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https://hdl.handle.net/2142/20186
Description
Title
Radiative transfer of ultrasound
Author(s)
Turner, Joseph Alan
Issue Date
1994
Doctoral Committee Chair(s)
Weaver, Richard L.
Department of Study
Mechanical Science and Engineering
Discipline
Mechanical Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Engineering, Materials Science
Physics, Acoustics
Language
eng
Abstract
Radiative transfer theory is used to model the multiple scattering of diffuse ultrasonic waves in two types of random media. The first type is an isotropic, homogeneous medium containing randomly oriented, randomly located scatterers. The scatterers are assumed to be uncorrelated. This assumption allows an equation of transfer to be written which governs the multiply scattered intensities. This ultrasonic radiative transfer equation (URTE) contains single scattering and propagation parameters that are calculated using the elastic wave equation. Polarization effects are included through the introduction of an elastodynamic Stokes vector which contains a longitudinal Stokes parameter and four shear Stokes parameters similar to the four Stokes parameters used in optical radiative transfer theory. The theory is applied to a statistically homogeneous isotropic half space containing randomly distributed spherical voids illuminated by a harmonic plane wave.
This approach is then extended to continuous polycrystalline media. In this case, because a representative scatterer is not readily identified, the URTE is derived directly from the elastic wave equation and first principles. Appropriate ensemble averaging of the elastic wave equation leads to Dyson and Bethe-Salpeter equations which govern the mean Green's function and the covariance of the Green's function, respectively. These equations are expanded for weak heterogeneity and the URTE obtained. The result is valid for attenuations that are small compared with a wave number. Along with steady-state solutions, results are presented for the time-dependent intensity backscattered from a polycrystalline medium submerged in a water bath and excited with a short burst of ultrasonic energy. It is shown that the radiative transfer solutions approach the appropriate single scattering and diffusion limits one would expect, providing confidence in the proposed model. It is anticipated that this work may be applicable to microstructural characterization through the study of the time, space, ultrasonic frequency, and angular dependence of diffusely scattered ultrasound in elastic media.
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