A Study on the Universality of a Calibration with Sample Temperature Compensation

Abstract

The applicability and universality of a sample combination method to develop a calibration with sample temperature compensation [ J. Near Infrared Spectrosc. 3, 211 (1995)] was investigated from mathematical and theoretical points of view. From a theoretical analysis it is clear that the development of the calibration will be successful when two conditions are satisfied. One condition is that the vectors whose elements are constituent values should be orthogonal to the vector whose elements are the dot product of spectral change and calibration coefficients. The other is that the inverse vectors of the spectrum related to chemical components should be orthogonal to the vector of spectral change. The first condition is always satisfied when we make a calibration following this method, but whether the second condition is satisfied or not is completely dependent on the regression algorithm. From a mathematical analysis, we concluded that simple multiple linear regression is not completely adequate to develop a calibration with temperature compensation.