Multivariate Optical Elements Research Articles

Taxonomic Classification of Phytoplankton with Multivariate Optical Computing, Part I: Design and Theoretical Performance of Multivariate Optical Elements

Phytoplankton are single-celled, photosynthetic algae and cyanobacteria found in all aquatic environments. Differential pigmentation between phytoplankton taxa allows use of fluorescence excitation spectroscopy for discrimination and classification. For this work, we applied multivariate optical computing (MOC) to emulate linear discriminant vectors of phytoplankton fluorescence excitation spectra by using a simple filter-fluorometer arrangement. We grew nutrient-replete cultures of three differently pigmented species: the coccolithophore Emiliania huxleyi, the diatom Thalassiosira pseudonana, and the cyanobacterium Synechococcus sp. Linear discriminant analysis (LDA) was used to determine a suitable set of linear discriminant functions for classification of these species over an optimal wavelength range. Multivariate optical elements (MOEs) were then designed to predict the linear discriminant scores for the same calibration spectra. The theoretical performance specifications of these MOEs are described.

Low-Cost Spectroscopy with a Variable Multivariate Optical Element

Here, successful realization of a variable multivariate optical element (VMOE) based on a transmissive liquid crystal (LC) panel is reported. In contrast to conventional multivariate optical elements (MOEs), a single VMOE is a dynamic system, allowing measurement of numerous analytes in different mixtures. Furthermore, VMOE has superior spectral resolution in comparison to a conventional MOE. It is demonstrated here that the system implemented in a Raman spectrometer predicts the concentration of each individual component in toluene-acetonitrile-cyclohexane mixtures with a prediction error of <6% (mass percentage). With a dedicated optical design of the setup, a prediction error smaller than 2% is expected to be feasible for the current chemical system.

Spectral resolution in multivariate optical computing

An examination of spectral resolution effects on multivariate optical computing (MOC) and the design of multivariate optical elements (MOEs) is presented. A solution of napthalene and pyrene in CCl 4 is used as a test mixture, with spectra recorded in the nominal 2–2.5 μm spectral region at resolutions varying from 1 to 128 cm −1. Spectra were treated in absorption mode and in transmission mode at sample pathlengths of 1, 0.5, and 0.2 cm. Principal components regression is used to provide comparison to MOE models. Conventional model prediction errors using all methods are presented as well as results of applying low-resolution models to high-resolution validation sets. This latter calculation is aimed at understanding the limits of calibration transfer when a model is based on spectra acquired with marginal spectral resolution. A theory is developed describing calibration transfer in the case of linear spectroscopy, which is shown to be consistent with the results observed in absorption mode and to represent the case of the short-pathlength limit in transmission mode. A definition of the necessary spectral resolution as a function of apodization function is given for linear spectroscopy, and a brief discussion of how non-linearity affects the results is provided.

On-line reoptimization of filter designs for multivariate optical elements.

An automated method for producing multivariate optical element (MOE) interference filters that are robust to errors in the reactive magnetron sputtering process is described. Reactive magnetron sputtering produces films of excellent thickness and uniformity. However, small changes in the thickness of individual layers can have severe adverse effects on the predictive ability of the MOE. Adaptive reoptimization of the filter design during the deposition process can maintain the predictive ability of the final filter by changing the thickness of the undeposited layers to compensate for the errors in deposition. The merit function used, the standard error of calibration, is fundamentally different from the standard spectrum matching. This new merit function allows large changes in the transmission spectrum of the filter to maintain performance.

Novel Imaging Systems: Multivariate Optical Computing in the UV-VIS

Imaging Multivariate Optical Computing (MOC) is a powerful analytical tool that combines digital imaging and predictive spectroscopy without the use of a spectrometer. Traditional techniques for multivariate analysis are both time consuming and costly involving expensive multichannel instruments, difficult computations on large data sets and confinement to the laboratory. By encoding an angle-tolerant spectral pattern specific to a target analyte onto an interference filter, a snapshot of the chemical distribution and concentration can be obtained quickly and inexpensively.This paper summarizes the advances in chemical imaging utilizing angle-tolerant Imaging Multivariate Optical Elements (IMOE) from the UV to visible regions of the spectrum using uncollimated sources. Two applications are demonstrated using both transmission and diffuse reflectance data. These optical elements are fabricated via reactive magnetron sputtering of alternating layers of high and low refractive index materials, (Nb2O5 and SiO2, respectively). A single CCD camera in a swivel design rotating about the IMOE filter axis is employed for both transmittance and reflectance imaging. Our current UV diffuse reflectance technique miniaturizes the chemical imaging prototype with a catadioptric image-splitting prism block and a single monochrome camera controlled by a handheld computer.

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.

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.