The departure of speckle magnitude from Rayleigh statistics was applied to examine insonated phantoms with both low and high concentrations of scatterers. A mathematical model, the K distribution of Jakeman, was used to characterize non-Rayleigh statistics. This model contains a parameter, alpha, which characterizes the clustering of the scattering sites in a medium. It is shown from phantom experiments that alpha is linearly proportional to the log-scaled scatterer concentration in a range from about 1 to 30 scatterers per sample volume.
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Weng et al. (1991) studied this question.