Obtaining limited diffraction beams with the wavelet transform

Hehong Zou, Jian yu Lu, James F. Greenleaf

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

5 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Ultrasonics Symposium
PublisherPubl by IEEE
Number of pages4
ISBN (Print)0780312783
StatePublished - 1993
EventProceedings of the IEEE 1993 Ultrasonics Symposium - Baltimore, MD, USA
Duration: Oct 31 1993Nov 3 1993

Publication series

NameProceedings of the IEEE Ultrasonics Symposium
ISSN (Print)1051-0117


OtherProceedings of the IEEE 1993 Ultrasonics Symposium
CityBaltimore, MD, USA

ASJC Scopus subject areas

  • Acoustics and Ultrasonics


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