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Univariate calibration

In univariate calibration the aim is to find a relationship which relates a sample property to a peak area, a ratio of peak areas or a spectral intensity at characteristic positions. This technique is widely accepted for quantitative analysis in UV, IR and NIR spectroscopy, where the correlation of the concentration of a sample and the spectral intensity is stated by Lambert Beer's Law.

Univariate Calibration Algorithm

In regression the relationship which relates a sample property like the concentration C and one or more explanatory spectral variables X1, X2, ... Xn is defined by a

polynomial function of nth order.  Thus the physical property is expressed by spectral variables as shown in the following equation:

C = c0 + c1 X1 + c2 X2 + ... + cn Xn + e



Amount of an investigated sample property such as the concentration.


measurement error or random error

c0, c1, ..., cn

usually unknown regression coefficients, which need to be determined during construction of the calibration model.

X1, X2, ..., Xn

explanatory variables taken from spectral data.


The simplest case is, when there is a single variable X1 and the relationship is linear:

C = c0 + c1 X1 + e

Usually, the regression coefficients c0 and c1 are unknown and e is some kind of measurement or random error.

In construction of a calibration with suitable reference data and known property values, the regression coefficients need to be calculated by polynomial regression following one of the equations given above. The quality of regression can be seen from the correlation coefficient and must be optimized by the user.

Once a calibration model has been established, the property C can also be calculated for unknown samples. This procedure is called prediction.