# Calculation of Transient Radiation Fields from Axial Symmetric Sources

## Abstract

Proper understanding of the results of acoustic imaging, tissue characterization, and tomography utilizing pulsed ultrasound requires inclusion of the diffraction effects of the pulsed wave. A method is presented for the efficient calculation of pulsed ultrasonic waves from an axially symmetric source mounted in a rigid baffle and excited with an arbitrary time excitation. The technique uses a spatial modal analysis based on a series expansion of the source velocity term in either of two sets of basis functions. The choice of basis functions is arbitrary. The expansion is equivalent to a decomposition of the excitation into a set of propagation modes. Each mode is then simply propagated by the technique with rapid convergence of the solution that requires evaluation of approximately thirty (or less) terms of a series, allowing rapid computer-based solutions of the field at an object plane or at a receiver plane. Several numerical solutions are given.

## Keywords

Spatial Frequency Observation Plane Lower Order Mode Naval Postgraduate School Source Velocity## Preview

Unable to display preview. Download preview PDF.

## References

- Erdelyi, A.; Magnus, W.; Oberhettinger, F.; and Triconi, F.G.;
**Tables of Integral Transforms, Vols. 1 and 2**, (McGraw-Hill, New York, 1954)Google Scholar - Greenspan, M., “Piston radiator: Some extensions of the theory”, J. Acous. Soc. Am.,
**65**(3), pp. 608–621, 1979CrossRefGoogle Scholar - Guyomar, D.; Fink, M.; and Coursant, R.; “Acoustical displacement reconstruction of axisymmetric transducers”. Presented at the 1983 IEEE Ultrasonics Symposium, Atlanta, 1983Google Scholar
- Guyomar, D., and Powers, J., “Boundary effects on transient radiation fields from vibrating surfaces”, J. Acous. Soc. Am.,
**77**(3), pp. 907–915, 1985CrossRefGoogle Scholar - Guyomar, D., and Powers, J., “A Fourier approach to diffraction of pulsed ultrasonic waves in lossless media”, submitted for publication, 1986Google Scholar
- Harris, G.R., “Review of transient field theory for a baffled planar piston”, J. Acous. Soc. Am.,
**70**(1), pp. 10–20, 1981aCrossRefGoogle Scholar - Harris, G.R., “Transient field of a baffled piston having an arbitrary vibration amplitude distribution”, J. Acous. Soc. Am.,
**70**(1), pp. 186–204, 1981bCrossRefGoogle Scholar - Meideros, A.F., and Stepanishen, P.R., “The forward and backward propagation of acoustic fields from axisymmetric ultrasonic radiators using the impulse response and Hankel transform techniques”, J. Acous. Soc. Am.,
**75**(6), pp. 1732–1740, 1984CrossRefGoogle Scholar - Oberheltinger, F., “On transient solutions of the baffled piston problem”, J. Natl. Bur. Standards,
**65B**, pp. 1–6, 1961Google Scholar - Stepanishen, P.R., “Transient radiation from pistons in an infinite planar baffle”, J. Aeons, Soc. Am.,
**49**(5), pp. 1629–4637, 1971CrossRefGoogle Scholar - Stepanishen, P.R., “Acoustic transients from planar axisymmetric vibrators using the impulse response approach”, J. Acous. Soc. Am.,
**70**(4), pp. 1176–1181, 1981CrossRefGoogle Scholar - Tupholme, G.E., “Generation of acoustic pulses by baffled plane pistons”, Mathematika,
**16**, pp. 209–226, 1969CrossRefGoogle Scholar - Weight, J., and Hayman, A., “Observation of the propagation of very short ultrasonic pulses and their reflection by small targets”, J. Acous. Soc. Am., 63(2), pp. 96–404, 1978CrossRefGoogle Scholar