Statistical uncertainty in estimates of an effective scatterer number density for ultrasound

In a previous paper [J. Acoust. Soc. Am. 95, 77-85 (1994)], a method for determining an effective scatterer number density in ultrasonography was presented. This is the actual number density multiplied by a frequency-dependent factor that depends on the differential scattering cross sections of all scatterers. This method involves evaluating the ratio of the fourth moment to the square of the second moment of echo signals scattered from the sample. The random processes involved in forming these echo signals give rise to an uncertainty in the estimated effective scatterer number density. This uncertainty is evaluated here using error propagation. The statistical uncertainty depends on the effective number of scatterers contributing to the segmented echo signal; it increases when the effective number of scatterers increases. Tests of the statistical uncertainty estimator were in good agreement with uncertainties computed from experimental data.