Normalization of ultrasonic scattering measurements to obtain average differential scattering cross sections for tissues

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Abstract
An integral expression is derived for the normalization of ultrasonic scattering data to obtain an average differential scattering cross section per unit volume for tissue which is modeled as a random, fluidlike medium. The expression assumes narrowband signals and involves the incident beam, receiver beam pattern and time gates. The beams and gates combine to form a window which limits the scattering volume. The derivation of the expression requires that the dimensions of the window be large compared to the correlation length of the scattering medium. Numerical values of the normalizing integral are given for cylindrical and beamlimited scattering volumes as a function of incident frequency and scattering angle under the assumptions of Gaussian beams and rectangular time gates. A set of curves is presented to relate the percent difference between the result for backscatter from a cylindrical scattering volume and from a beamlimited scattering volume which does not include the truncation effect of the cylinder boundary. Although similar in form to normalizations used by others, the integral in this paper is obtained from a derivation which treats physical parameters rigorously and provides a precise statement of conditions which are sufficient to obtain system-independent scattering data.

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