Ultrasonic Beams with Bessel and Gaussian Profiles

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Hsu, D. K.
Hasselbusch, M.
Wormley, S.
Hughes, M.
Thompson, D.
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Margetan, Frank
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Review of Progress in Quantitative Nondestructive Evaluation
Center for Nondestructive Evaluation

Begun in 1973, the Review of Progress in Quantitative Nondestructive Evaluation (QNDE) is the premier international NDE meeting designed to provide an interface between research and early engineering through the presentation of current ideas and results focused on facilitating a rapid transfer to engineering development.

This site provides free, public access to papers presented at the annual QNDE conference between 1983 and 1999, and abstracts for papers presented at the conference since 2001.


A novel technique has been developed for generating ultrasonic beams with spatial profiles of amplitude governed by a truncated Bessel function or Gaussian function [1,2]. Bessel beams have very unique properties; in optics Bessel beams have been shown to be diffractionless (J. Durnin et al, 1987 [3,4]). In a related work, R. W. Ziolkowski et al [5] reported experimental measurements of “acoustic directed energy pulse trains” generated by synthetic line array of ultrasonic transmitters in water. However, a Bessel function ultrasonic transducer has never been reported before. Gaussian beams also have desirable properties; they are very easy to model analytically, and a circular Gaussian function ultrasonic transducer is free of near-field nulls and far-field sidelobes associated with conventional “piston source” transducers [6]. At least three designs of Gaussian transducers have been reported in the literature in the past 30 years [7–9]. We report a method in which piezoelectric ceramic elements are poled with nonuniform electric fields shaped like Bessel or Gaussian functions such that the resulting polarization (and hence the ultrasonic amplitude) follows that of the applied poling field. Like conventional piston source transducers, such Bessel or Gaussian transducers also possess the simple “parallel plate capacitor” configuration and can be packaged likewise. Beam profiles and propagation behavior of these Bessel and Gaussian transducers have been measured experimentally in an immersion tank and the results compared well with model predictions

Mon Jan 01 00:00:00 UTC 1990