Nonlinear optimization algorithm for multivariate optical element design

A new algorithm for the design of optical computing filters for chemical analysis, otherwise known as multivariate optical elements (MOEs), is described. The approach is based on the nonlinear optimization of the MOE layer thicknesses to minimize the standard error in sample prediction for the chemical species of interest using a modified version of the Gauss-Newton nonlinear optimization algorithm. The design algorithm can either be initialized with random layer thicknesses or with layer thicknesses derived from spectral matching of a multivariate principal component regression (PCR) vector for the constituent of interest. The algorithm has been successfully tested by using it to design various MOEs for the determination of Bismarck Brown dye in a binary mixture of Crystal Violet and Bismarck Brown.