Analytic Diffraction Corrections to Ultrasonic Scattering Measurements

Abstract

Ultrasonic theories generally predict a scattering amplitude which relates a spherically spreading, far-field scattered wave to an incident plane wave. In ultrasonic immersion measurements, the frequency and angular dependences of the scattering amplitude are convolved with those of the transmitting and receiving trans- ducers and the propagation through the liquid-solid and solid- liquid interfaces. This paper presents a set of approximate correc- tions for these effects for the cases of angle beam inspection through planar, spherically curved or cylindrically curved surfaces. The primary parameters in the correction are the function D, which corrects for the diffraction effects occurring during a transducer calibration experiment, and the function C, which describes the on-axis pressure variation of the beam. Values of C and Dare available in the literature for the case of a piston transducer radiating into an infinite fluid medium. The major portion of this paper is concerned with the extension of those results to the afore- mentioned two media problems in which mode conversion, refraction, diffraction, and focussing all play interrelated roles. Results of preliminary experiments to test the corrections are also included.