Assessing the effect of foam layers on transport phenomena is of significant interest in many industries, so a method for predicting foam layer properties has been developed. A model of the propagation of radiation from an amplitude-modulated laser beam through a non-absorbing foam layer has been developed using diffusion theory. Measurements predicted by diffusion theory were compared to results generated using Monte Carlo methods for a variety of foam layer properties in both the time-domain and the frequency-domain. The properties that were varied include the layer thickness, the scattering coefficient, and the asymmetry parameter. Layer thicknesses between 8.5 mm and 18 cm were considered. Values of the scattering coefficient ranged from about 600 m-1 to 14000 m-1, while the asymmetry parameter varied between 0 and 1. A conjugate-gradient algorithm was used to minimize the difference between simulated Monte Carlo measurements and diffusion theory predicted measurements. A large set of simulated measurements, calculated at various source-detector separations and three discrete frequencies were used to predict the layer properties. Ten blind cases were considered and property predictions were made for each. The predicted properties were within approximately 10% of the actual values, and on average the errors were approximately 4%. Predictions of the reduced scattering coefficient were all within approximately 5% with the majority being within 3%. Predictions of L were all within approximately 10% with the majority being within 7%. Attempts to separate g from the reduced scattering coefficient were unsuccessful, and it was determined that implementation of different source models might make such attempts possible. It was shown that with a large number of measurements, properties could be accurately predicted. A method for reducing the number of measurements needed for accurate property estimation was developed. Starting with a single measurement location, property predictions were made. An approach for updating the optimal detector location, based on the current estimate of the properties, was developed and applied to three cases. Property predictions for the three cases were made to within 10% of the actual values. A maximum of three measurement locations were necessary to obtain such predictions, a significant reduction as compared to the previously illustrated method.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





spectroscopy, frequency-domain, time-domain, diffusion theory, inverse problems, conjugate-gradient, Monte Carlo, foam layers