### Abstract

Generating limited diffraction (or nondiffracting theoretically) beams involves deriving special solutions to a homogeneous wave equation. Previous results have been derived by the Fourier and Laplace transforms. In this paper, we use the wavelet transform to obtain a novel nondiffracting solution. It can be shown that this new solution is equivalent to the second derivative of Lu-Greenleaf's zero-th order X wave or the first derivative of Donnelly's Localized wave. The advantage of the wavelet beams is their localization property, that is, they have smaller sidelobes compared with the previous results. The magnitude decays as 1/r^{3} along the lateral (r) direction. Although the slowest decay is still 1/√r asymptotically, the sidelobes are reduced to about half those of the broadband X wave. We also show that this new nondiffracting beam can be realized as a limited diffraction beam with finite energy and finite aperture ultrasound transducers.

Original language | English (US) |
---|---|

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

Place of Publication | Piscataway, NJ, United States |

Publisher | Publ by IEEE |

Pages | 1087-1090 |

Number of pages | 4 |

Volume | 2 |

ISBN (Print) | 0780312783 |

State | Published - 1993 |

Event | Proceedings of the IEEE 1993 Ultrasonics Symposium - Baltimore, MD, USA Duration: Oct 31 1993 → Nov 3 1993 |

### Other

Other | Proceedings of the IEEE 1993 Ultrasonics Symposium |
---|---|

City | Baltimore, MD, USA |

Period | 10/31/93 → 11/3/93 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the IEEE Ultrasonics Symposium*(Vol. 2, pp. 1087-1090). Piscataway, NJ, United States: Publ by IEEE.

**Obtaining limited diffraction beams with the wavelet transform.** / Zou, Hehong; Lu, Jian yu; Greenleaf, James F.

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

*Proceedings of the IEEE Ultrasonics Symposium.*vol. 2, Publ by IEEE, Piscataway, NJ, United States, pp. 1087-1090, Proceedings of the IEEE 1993 Ultrasonics Symposium, Baltimore, MD, USA, 10/31/93.

}

TY - GEN

T1 - Obtaining limited diffraction beams with the wavelet transform

AU - Zou, Hehong

AU - Lu, Jian yu

AU - Greenleaf, James F

PY - 1993

Y1 - 1993

N2 - Generating limited diffraction (or nondiffracting theoretically) beams involves deriving special solutions to a homogeneous wave equation. Previous results have been derived by the Fourier and Laplace transforms. In this paper, we use the wavelet transform to obtain a novel nondiffracting solution. It can be shown that this new solution is equivalent to the second derivative of Lu-Greenleaf's zero-th order X wave or the first derivative of Donnelly's Localized wave. The advantage of the wavelet beams is their localization property, that is, they have smaller sidelobes compared with the previous results. The magnitude decays as 1/r3 along the lateral (r) direction. Although the slowest decay is still 1/√r asymptotically, the sidelobes are reduced to about half those of the broadband X wave. We also show that this new nondiffracting beam can be realized as a limited diffraction beam with finite energy and finite aperture ultrasound transducers.

AB - Generating limited diffraction (or nondiffracting theoretically) beams involves deriving special solutions to a homogeneous wave equation. Previous results have been derived by the Fourier and Laplace transforms. In this paper, we use the wavelet transform to obtain a novel nondiffracting solution. It can be shown that this new solution is equivalent to the second derivative of Lu-Greenleaf's zero-th order X wave or the first derivative of Donnelly's Localized wave. The advantage of the wavelet beams is their localization property, that is, they have smaller sidelobes compared with the previous results. The magnitude decays as 1/r3 along the lateral (r) direction. Although the slowest decay is still 1/√r asymptotically, the sidelobes are reduced to about half those of the broadband X wave. We also show that this new nondiffracting beam can be realized as a limited diffraction beam with finite energy and finite aperture ultrasound transducers.

UR - http://www.scopus.com/inward/record.url?scp=0027872250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027872250&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027872250

SN - 0780312783

VL - 2

SP - 1087

EP - 1090

BT - Proceedings of the IEEE Ultrasonics Symposium

PB - Publ by IEEE

CY - Piscataway, NJ, United States

ER -