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United States Department of Agriculture

Agricultural Research Service

Title: Monte Carlo Simulations of Light Propagation in Apples)

item Qin, Jianwei
item Lu, Renfu

Submitted to: ASABE Annual International Meeting
Publication Type: Proceedings
Publication Acceptance Date: 5/13/2007
Publication Date: 6/17/2007
Citation: Qin, J., Lu, R. 2007. Monte Carlo Simulations of Light Propagation in Apples. ASABE Annual International Meeting. Paper No. 073058.

Interpretive Summary: Light interaction with biological materials is a complex process involving both absorption and scattering. Absorption is related to the chemical properties of the material, whereas scattering is often influenced by structural or physical properties such as density, cell, and intra- and extra-cellular structures. Hence quantitative analysis of light absorption and scattering in the fruit can help us gain a better understanding of light interaction with the fruit tissue and quantify its physical and chemical properties that are indicative of fruit quality. In this research, the optical properties of ‘Golden Delicious’ apples were measured using a novel optical method recently developed in our lab. Monte Carlo simulation models incorporating the optical property data obtained from ‘Golden Delicious’ apples were developed to quantify photon migration and scattering in the fruit tissue over the visible and near-infrared (longer in wavelengths than the visible) region. Monte Carlo simulations are a statistical approach to solving complex mathematical problems that otherwise cannot be solved analytically. The simulation models provided quantitative information on light distribution and penetration depth in the fruit, as affected by its optical properties. Through simulations, we were able to determine the optimum sensing configuration for a given set of design parameters. This research provides a new means for quantifying light scattering and propagation in fruit, which would be otherwise expensive and difficult to measure experimentally. Researchers and instrumentation engineers can now use this simulation method, coupled with the novel optical property measurement technique developed in our lab, to study a wide range of food and agricultural products. This could lead to the development of more efficient and effective optical sensing techniques for nondestructive assessment of quality attributes of fruits and other agricultural products.

Technical Abstract: This paper reports on the investigation of light propagation in fresh apples in the visible and short-wave near-infrared region using Monte Carlo simulations. Optical properties of ‘Golden Delicious’ apples were determined over the spectral range of 500-1100 nm using a hyperspectral imaging method, and they were used in Monte Carlo (MC) models to simulate light propagation in fruit tissue. MC simulation models were validated by comparing with the diffusion theory model and experimental data. The patterns of diffuse reflectance, internal absorption, and penetration depth were determined using typical values of the absorption and reduced scattering coefficients for the apples. Up to 58.2% of the photons were absorbed under the maximum absorption condition, and 97.8% photons exited as diffuse reflectance for the zero absorption cases. The optimum sensing range for the apple samples under our imaging system setup was found to be 13 mm for the ‘Golden Delicious’ apples. Fruit tissue with a larger absorption coefficient value absorbed light energy rapidly in short depth and radial distances, and light in the tissue with small values for the reduced scattering coefficient tended to propagate forward to the deeper area of the sample. Light penetration depths in ‘Golden Delicious’ apples were in the range of 2.9 to 11.3 mm over the 500-1000 nm spectral range. Pigments and water in fruit tissue greatly influenced light penetration depth.

Last Modified: 8/24/2016
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