Improved algorithm for estimating optical properties of food and biological materials using spatially-resolved diffuse reflectance

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

Submitted to: Optics Express
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 5/9/2017
Publication Date: 5/11/2017
Citation: Wang, A., Lu, R., Xie, L. 2017. Improved algorithm for estimating optical properties of food and biological materials using spatially-resolved diffuse reflectance. Optics Express. 212:1-11.

Interpretive Summary: Accurate measurement of optical absorption and scattering properties can provide an effective means for determining the quality and composition of food and agricultural products. A hyperspectral imaging-based spatially-resolved technique has been developed by the USDA/ARS laboratory at East Lansing, Michigan. The technique enables fast measurements of the optical absorption and scattering properties over the spectral region of 500-1,000 nm. However, the technique is still prone to error caused by experimental measurements and the estimation algorithm for the optical parameters. This research was aimed at improving the mathematical algorithm for more accurate estimation of the optical parameters from the reflectance data measured using the hyperspectral imaging-based spatially-resolved technique. Forty modeling samples with a large range of optical absorption and scattering values were created to study the effect of data smoothing and normalization methods and the optimal spatial region of reflectance profiles on the estimation of optical parameters. In view of the shortcomings of conventional one-step estimation method, an improved step-by-step method was proposed for parameter estimation. Results showed that the mean scaling normalization method performed the best among the three normalization methods investigated, with the optimal data points of 10, 5 and 3 for the spatial resolutions of 0.05, 0.1 and 0.2 mm, respectively. With the optimal spatial regions, the proposed step-by-step method improved parameter estimation accuracy by 33% to 62% for the absorption and scattering parameters, compared with convention one-step method. Moreover, a modified one-step method was also proposed for estimating the optical parameters, which would reduce estimation errors by 15%-58%, compared with conventional one-step method. Implement of the improved algorithm is expected to result in great improvements for the estimation of optical properties of food and biological materials.

Technical Abstract: In this research, the inverse algorithm for estimating optical properties of food and biological materials from spatially-resolved diffuse reflectance was optimized in terms of data smoothing, normalization and spatial region of reflectance profile for curve fitting. Monte Carlo simulation was used to generate spatially-resolved reflectance profiles for 40 modeling samples covering a wide range of absorption and reduced scattering coefficients, which were then fitted using a diffusion model coupled with a trust-region-reflective nonlinear least-squares algorithm. Two normalization methods, i.e., mean scaling and smoothing, were proposed for normalizing the reflectance data. The optimal spatial regions of reflectance profiles in terms of start and end data points were determined for estimation of the optical parameters. Moreover, an improved step-by-step method was proposed based on conventional 1-step (C-1-step) method. In addition, the C-1-step method was also modified with the use of the optimized end point of 16 mean free paths (mfp’s) (designated as M-1-step method). Results showed that data smoothing did not improve the curve fitting results. Mean scaling normalization performed the best, compared with regular and smoothing normalization methods. The optimal numbers of data points for mean scaling normalization were 10, 5 and 3 for the spatial resolutions of 0.05 mm, 0.1 mm and 0.2 mm, respectively. Based on the relative error contour maps, it was found that the optimal start point decreased from 3 mfp’s to 1.6 mfp's with the increase of the ratio of absorption coefficient to reduced scattering coefficient value from 10 to 60, while the recommended end point was kept at 16 mfp’. Absolute relative errors for the best estimates of the absorption and reduced scattering coefficients using C-1-step and step-by-step methods were 8.7%, 5.6% and 3.5%, 2.3%, respectively, for a spatial resolution of 0.1 mm. The M-1-step method with the spatial resolution of 0.1 mm reduced the estimation errors by 56% and 34%, compared with the C-1-step method. Based on the results of M-1-step method, the step-by-step method could also improve estimation accuracy, with the best improvements for the absorption and reduced scattering coefficients by 18.4% and 51.4% for 0.1 mm spatial resolution.