A method for determination of frequency-dependent effective scatterer number density.

Previous researchers have shown that for low scatterer concentrations, the scatterer number density in an ultrasound pulse-echo experiment can be obtained from ratios of the fourth to the second moment of the backscattered signal. In this paper a new method is presented for determining an effective scatterer number density, which is the actual number density multiplied by a frequency-dependent factor that depends on the differential scattering cross sections of all scatterers. The method of data reduction goes beyond the work of previous authors in that, in addition to accounting for the possibility that different sets of scatterers may dominate the echo signal at different frequencies, it also explicitly retains both the temporal nature of the data acquisition and the properties of the ultrasound field in the data reduction. Tests of the method in phantoms yielded good agreement between measured values of the effective scatterer number density and number densities calculated using first principles.