Measurements of differential scattering cross section using a ring transducer

A procedure for the measurement of intrinsic scattering object properties is presented and used to obtain illustrative results. The procedure is based on the measurement of the scattered acoustic field as a function of scattering angle and frequency. Measurements are normalized using analytically determined expressions for emitter and detector beams resulting from a combination of unfocused linear elements arranged in a circular configuration. The spatial effects of finite emitter pulse length and detector gate length are represented by a convolution formula valid for narrow-band transmitted signals and long receiver gates. The normalization includes correction for target absorption as well as measurement of the directly transmitted acoustic power in the free field and yields the average differential scattering cross section per unit volume. Under the Born approximation, this quantity is directly proportional to the spatial-frequency spectrum of the scattering medium inhomogeneities. Measured results are reported for two phantoms consisting of glass microspheres embedded in a weakly absorbing agar background medium. For the phantoms employed, scattering effects, rather than increased absorption, are shown to account for most of the difference in transmission loss between pure agar and agar with glass spheres. The measured differential scattering cross sections are compared with theoretical cross sections for distributions of glass spheres measured experimentally. The measured values show good relative agreement with theory for varying angle, frequency, and phantom properties. The results are interpreted in terms of wave space resolution and the potential for tissue characterization using similar fixed transducer configurations.