Analysis and computations of measurement system effects in ultrasonic scattering experiments

Abstract

A model that characterizes the effects of beams and waveforms on the measurement of ultrasonic scattering is described and analyzed. The model includes arbitrary emitter beam patterns and detector apertures as angular spectra of plane waves. Arbitrary emitted pulses and detector time gates are incorporated through frequency spectra of temporal harmonics. A transformation of variables is employed to express the spectrum of the measured pressure as a product in wave space of a system function and the Fourier transform of the medium variations. The analysis shows the influence of beam patterns and a finite detector gate, relates the current model to a prior narrowband analysis, provides asymptotic expressions for beam pattern effects produced by radially symmetric Gaussian apertures, and treats the backscattering configuration for arbitrary apertures and correlated scattering. Numerical computations illustrate the effect of Gaussian, exponential, and uniform circularly symmetric spatial aperture functions on the measurement of the power spectrum of medium variations. The results may be used to design scattering experiments in which measurements yield scaled values of intrinsic parameters of scattering.