Wigner distribution of a transducer beam pattern within a multiple scattering formalism for heterogeneous solids

Goutam Ghoshal, Joseph A. Turner, Richard L. Weaver

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

Diffuse ultrasonic backscatter measurements have been especially useful for extracting microstructural information and for detecting flaws in materials. Accurate interpretation of experimental data requires robust scattering models. Quantitative ultrasonic scattering models include components of transducer beam patterns as well as microstructural scattering information. Here, the Wigner distribution is used in conjunction with the stochastic wave equation to model this scattering problem. The Wigner distribution represents a distribution in space and time of spectral energy density as a function of wave vector and frequency. The scattered response is derived within the context of the Wigner distribution of the beam pattern of a Gaussian transducer. The source and receiver distributions are included in the analysis in a rigorous fashion. The resulting scattered response is then simplified in the single-scattering limit typical of many diffuse backscatter experiments. Such experiments, usually done using a modified pulse-echo technique, utilize the variance of the signals in space as the primary measure of microstructure. The derivation presented forms a rigorous foundation for the multiple scattering process associated with ultrasonic experiments in heterogeneous media. These results are anticipated to be relevant to ultrasonic nondestructive evaluation of polycrystalline and other heterogeneous solids.

Original languageEnglish (US)
Pages (from-to)2009-2021
Number of pages13
JournalJournal of the Acoustical Society of America
Volume122
Issue number4
DOIs
StatePublished - Oct 3 2007

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transducers
formalism
ultrasonics
scattering
wave equations
Eugene Wigner
Formalism
echoes
derivation
flux density
receivers
microstructure
evaluation
defects
Experiment
pulses
Waves

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics

Cite this

Wigner distribution of a transducer beam pattern within a multiple scattering formalism for heterogeneous solids. / Ghoshal, Goutam; Turner, Joseph A.; Weaver, Richard L.

In: Journal of the Acoustical Society of America, Vol. 122, No. 4, 03.10.2007, p. 2009-2021.

Research output: Contribution to journalArticle

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