Characterization of measurement system effects in ultrasonic scattering experiments

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Abstract
A general model is developed to characterize the effect of an ultrasonic measurement system on the experimental determination of ultrasonic scattering as a function of angle and frequency. The model includes arbitrary emitter beams 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 mean-square value of the measured pressure spectrum is similarly expressed as a product of the squared magnitude of the system function and the power spectrum of the medium variations. The measured quantities are shown to become scaled values of intrinsic scattering characteristics when the system function weight is concentrated relative to the medium characteristics in wave space. The assumption of an indefinitely long detector gate is used to represent the system function as a product in which one factor is a beam function dependent on spatial frequency and the other factors are dependent on temporal frequency. Beam-function calculations as well as calculations of second moments and overall beam weight are made for identical Gaussian-shaped emitter and detector apertures to illustrate the blurring and weighting effects of measurement system beam patterns as a function of scattering angle. The moment calculations are shown to identify circumstances when the medium variation function can be factored out from under the integral and the measurement represented as a simple product of the medium properties and a measurement system weight. The results may be used to design scattering experiments in which degradations due to system effects are within acceptable limits.