Finite element modeling of light propagation in turbid media under illumination of a continuous-wave beam

Authors: WANG, AICHEN - Zhejiang University; Lu, Renfu; XIE, LIJUAN - Zhejiang University

Submitted to: Applied Optics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 11/24/2015
Publication Date: 12/22/2015
Citation: Wang, A., Lu, R., Xie, L. 2015. Finite element modeling of light propagation in turbid media under illumination of a continuous-wave beam. Applied Optics. 55(1):95-103.

Interpretive Summary: Knowledge of light propagation in biological tissues like fruit can help us develop effective methods for measuring optical absorption and scattering properties, and better assessing quality and composition, of food products. Spatially-resolved spectroscopy is an emerging technique for measuring optical properties of fruits and other food products. However, the technique is prone to measurement error because it imposes strict requirements on the instrumental configuration (e.g., light beam and signal acquisition) and samples and relies on complicated mathematical algorithms. In this research, finite element method (FEM), a powerful numerical method, was used to simulate light propagation in turbid media like fruit, when they were illuminated in normal direction by a light beam of infinitely small or finite size. Three different boundary conditions, which are crucial in the finite element modeling, were evaluated against analytical solutions and Monte Carlo simulation, a stochastic statistical method that is considered the gold standard in modeling light propagation in biological tissues. Results showed that except the zero boundary condition, which did not yield accurate prediction of light transfer in the turbid tissue, the partial current and extrapolated boundary conditions produced similar results that were comparable to analytical solutions and also well matched Monte Carlo simulation results. Light beam size directly affected the diffuse reflectance profile at the boundary of the tissue. A smaller light beam with the diameter equal to or less than 1 mm is better for measuring the optical properties of biological tissues. Finite element method, coupled with an appropriate boundary condition, can accurately model light propagation in biological tissues like fruit. The method is fast and flexible in dealing with complex geometries and different light beam profiles, and it is useful for optimizing the design of spatially-resolved technique.

Technical Abstract: Spatially-resolved spectroscopy provides a means for measuring the optical properties of biological tissues, based on analytical solutions to diffusion approximation for semi-infinite media under the normal illumination of infinitely small size light beam. The method is, however, prone to error in measurement because the actual boundary condition and light beam often deviate from that used in deriving the analytical solutions. It is, therefore, important to quantify the effect of different boundary conditions and light beams on spatially-resolved diffuse reflectance in order to improve measurement accuracy by the technique. In this research, finite element method (FEM) was used to model light propagation in fruit, subjected to the normal illumination by a continuous-wave beam of infinitely small or finite size. Three types of boundary conditions [i.e., partial current (PCBC), extrapolated (EBC) and zero (ZBC)] were evaluated and compared against Monte Carlo simulations, which provided accurate results in fluence rate and diffuse reflectance. The effect of beam size was also investigated. Overall results showed that FEM provided as accurate results as analytical method when an appropriate boundary condition was applied. ZBC did not give satisfactory results in most cases. FEM-PCBC yielded better fluence rate at the boundary than did FEM-EBC, while they were almost identical in predicting diffuse reflectance. Results further showed that FEM coupled with EBC simulated spatially-resolved diffuse reflectance under the illumination of finite size beam effectively. Large size beam introduced more error, especially within the region of illumination. Research also confirmed an earlier finding that a light beam of less than 1 mm diameter should be used for estimation of optical parameters. FEM is effective for modeling light propagation in biological tissues and can be used for improving the optical property measurement by spatially-resolved technique.