Curve fitting and linearity: Data processing in Raman spectroscopy

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, mas 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 x(2) 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.