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Scattering And Absorption of Light in Planetary Regoliths

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Effective scatterer diameter estimates for broad scatterer size distributions.

Eric P Nordberg¹, Timothy J Hall²

¹Department of Medical Physics, University of Wisconsin, Madison, WI, USA.

Ultrasonic Imaging

|May 17, 2014

Summary

A single effective scatterer model inaccurately represents broad acoustic scatterer size distributions. An exponential scattering model better approximates scattering correlation functions for diverse scatterer sizes than a Gaussian model.

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Area of Science:

Acoustic physics
Biomedical imaging
Ultrasound scattering

Background:

Acoustic form factors model frequency-dependent scattering in tissues and phantoms.
Single effective scatterer models often fail to accurately represent broad distributions of scatterer sizes.

Purpose of the Study:

To evaluate the accuracy of single-diameter acoustic form factor models for broad scatterer size distributions.
To compare the performance of Gaussian and exponential form factor models in representing complex scattering scenarios.

Main Methods:

Simulated composite form factors from distributions of scatterer sizes using Gaussian and Faran theories.
Generated scatterer distributions assuming either Gaussian number density or volume fraction.
Fit simulated composite form factors to single-diameter Gaussian and exponential models.

Keywords:

backscatter effective scatterer diameter microstructure quantitative ultrasound tissue characterization

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Calculated mean-squared error (MSE) to assess model fit.

Main Results:

An exponential form factor model showed a smaller MSE than a Gaussian model for scatterer distributions with large standard deviations (>30% of centroid).
Exponential models demonstrated superior ability to differentiate Faran scattering model-based distributions with varying center diameters compared to Gaussian models.
The choice of distribution assumption (number density vs. volume fraction) impacted model performance.

Conclusions:

A single effective scatterer is insufficient for modeling broad scatterer size distributions.
An exponential scattering model offers a more accurate approximation for the scattering correlation function of diverse, spherically symmetric scatterers than a Gaussian model.
The exponential model is recommended when limited information is available about the scattering medium's properties.