Submitted to: Inverse Problems in Science and Engineering
Publication Type: Peer reviewed journal
Publication Acceptance Date: 5/8/2010
Publication Date: 8/1/2010
Citation: Cen, H., Lu, R., Dolan, K. 2010. Optimization of the inverse algorithm for estimating the optical properties of biological materials using spatially-resolved diffuse reflectance technique. Inverse Problems in Science and Engineering. 18(6):853-872. Interpretive Summary: Optical characterization of absorption and scattering properties can provide an effective means for nondestructive quality evaluation of horticultural and food products. It, however, requires proper implementation of mathematical model and algorithm, instrumentation and experiment to attain acceptable measurement accuracy. This research was aimed at optimizing the mathematical algorithm for estimating the absorption and scattering parameters of biological materials, specifically horticultural and food products, using a new hyperspectral imaging-based technique developed by our lab. Computer simulations were performed on modeling light transfer in samples of different optical properties. Data transformation methods, including logarithm and integral, and relative weighting method were evaluated for determining the optimal procedure of estimating the optical parameters. Statistical analysis was carried out to assess the robustness of these methods. The research shows that the logarithm transformation and relative weighting methods give more accurate and reliable estimation of optical absorption and scattering parameters. Proper selection of the scattering distance range coupled with an adequate signal to noise ratio is also important for accurate estimation of the optical parameters. This research provides a guide in optimizing the mathematical algorithm for estimating the optical parameters, which is critical for application of the new optical property measurement technique for horticultural and food products.
Technical Abstract: Determination of the optical properties from intact biological materials based on diffusion approximation theory is a complicated inverse problem, and it requires proper implementation of inverse algorithm, instrumentation, and experiment. This work was aimed at optimizing the procedure of estimating the absorption and reduced scattering coefficients of turbid homogeneous media from spatially-resolved diffuse reflectance data. A diffusion model and the inverse algorithm were first validated by Monte Carlo simulations. Sensitivity analysis was performed to gain an insight of the relationship between the estimated parameters and the dependent variables in the inverse algorithm for improving the parameters estimation procedure. Three data transformation and relative weighting methods were compared in the nonlinear least squares regression. It is found that the logarithm and integral data transformation and relative weighting methods greatly improve the parameters estimation accuracy with the relative errors of 10.4%, 10.7% and 11.4% for absorption, and 6.6%, 7.0% and 7.1% for scattering, respectively. Further statistical analysis shows that the logarithm transformation and relative weighting methods give more reliable estimations of the optical parameters. To accurately estimate the optical parameters, it is important to study and quantify the characteristics and properties of the mathematical model and its inverse algorithm.