Mathematical Transformation of Multidimensional Correlated Data into Uncorrelated Raman Spectra to Increase the Sensitivity of Identification with Silver Nanoparticles

The article discusses approaches to translating correlated statistical data into uncorrelated form. The results of the transformation of mathematical models with silver nanoparticles and without nanoparticles into uncorrelated form with simultaneous solution of a system of equations with uncorrelated matrices are presented. Solutions of a system of multi-dimensional equations for determining the probability densities p0 and p1 are obtained. These mathematical models are based on the Raman polarization spectra of polyester fibers in recognizing silver nanoparticles, taking into account the polarization of laser radiation in two directions: X-across and Y-along the fibers. A method for increasing the resolution of the identification of silver nanoparticles on polyester fibers is proposed. When solving the system using nonlinear quadratic and XY differential equations of probability densities of distribution ellipses, the resolution of identification of silver nanoparticles p0 and p1 in the range 10-2- 10-547 was obtained.