Fast beam shape computation and wave propagation via the Radon transform

Todd A. Pitts, James F. Greenleaf

Research output: Contribution to journalConference articlepeer-review


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)
Pages (from-to)1239-1244
Number of pages6
JournalProceedings of the IEEE Ultrasonics Symposium
StatePublished - Dec 1 1999
Event1999 IEEE Ultrasonics Symposium - Caesars Tahoe, NV, USA
Duration: Oct 17 1999Oct 20 1999

ASJC Scopus subject areas

  • Acoustics and Ultrasonics


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