Describing small-scale structure in random media using pulse-echo ultrasound

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Abstract
A method for estimating structural properties of random media is described. The size, number density, and scattering strength of particles are estimated from an analysis of the radio frequency (rf) echo signal power spectrum. Simple correlation functions and the accurate scattering theory of Faran [J. J. Faran, J. Acoust. Soc. Am. 23, 405–418 (1951)], which includes the effects of shear waves, were used separately to model backscatter from spherical particles and thereby describe the structures of the medium. These methods were tested using both glass sphere-in-agar and polystyrene sphere-in-agar scattering media. With the appropriate correlation function, it was possible to measure glass sphere diameters with an accuracy of 20%. It was not possible to accurately estimate the size of polystyrene spheres with the simple spherical and Gaussian correlation models examined because of a significant shear wave contribution. Using the Faran scattering theory for spheres, however, the accuracy for estimating diameters was improved to 10% for both glass and polystyrene scattering media. It was possible to estimate the product of the average scattering particle number density and the average scattering strength per particle, but with lower accuracy than the size estimates. The dependence of the measurement accuracy on the inclusion of shear waves, the wavelength of sound, and medium attenuation are considered, and the implications for describing the structure of biological soft tissues are discussed.