A statistical approach to determining the number density of random scatterers from backscattered pulses

Abstract

This paper describes a method of using the statistical character of the waveform backscattered from random scatterers to estimate the scatterer number density. The moments of the probability density function of the backscattered intensity depend on the scatterer number density. Expressions exist for these moments in terms of the number of scatterers contributing to the echo signal. These expressions can give an estimate for the scatterer number density, provided the resolution cell size of the backscattering configuration is known, and provided the number of scatterers in the resolution cell is small. This latter constraint is equivalent to a requirement that the statistics of the return signal envelope deviate significantly from a Rayleigh distribution. The validity of these expressions is investigated by analyzing the acoustic waveform backscattered from a randomized volume distribution of polystyrene spheres suspended in water when insonified by a short acoustic pulse. Experimentally, the second-order moment of intensity is found to be given the most accurate predictions of number density. A specific application suggested for this work is acoustic fish-stock assessment. Other possible applications are ultrasonic tissue characterization and acoustic ocean bottom identification.