Curve Fitting and Linearity: Data Processing in Raman Spectroscopy

Abstract

A study has been made of the use of polynomial curve fitting for removal of nonlinear background and high-spatial-frequency noise components from Raman spectra. Two variations on polynomial curve fitting through a least-squares calculation are used. One, involving fitting data x values to corresponding y values, was used to approximate background functions, which are subtracted from the original data. For smoothing, a reference matrix of six vectors that contains a unity d.c. level, a ramp made up of x values, a quadratic made up of x2 values, etc., is fitted to a section of data. The reference vectors are scaled by the fit values and added to give the smoothed estimate of a spectral peak. It is demonstrated, with factor analysis as a test procedure, that the background removal procedure does remove nonlinearities that were present in the original data. The smoothing procedure rejects high-spatial-frequency noise without introducing detectable nonlinearities.

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