Maximum likelihood factor analysis for resolution of noisy smartphone based diffuse reflectance data from CdS pigments

Abstract

This study aims to use multivariate chemometric methods such as principal component analysis (PCA), maximum likelihood common factor analysis (MLFA), and multivariate curve resolution alternating least squares (MCR-ALS) to analyze a designed data set and obtain an estimation of measurement error structure in the absence of replicates. For this purpose, we developed a smartphone-based diffuse reflectance spectrophotometer (smartDRS) with the advantage of being rapid, simple, and cost-effective in acquiring spectral information from the produced pigment samples based on a designed experiment. In our experimental design, the effects of different factors on the color of synthesized cadmium sulfide (CdS) pigment are investigated. DR spectral data from synthesized CdS samples were rapidly and successfully measured using the homemade device. The contribution of three forms (two crystalline and one amorphous) of CdS with three different spectra in each of the 16 synthesized pigment samples was illustrated and confirmed by using MLFA-MCR-ALS. Based on RGB values obtained from spectral information, the concentration profile of the brightest form of CdS was considered as a quantitative criterion of the whiteness of CdS samples and the response in the experimental design. The experimental design results showed pH, use of the furnace, and time for CdS drying as the main factors, in addition to a two-factor (Cd/S molar ratio × drying time) and a three-factor (pH × furnace × drying time) interactions are statistically significant on experimental design response. MLFA results also showed that independent noise in the measured diffuse reflectance data is heteroscedastic but not simply proportional to the signal intensities. This study shows the success of maximum likelihood-based multivariate analysis of diffuse reflectance spectral data from smartDRS for quantitatively investigating affecting factors on synthesized CdS color. Results from the application of PCA before MCR-ALS were considerably different from what was obtained from MLFA and MCR-ALS and were not in accordance with the previous reports.