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 <i>x</i> values to corresponding <i>y</i> 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 <i>x</i> values, a quadratic made up of <i>x</i>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.

Sellmeier fits with linear regression; multiple data sets; dispersion formulas for helium

Edson R. Peck
Appl. Opt. 22(18) 2906-2913 (1983)

Method of Least Squares and Curve Fitting

H. S. Uhler
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Global approach for fitting 2D interferometric data

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Linear optics, Raman scattering, and spin noise spectroscopy

M. M. Glazov and V. S. Zapasskii
Opt. Express 23(9) 11713-11723 (2015)

Regularized algorithm for Raman lidar data processing

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Appl. Opt. 46(22) 4879-4889 (2007)