### 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 language | English (US) |
---|---|

Title of host publication | Proceedings of the IEEE Ultrasonics Symposium |

Publisher | IEEE |

Pages | 1239-1244 |

Number of pages | 6 |

Volume | 2 |

State | Published - 1999 |

Event | 1999 IEEE Ultrasonics Symposium - Caesars Tahoe, NV, USA Duration: Oct 17 1999 → Oct 20 1999 |

### Other

Other | 1999 IEEE Ultrasonics Symposium |
---|---|

City | Caesars Tahoe, NV, USA |

Period | 10/17/99 → 10/20/99 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Ultrasonics Symposium.*vol. 2, IEEE, pp. 1239-1244, 1999 IEEE Ultrasonics Symposium, Caesars Tahoe, NV, USA, 10/17/99.

}

TY - GEN

T1 - Fast beam shape computation and wave propagation via the Radon transform

AU - Pitts, Todd A.

AU - Greenleaf, James F

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033296264&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033296264&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0033296264

VL - 2

SP - 1239

EP - 1244

BT - Proceedings of the IEEE Ultrasonics Symposium

PB - IEEE

ER -