The phenomenon of scintillation of radio waves propagating through the ionosphere is reviewed in this paper. The emphasis is on propagational aspects, including both theoretical and experimental results. The review opens with a discussion of the motivation for stochastic formulation of the problem. Based on measurements from in-situ, radar, and propagation experiments, ionospheric irregularities ate found to be characterized, in general, by a power-law spectrum. While earlier measurements indicated a spectral index of about 4, there is recent evidence showing that the index may vary with the strength of the irregularity and possibly a two-component spectrum may exist with different spectral indices for large and small structures. Several scintillation theories including the Phase Screen, Rytov, and Parabolic Equation Method (PEM) are discussed next. Statistical parameters of the signal such as the average signal, scintillation index, rms phase fluctuations, correlation functions, power spectra, distributions, etc., are investigated. Effects of multiple scattering are discussed. Experimental results concerning irregularity structures and signal statics are presented. These results are compared with theoretical predictions. The agreements are shown to be satisfactory in a large measure. Next, the temporal behavior of a transionospheric radio signal is studied in terms of a two-frequency mutual coherence function and the temporal moments. Results including numerical simulations are discussed. Finally, some future efforts in ionospheric scintillation studies in the areas of transionospheric communication and space- and geophysics are recommended.

Radio wave scintillations in the ionosphere

To allow the determination of scattering and absorption parameters of a turbid material from reflection measurements the relation of these parameters to the reflection has been described by two theoretical approaches. One approach is based on the diffusion theory which has been extended to include anisotropic scattering. This results in a reflection formula in which the scattering and absorption are described by one parameter each. As a second more general approach a Monte Carlo model is applied. Comparison of the results indicates the range of values of the scattering and absorption parameters where the computationally fast diffusion approach is applicable.

Scattering and absorption of turbid materials determined from reflection measurements. 1: theory.

Summary. In order to separate the scattering effect from the intrinsic attenuation, we need a multiple scattering model for seismic wave propagation in random heterogeneous media. In this paper, we apply radiative transfer theory to seismic wave propagation and formulate in the frequency domain the energy density distribution in space for a point source. We consider the cases of isotropic scattering and strong forward scattering. Some numerical examples are shown. It is seen that the energy density-distance curves have quite different shapes depending on the values of medium seismic albedo Bo = qs/(qs t q,), where vs is the scattering coefficient and va is the absorption coefficient of the medium. For a high albedo (B> 0.5) medium, the energy-distance curve is of arch shape and the position of the peak is a function of the extinction coefficient of the medium ve = qs + qa. Therefore it is possible to separate the scattering effect and the absorption based on the measured energy density distribution curves.

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Multiple scattering and energy transfer of seismic waves - separation of scattering effect from intrinsic attenuation - I. Theoretical modelling

Various characteristics of photon diffusion in turbid biological media are examined. Applications include the interpretation of data acquired with laser Doppler blood-flow monitors and the design of protocols for therapeutic excitation of tissue chromophores. Incident radiation is assumed to be applied at an interface between a turbid tissue and a transparent medium, and the reemission of photons from that interface is analyzed. Making use of a discrete lattice model, we derive an expression for the joint probability Γ(n, ρ)d2ρ that a photon will be emitted in the infinitesimal area d2ρ centered at surface point ρ = (x, y), having made n collisions with the tissue. Mathematical expressions are obtained for the intensity distribution of diffuse surface emission, the probability of photon absorption in the interior as a function of depth, and the mean path length of detected photons as a function of the distance between the site of the incident radiation and the location of the detector. We show that the depth dependence of the distribution of photon absorption events can be inferred from measured parameters of the surface emission profile. Results of relevant computer simulations are presented, and illustrative experimental data are shown to be in accord with the theory.

Model for photon migration in turbid biological media

Recent researches have revealed that there exists an intimate connection between radiometry and the theory of partial coherence. In this paper a review is presented of some of these developments. After a brief discussion of various models for energy transport in optical fields and of some of the basic concepts of the classical theory of optical coherence, the following topics are discussed: the foundations of radiometry, the coherence properties of Lambertian sources, and the relationship between the state of coherence of a source and the directionality of the light that the source generates. Some very recent work is also described which reveals that certain sources that are spatially highly incoherent in a global sense will generate light that is just as directional as a laser beam.

Coherence and radiometry

This paper presents a review of basic theories and recent advances in the studies of wave propagation and scattering in random media. Examples of the random media include the atmosphere, the ocean, and biological media whose characteristics are randomly varying in time and space. The study of electromagnetic, optical, and acoustic waves in such media has become increasingly important in recent years in the areas of communication, detection, and remote-sensing. Topics covered in this paper are divided into "waves in randomly distributed scatterers," "waves in random continua," and "remote-sensing of random media." Transport theory with various approximate solutions and multiple scattering theories are discussed and their relationships are clarified. Included in the analyses are propagation characteristics of intensities, wave fluctuations, pulse propagation and scattering, coherence bandwidth, and coherence time of communication channels through random media. Remote-sensing techniques include recent advances in the use of inversion techniques to deal with ill-posed problems.

A. Ishimaru

Papers

Theory and application of wave propagation and scattering in random media