Biomedical subjects

Reuven Mazar

Publications and source records attributed to Reuven Mazar.

6 recordsLinked to original sources

PubMed2005

Phase-space beam summation analysis of rough surface waveguide.

A Gaussian beam summation (GBS) formulation is introduced for a doubly rough boundary waveguide, wherein the coherent and incoherent scattered fields are decomposed into a discrete phase-space summation of Gaussian beams (GB) that emanate from the rough surfaces in all directions. The scheme involves deterministic GB propagators and stochastic GB-to-GB (GB2GB) scattering matrices for the coherent and incoherent fields, where each scattered beam is propagated inside the waveguide and is scattered again from the rough boundaries. The GB2GB matrices are calculated from the statistical moments of the scattering amplitude, which are given either analytically or empirically. An analytical and numerical example for a waveguide with weak boundary roughness is presented and discussed. The formulation reveals explicitly the phase-space footprint of the stochastic multiple scattering process at the rough boundaries, thus providing a cogent physical interpretation and an effective mathematical representation to the field. The formulation also accommodates the receiver's pattern in the same phase-space format. Bistatic reverberations inside a rough surface waveguide as a function of the range and of the source and the receiver directions are thus examined as an implementation example.

Journal Article↗

PubMed2005

A phase-space Gaussian beam summation representation of rough surface scattering.

A Gaussian beam (GB) summation representation for rough surface scattering is introduced. In this scheme, the coherent and incoherent scattered fields are described by a phase-space summation of GBs that emanate from the rough surface at discrete set of points and directions. It thus involves stochastic GB2GB scattering matrices for the coherent and incoherent fields, and deterministic GB propagators. It benefits from the simplicity and accuracy of the latter, and can be used in applications involving propagation in complex scenarios comprising inhomogeneous media with rough surface boundaries. The GB2GB matrices are calculated from the statistical moments of the scattering amplitude, which are given either analytically or empirically. An analytical and numerical example for weakly rough surface is presented and discussed. Applications to the more complicated propagation scenario of doubly rough surface waveguide with multiple reflection phenomena will be presented in a follow-up publication.

Journal Article↗

PubMed2004

Reference-wave solution for the two-frequency propagator in a statistically homogeneous random medium.

Spatial and temporal structures of ultrawide-band high-frequency fields can be appreciably affected by random changes of the medium parameters characteristic of almost all geophysical environments. The dispersive properties of random media cause distortions in the propagating signal, particularly in pulse broadening and time delay. Theoretical analysis of pulsed signal propagation is usually based on spectral decomposition of the time-dependent signal and the analysis of the two-frequency mutual coherence function. In this work we present a new reference-wave method and apply it to solving the equation of the two-frequency mutual coherence function propagator. This method is based on embedding the problem into a higher-dimensional space and is accompanied by the introduction of additional coordinates. Choosing a proper transform of the extended coordinate system allows us to emphasize "fast" and "slow" varying coordinates which are consequently normalized to the scales specific to a given type of problem. Such scaling usually reveals the important expansion parameter defined as a ratio of the characteristic scales and allows us to present the equation being solved as a hierarchy of terms having a decreasing order of expansion with respect to this parameter. We present an analytical result for the two-frequency mutual coherence function propagating in a random medium with arbitrary refractive index fluctuations and show that when approximating the transverse structure function of the medium by a quadratic form, the solution reduces to the exact result derived previously. Extension of the reference-wave method to the analysis of the pulse distortion effects is considered.

Journal Article↗

PubMed2003

Reference-wave solutions for the high-frequency fields in inhomogeneous-background random media.

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. For computations of the statistical measures it is therefore desirable to have a solution for the high-frequency field propagating along an isolated ray trajectory. A new reference wave is applied to obtain an analytic solution of the parabolic wave equation that describes propagation along the ray trajectory of the deterministic-background medium. The methodology is based on defining a paired-field measure as a product of an unknown field propagating in a disturbed medium and the complex-conjugate component propagating in a medium without random fluctuations. When a solution of the equation for the paired-field measure is obtained, the solution of the deterministic component can be extracted from the paired solution to determine the solution of the unknown field in an explicit form.

Journal Article↗

PubMed2002

Reference-wave solutions for the high-frequency field in random media.

Ray trajectories, as has been shown in the recently formulated stochastic geometrical theory of diffraction, play an important role in determining the propagation properties of high-frequency wave fields and their statistical measures in complicated random environments. The field at the observer can be presented as the superposition of a variety of field species arriving at the observer along multiple ray trajectories resulting from boundaries and scattering centers embedded into the random medium. In such situations the intensity products from which the average intensity measures can be constructed and which, in general, are presented as even products of the total field, will contain sums of products of mixed field species arriving along different ray trajectories. For computations of the statistical measures of the field it is desirable, therefore, to possess a solution for the high-frequency field propagating along an isolated ray trajectory. The main concern of this work is the construction of high-frequency asymptotic propagators, relating the values of the random field and its statistical measures at some observation plane to their source (actual or virtual) distributions at the initial plane. For this reason a reference-wave method was developed to obtain an approximate solution of the parabolic wave equation in a homogeneous background random medium.

Journal Article↗

PubMed2002

Modeling of high-frequency propagation in inhomogeneous background random media.

When a high-frequency electromagnetic wave propagates in a complicated scattering environment, the contribution at the observer is usually composed of a number of field species arriving along different ray trajectories. In order to describe each contribution separately the parabolic extension along an isolated ray trajectory in an inhomogeneous background medium was performed. This leads to the parabolic wave equation along a deterministic ray trajectory in a randomly perturbed medium with the possibility of presenting the solution of the high-frequency field and the higher-order coherence functions in the functional path-integral form. It is shown that uncertainty considerations play an important role in relating the path-integral solutions to the approximate asymptotic solutions. The solutions for the high-frequency propagators derived in this work preserve the random information accumulated along the propagation path and therefore can be applied to the analysis of double-passage effects where the correlation between the forward-backward propagating fields has to be accounted for. This results in double-passage algorithms, which have been applied to analyze the resolution of two point scatterers. Under strong scattering conditions, the backscattering effects cannot be neglected and the ray trajectories cannot be treated separately. The final part is devoted to the generalized parabolic extension method applied to the scalar Helmholtz's equation, and possible approximations for obtaining numerically manageable solutions in the presence of random media.

Acoustics↗