Multiple polynomial regression method for determination of biomedical optical properties from integrating sphere measurements

We present a new, to our knowledge, method for extracting optical properties from integrating sphere measurements on thin biological samples. The method is based on multivariate calibration techniques involving Monte Carlo simulations, multiple polynomial regression, and a Newton–Raphson algorithm for solving nonlinear equation systems. Prediction tests with simulated data showed that the mean relative prediction error of the absorption and the reduced scattering coefficients within typical biological ranges were less than 0.3%. Similar tests with data from integrating sphere measurements on 20 dye–polystyrene microsphere phantoms led to mean errors less than 1.7% between predicted and theoretically calculated values. Comparisons showed that our method was more robust and typically 5–10 times as fast and accurate as two other established methods, i.e., the inverse adding–doubling method and the Monte Carlo spline interpolation method.