Design of angle-tolerant multivariate optical elements for chemical imaging.

Multivariate optical elements (MOEs) are multilayer optical interference coatings with arbitrary spectral profiles that are used in multivariate pattern recognition to perform the task of projecting magnitudes of special basis functions (regression vectors) out of optical spectra. Because MOEs depend on optical interference effects, their performance is sensitive to the angle of incidence of incident light. This angle dependence complicates their use in imaging applications. We report a method for the design of angle-insensitive MOEs based on modification of a previously described nonlinear optimization algorithm. This algorithm operates when the effects of deviant angles of incidence are simulated prior to optimization, which treats the angular deviation as an interferent in the measurement. To demonstrate the algorithm, a 13-layer imaging MOE (IMOE, with alternating layers of high-index Nb2O5 and low-index SiO2) for the determination of Bismarck Brown dye in mixtures of Bismarck Brown and Crystal Violet, was designed and its performance simulated. For angles of incidence that range from 42 degrees to 48 degrees, the IMOE has an average standard error of prediction (SEP) of 0.55 microM for Bismarck Brown. This compares with a SEP of 2.8 microM for a MOE designed by a fixed-angle algorithm.