Metrohm Vision – Theory - Manual (Page 15)

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The polynomial function models the effects in a cumulative fashion as its order increases from 0 th to
1 st and 2 nd degrees:
Order of the
Polynomial Function Baseline
Effect(s) Removed
0 offset
1 offset and slope
2 offset, slope, and parabolic
curvature
2.8 Savitzky-Golay
This well known method of smoothing and derivative calculation relies on the least squares fit of a
polynomial to a spectral segment. Though both the Savitzky-Golay (S-G) and Detrend methods are
based on the least squares fit of polynomial functions, they differ in both scope and effect:
Method What is modeled The Result
Detrend Broad features across the whole spectrum,
i.e. offset, slope and curvature (a single
polynomial function is fit to the entire
spectrum) The modeled function is
subtracted from the
spectrum
Savitzky-Golay Fine spectral features defined by fitting a
polynomial function to a limited number of
data points centered on a single data point
(the data points in the segment are
modeled by a polynomial function) The modeled value at the
central wavelength
replaces the original
spectral value at that point
In the S-G method, a smoothed spectrum or a derivative spectrum of any order can be calculated
using coefficients of the polynomials fitted to a spectrum.
Three parameters must be defined to apply the S-G pretreatment:
S-G Parameter Purpose
Number of points Defines the size of the convolution window (the size of the
spectral segment to which the polynomial is fit)
The order of the
convolution polynomial Determines the complexity of the polynomial function
presumed to be contained in the convolution window
Method outcome Smoothed spectrum; or 1 st , 2 nd and 3 rd derivatives
2.9 Multiplicative Scatter Correction
All math pre-treatments discussed so far are based on and applied to individual spectra: they operate
on data points in a given spectrum, and yield results determined by the unique characteristics of that
spectrum. By contrast, Multiplicative Scatter Correction (MSC) is set-dependent: it is a scatter
correction method based on a related set of spectra.
In MSC, the mean spectrum is calculated from all spectra in a defined data set. Then a least squares