Fast beam shape computation and wave propagation via the Radon transform

Todd A. Pitts, James F Greenleaf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

An M-dimensional (M ≥ 2) linear shift-invariant operator equation may be reduced to a set of decoupled (M - 1)-dimensional equations via the Radon transform. This decoupling allows the solution of each reduced equation separately on different processors in parallel. The solution to the full M-dimensional equation is then recovered via an inverse Radon transform. This solution method is particularly well suited to computation of beam shape and wave propagation in a homogeneous medium. For beam shape computation, Huygens' integration over a two-dimensional aperture is reduced to a set of one-dimensional integrations (the number of one-dimensional integrations is determined via Shannon sampling theory from the highest angular harmonic present in the aperture distribution). The method is applied to computation of a wide bandwidth pulse distribution from a semi-circular aperture with a center frequency of 2.25 MHz. The results are compared with the full two-dimensional surface integration. Discussion of the increase in computational speed and sampling considerations affecting the accuracy of the distributed one-dimensional computations are presented.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Ultrasonics Symposium
PublisherIEEE
Pages1239-1244
Number of pages6
Volume2
StatePublished - 1999
Event1999 IEEE Ultrasonics Symposium - Caesars Tahoe, NV, USA
Duration: Oct 17 1999Oct 20 1999

Other

Other1999 IEEE Ultrasonics Symposium
CityCaesars Tahoe, NV, USA
Period10/17/9910/20/99

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Radon
Wave propagation
Sampling
Bandwidth

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Pitts, T. A., & Greenleaf, J. F. (1999). Fast beam shape computation and wave propagation via the Radon transform. In Proceedings of the IEEE Ultrasonics Symposium (Vol. 2, pp. 1239-1244). IEEE.

Fast beam shape computation and wave propagation via the Radon transform. / Pitts, Todd A.; Greenleaf, James F.

Proceedings of the IEEE Ultrasonics Symposium. Vol. 2 IEEE, 1999. p. 1239-1244.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pitts, TA & Greenleaf, JF 1999, Fast beam shape computation and wave propagation via the Radon transform. in Proceedings of the IEEE Ultrasonics Symposium. vol. 2, IEEE, pp. 1239-1244, 1999 IEEE Ultrasonics Symposium, Caesars Tahoe, NV, USA, 10/17/99.
Pitts TA, Greenleaf JF. Fast beam shape computation and wave propagation via the Radon transform. In Proceedings of the IEEE Ultrasonics Symposium. Vol. 2. IEEE. 1999. p. 1239-1244
Pitts, Todd A. ; Greenleaf, James F. / Fast beam shape computation and wave propagation via the Radon transform. Proceedings of the IEEE Ultrasonics Symposium. Vol. 2 IEEE, 1999. pp. 1239-1244
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