Measurement of dependence of backscatter coefficient from cylinders on frequency and diameter using focused transducers--with applications in trabecular bone.

A theory for the elastic scattering response from a cylinder insonified by a plane wave was previously derived by Faran. In the present paper, the empirical relationship between Faran's theory and measurements of backscatter coefficient from cylindrical targets using focused transducers is investigated. Experimental measurements of dependence of backscatter coefficient on frequency and diameter for nylon wires are reported. It is found that, under certain conditions (including weak, incoherent scattering), backscatter coefficient measurements from collections of cylindrical scatterers may be meaningfully compared with Faran's model predictions. At low frequencies, the theory and experimental measurements exhibit similar dependences on frequency and diameter, provided that the scatterers are not too densely packed. At higher frequencies, the fine structure of Faran's predictions becomes difficult to reproduce experimentally with a focused transducer. Implications regarding applications to characterization of trabecular bone are discussed.