Cross-Sectional Measurements and Extrapolations of Ultrasonic Fields

Abstract

Ultrasonic fields produced by a disk transducer have been measured in two planes normal to the transducer axis and then extrapolated from one measurement plane to the other and also back to the face of the transducer. The measurements were performed with a small PVF hydrophone and a quadrature detector which yielded kthe complex values of the pressure at regularly spaced points in the scanned planes. Wave field extrapolation was carried out digitally using Fourier transformation methods which characterize the propagation of a field from one plane to another as a linear filtering operation. The filtering process was implemented as a product of the angular spectrum of the measured pressure field and a propagation matrix comprised of phase factors computer from parameters which included the wavelength of the measured field, the distance over which the field was to be extrapolated, and a maximum spatial frequency. The extrapolated field was then obtained by inverse Fourier transformation of the angular spectrum-phase matrix product. Comparisons of extrapolation results with measured data and with theoretical predictions show reasonable agreement and also demonstrate the sensitivity of the extrapolation process to the extent and shape of the spatial frequency window employed to determine the non-zero elements in the phase matrix. The results indicate fields can be extrapolated more accurately by sampling higher than the Nyquist rate and extending the size of the plane over which the measurements are made.

Supported in part by NSF Grant ECS8017683 and NATO Grant 09381.