Calibration of Imaging Systems by Means of Spherical Targets
The problem of calculating the impulsive signal scattered on a target of spherical symmetry, when directivity functions of both transmitting and receiving transducers are known, is mathematically expressed.
In cases where the rigid spherical target is not very small, computations of the received signal become difficult because we deal with quotients of ill-conditioned polynomials. But as these polynomials have integral coefficients and particular properties, a solution has been found on condition of a frequency limitation of the signal.
An experimental set up has been built in order to drop the ball. The echo on the falling ball is then recorded by means of a storage oscilloscope. Various ball diameters have been used and results are compared with the computerized curves. The discrepancy is within the relatively large experimental errors. They are mainly due to the non piston-like behaviour of transducers and to the assumption of a rigid target (Rayleigh surface waves on the ball are neglected).
KeywordsRayleigh Wave Inverse Fourier Transform Storage Oscilloscope Integral Coefficient Straight Vertical Line
Unable to display preview. Download preview PDF.
- 1.R.H. Hill and N.L. Adams, Reinterpretation of the reciprocity theorem for the calibration of acoustic emission transducers operating on a solid, Acoustica 1979, vol. 43, pp. 305–312.Google Scholar
- 2.W.P. Mason and R.N. Thurston, Physical Acoustics, vol. XII, Academic Press 1976.Google Scholar
- 3.G. Deprez and R. Hazebroock, Mesure d’une réponse impulsionnelle en acoustique. Application à la diffraction d’une onde sonore par une sphère, Acoustica 1980, vol. 45, pp. 96–102.Google Scholar
- 4.F.B. Stumpf and A.M. Junit, Effect of a spherical scatterer on the radiation reactance of a ransducer at an air-water surface, JASA 1980, vol. 67 (2), pp. 715–716.Google Scholar
- 5.P.L. Edwards and J. Jarzynski, Use of a microsphere probe for pressure field measurements in the megahertz frequency range, JASA 1980, vol. 68 (1), pp. 356–359.Google Scholar
- 6.M. Auphan, R.H. Coursant and C. Mequio, Paper to be published in the Philips Journal of Research.Google Scholar
- 7.P.M. Morse and K.U. Ingard, Theoretical Acoustics, Mc Graw Hill book Company, 1968.Google Scholar
- 9.R.H. Coursant, Les transducteurs ultrasonores, Acta Electronica 1979, vol. 22 (2), pp. 129–141.Google Scholar
- 11.E. Grosswald, Bessel polynomials, Springer-Verlag 1978.Google Scholar
- 12.R. Hickling, Analysis of echoes from a solid elastic sphere in water, JASA 1962, vol. 34, no 10, pp. 1582–1592.Google Scholar