Analysis and computations of measurement system effects in ultrasonic scattering experiments

A model that characterizes the effects of beams and waveforms on the measurement of ultrasonic scattering is analyzed in detail. The analysis obtains a wideband expression for the system function in terms of an integration over spatial- and temporal-frequency variables. The temporal-frequency integration is reduced to a convolution in the direction of the scattering vector when the temporal frequencies are concentrated in a narrow band around a central frequency. The spatial-frequency integration is simplified to a straight line path when the spatial frequencies in the angular spectra of the emitter are concentrated around a point on the axis of the emitter and the spatial frequencies of the detector sensitivity pattern are similarly concentrated around a point on the axis of the detector. Expressions that result from the temporal and spatial approximations are evaluated analytically for circularly symmetric Gaussian spatial apertures and Gaussian temporal waveforms. In addition, numerical results are obtained to compare the effects of circularly symmetric Gaussian, exponential, and uniform spatial aperture functions on the weight that beam patterns have on measurements of scattering. The results may be used to design experiments from which intrinsic parameters of scattering media can be obtained by an appropriate normalization to remove measurement system effects from the data.