Correction Multiplicative Effects in Raman Spectra through Vector Angle Transformation
YAO Zhi-xiang1，3, SUN Zeng-qiang1, 3, SU Hui1, 3, YUAN Hong-fu2
1. Guangxi Key Laboratory of Sugar Resources Green Processing，Guangxi University of Science and Technology，Liuzhou 545006, China 2. College of Materials Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China 3. College of Biological and Chemical Engineering, Guangxi University of Science and Technology, Liuzhou 545006, China
Abstract：The linear relationship between the Raman spectral intensity and the analyte amount is frequently disrupted for a variety of complex reasons, which include these variations in laser source, focusing effect, sample scattering and refracting, so that causes poor quantitative results. As a whole, these disturbing effects can be divided to be additive and multiplicative, and the multiplicative effects are generally more difficult to be eliminated. A spectrum is a series data, also can be treated as a vector. In principle, unstable motions in spectrum intensity/amplitude corresponding to the module shifts for a vector, doesn’t impact the vector direction which is the essence of the vector, so it is reasonable to rewrite the data form on module to on space angle for the same measurement. This thesis employed a data transformation to eliminate the multiplicative effects within spectra, i. e., the spectrum signal on its amplitude has been transformed to be on the vector angles. The first step of the transformation is the selection of a stand vector which is near to the analyte and almost orthogonal to the background within the sample space; and the next step is to define a moving window, then to find out the angle between the sample vector (i. e. the transformed spectrum) and the stand vector within the window; while the window is moved along the spectrum data series, the transformation for vector angle (VA) series has been finished. The thesis has proved that an approximate linear quantitative relationship has been remained in the VA series. Multivariate calibration need full rank matrix which is combined by spectrum from variety samples, and variety VA series also can combine a full rank VA matrix, so the approximate linear VA matrix still perfectly meeting the demand for multivariate calibration. A mixed system consisted by methanol-ethanol-isopropanol has been employed to verify the eliminations to the multiplicative effects. These measuring values of the system are obtained at different Raman integral times and have remarkable multiplicative effects. In predicting results, the correlation coefficient (r) and the root mean squared error of prediction (RMSEP) from class PLS respectively are 0.911 9 and 0.110 2, and 0.906 0 and 0.100 8 are for the preprocessing by multiplicative scatter correction (MSC). In contrast, r and RMSEP under the VAPLS, presented by this thesis, respectively are 0.998 7 and 0.015 2 and are significantly better than others. The VAPLS has eliminated the multiplicative effects of Raman spectra and improved the accuracy of Raman quantitative analysis and it owes to the preprocessing of the vector angle transformation.
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