between the range behavior of the cross‐modal coherence functions and the previously studied self‐modal coherence functions is shown. In particular, calculations are made to evaluate the characteristic scales that govern the range decay of the cross‐modal coherence functions. A particular example is given to illustrate the effect of the choice of different parameters.

Scintillation index calculations using an altitude-dependent structure constant

We present calculations of the scintillation index that result from a plane wave of light impinging on the atmosphere. Calculations are made using the two-scale theory and assuming a Kolmogorov structure function with an altitude-dependent structure constant. A plot of the scintillation index for typical nighttime viewing is given as a function of angle from the zenith. A further approximation is then introduced which allows the calculation of the scintillation index in terms of a single nondimensional parameter. This parameter is a direct generalization of the parameter used when the structure constant is an absolute constant.

Propagation of a finite beam through a random medium

The differential equation for the fourth-order statistical moment of the field of a finite beam propagating in a statistically homogeneous and isotropic two-dimensional random medium is solved numerically. Results are presented for the variance and covariance of irradiance scintillations of a Gaussian beam that propagates in a medium with a Gaussian correlation function. It is shown that the range dependence of the variance is highly dependent on the ratio D/ln (D) is the initial beam width; ln is the correlation length of the medium) and approaches that of a plane wave for large enough D/ln. An increase in the variance toward the edge of the beam is also manifested.

Wave propagation in random media: a comparison of two theories

The variance of the irradiance scintillations of a wave that propagates in a random medium is calculated by using the extended Huygens–Fresnel principle (EHFP) and then compared with numerical solutions of the parabolic equation for the fourth-order statistical moment. Results are presented for the propagation of Gaussian beams and plane waves in a two-dimensional random medium with a Gaussian correlation function. Various formulations of the EHFP are considered, with particular emphasis on the often-used phase approximation of the EHFP. It is shown that, although both methods predict saturation, there is a considerable disagreement at moderate ranges.

V - Imaging Through Turbulence in the Atmosphere

This chapter discusses imaging through turbulence in the atmosphere. Turbulent velocity fluctuations in the propagation medium cause image distortion by generating a statistical temperature field, which gives rise to random inhomogeneities in the index of refraction. Imaging through turbulent media is of importance in optical and radio astronomy, remote sensing, target identification, and the investigation of the properties of the medium itself. The chapter also discusses the current state of understanding of the propagation of light through the atmosphere and summarizes the available theory and experiments that may be used to analyze image distortion and compensate for it. The most important methods that are used to compensate for image distortion caused by atmospheric turbulence are also discussed. The chapter emphasizes the assumptions that are used in the underlying propagation theory and the compensation methods. The importance of optical intensity fluctuations in addition to phase fluctuations and the far-reaching effects of the assumption of isoplanicity in compensation techniques are also discussed in the chapter.