Data requirements for the mapping of ultrasonic fields with conventional light diffraction

Abstract

A procedure has been proposed by Cook [J. Acoust. Soc. Am. 53, 330(A)(1972)] through which a cross-sectional mapping of a progressive sound beam could be obtained by conventional light diffraction. This technique requires that a series of optical diffraction measurements be taken using a parallel beam of light passing through and perpendicular to the sound beam. These measurements are taken laterally across the field, for a large number of rotations about the sound field's major axis. Since the number of measurements could become excessive, an investigation of the data requirements of this technique has been performed. Computer-generated data were calculated of the integrated optical effect (both magnitude and phase) produced by the pressure field of a circular plane piston in an infinite rigid baffle. From these data a cross-sectional map was obtained using an effective two-dimensional Fourier transform, as well as the two-dimensional fast-Fourier-transform algorithm. The cross-sectional mapping was evaluated at different axial positions, using one set of data generated at a single axial distance. Data requirements were obtained by varying the data set and comparing the results to those obtained from the diffraction integral. The data requirements were found to be not excessive.