D. A. de Wolf

Electromagnetic reflection from an extended turbulent medium: Cumulative forward-scatter single-backscatter approximation

The backscatter cross section Q for high-frequency irradiated turbulent dielectric media, many mean free paths L_{1} wide, is computed. The length L_{1} is the distance into the medium over which the mean electric field decreases in amplitude by a factor e^{-1} . Previous calculations have always been restricted to L \ll L_{1} . It is found that Q increases from the Born approximation Q = Q_{1} for medium width L \ll L_{1} to Q = 2Q_{1} for L \gg L_{1} , and the theory is valid as long as L \ll (kL_{0})^{5/3} L_{1} , a significant improvement over the Born approximation, when the macroscale L_{0} is much larger than the wavelength 2_{\pi}k^{-1} . The improvement is due to incorporation of the dominant effects of cumulative forward scattering in the local electric field in the medium. A rigorous and a heuristic derivation are given. The transitional behavior is discussed and a simple physical interpretation is given.

Strong irradiance fluctuations in turbulent air: plane waves*

Analytical results are found for irradiance statistics of a plane wave propagating through uniformly turbulent air. They result from a new error analysis of approximations made in selective summation of diagram contributions to the iterated moment equations (in integral form). The results are determined by three regimes of the parameter k7/6L11/6Cn2 determined by its location with respect to powers of the micro- and macroscale Fresnel numbers (κm2L/k)−1/6∾0.3 and (kL02/L)∾104 (the numerical values are for 0.6-μm radiation and a horizontal pathlength L ∾ 1 km). The modified-Rytov result is found in the lowest regime. Irradiance I is log-normal in the intermediate (saturation) regime and the log-amplitude variance decays asymptotically as 0.41 (κm7/3L3Cn2)−1/6. When k7/6L11/6Cn2 far exceeds the macroscale Fresnel number kL02/L, the irradiance tends to an exponential distribution (in agreement with previous results).

Waves in turbulent air: A phenomenological model

Waves propagating through random media undergo large phase and amplitude scintillations even when the scattering at other than very small angles is insignificant. A large number of literature on the subject has been written in recent years. Nevertheless many of the more interesting effects (amplitude scintillation) are not well understood because the theory of the interaction is formulated too abstractly to give insight. The purpose of this work is to provide a phenomenological model with which we derive most of the known expressions-and some new ones-by means of back-of-the-envelope calculations. The model appears to give the needed insights.

Coherence of a light beam through an optically dense turbid layer

A light beam propagating through a turbid medium (e.g., aerosol) can be severely attenuated by scattering losses and still retain coherence over distances comparable to particle diameters. An expression for the two-detector mutual-coherence function is rederived by means of approximations clarified by a physical model. Its spatial and temporal properties are further examined by means of a simplified physical aerosol model leading to tractable mathematical analysis.A light beam propagating through a turbid medium (e.g., aerosol) can be severely attenuated by scattering losses and still retain coherence over distances comparable to particle diameters. An expression for the two-detector mutual-coherence function is rederived by means of approximations clarified by a physical model. Its spatial and temporal properties are further examined by means of a simplified physical aerosol model leading to tractable mathematical analysis.

Strong irradiance fluctuations in turbulent air, III. Diffraction cutoff*

The theory of irradiance fluctuations of plane and spherical waves propagating through turbulent air is developed further to account for a saturation of the variance in the case where the Fresnel radius (L/k)1/2 exceeds the microscale l0. The crucial step is an expression for ray bending (excluding small eddies that cause diffraction effects) in the iterative solution of a set of nonlinear equations. Previous work was based upon a geometrical-optics expression, thus limiting the results to the case (L/k)1/2 < l0. The log-amplitude variance is found to be proportional to (Cn2k7/6L11/6)-1/6 in the saturation regime. The approximation also yields a log-amplitude covariance that appears to behave qualitatively as observed.

Strong irradiance fluctuations in turbulent air, II. Spherical waves*

This work is an extension of previous work, on plane waves propagating through uniformly turbulent air, to results for spherical waves. The main result is a saturation-regime asymptote for the log-amplitude variance , namely, 1.25 (κm7/3L3Cn2)1/6. Comparisons with recent data are made.

Optical propagation through turbulent air

Abstract Turbulent air causes optical rays to deviate from otherwise straight paths by irregular slight undulations, and it also changes the phase velocities irregularly. These fluctuations cause a host of unpleasant degradations to communications signals. This survey circumvents the Scylla of propagation theory and Charybdis of meteorological input by introducing simple physical concepts to explain the underlying interaction of random fluctuations of the refractive index typical of turbulence with basic electromagnetic waves.

Point-to-point wave propagation through an intermediate layer of random anisotropic irregularities: Phase and amplitude correlation functions

The problem of wave propagation from a point source to a point of observation through an intermediate slab containing random weak dielectric irregularities is considered. Under the assumption that the spatial correlation of the permittivity is a Gaussian one with correlation distances much larger than the wavelength, the phase and amplitude auto- and cross-correlations are computed for any distance of source and receiver to the slab. Comparison is made to the analyses by Karavainikov and Yeh which are shown to be limiting cases of the present work.

Waves in random media: Weak scattering reconsidered

Wave propagation in a weak random medium has generally been understood to give rise to log-normal field statistics, and first Born approximation of log amplitude and phase. Yet no derivation of the field probability distribution seems to exist; only an inference. The moments of the field (not just the amplitude) are derived from moment equations, and from these it is shown that extra terms must be identified with phase and amplitude in the customary representation of the field.

Radar reflectivity of metallic bodies of revolution

It is shown that the basic reason why Kerrs physical optics formula for the reflectivity of an axially viewed perfectly conducting body of revolution is also useful when the wavelength is not small compared to body dimensions is because the electric dipole and the magnetic dipole plus electric quadrupole are the dominant multipole sources for reflection.