Abstract

Multivariate calibration models are sensitive to wavelength shifts in calibration spectra as such disturbances are linearly independent from unshifted spectra and increase the calibration model's dimension. However, if wavelength shifts included in the calibration model are random, the predictability of the model is not improved. On the contrary, overfitting is introduced, thereby increasing the prediction error. Because calibration spectra are defined to be error free and are the only available data at that point, there is no analytical way to find out that the calibration model is erroneous. This study gives a mathematical explanation of how the model's dimension is increased by wavelength shifts and that the additional basis vectors, principal components for instance, possess derivative-shaped features. It is also demonstrated by means of an example that the reverse is not necessarily true. Hence, derivative-shaped features found in principal components are no indication of wavelength-shifted calibration spectra. A method is presented for analyzing calibration spectra for such shifts. The algorithm takes advantage of the fact that artificial shift compensations of true shifts increase the similarity, i.e., correlation, of shifted spectra with respect to the remaining, unshifted spectra. Synthetic and experimental data are used to demonstrate and assess the performance of the algorithm. It is shown that wavelength shifts in calibration spectra can be detected and corrected if a small number of spectra are disturbed. Significant improvements of the prediction errors of chemometric calibration models can be achieved by means of this shift-correction algorithm.

Evaluation of univariate and multivariate calibration strategies for the direct determination of total carbon in soils by laser-induced breakdown spectroscopy: tutorial

Wesley Nascimento Guedes, Diego Victor Babos, Vinícius Câmara Costa, Carla Pereira De Morais, Vitor da Silveira Freitas, Kleydson Stenio, Alfredo Augusto Pereira Xavier, Luís Carlos Leva Borduchi, Paulino Ribeiro Villas-Boas, and Débora Marcondes Bastos Pereira Milori
J. Opt. Soc. Am. B 40(5) 1319-1330 (2023)

Determination of tissue optical properties from diffuse reflectance profiles by multivariate calibration

Jan S. Dam, Peter E. Andersen, Torben Dalgaard, and Paul Erik Fabricius
Appl. Opt. 37(4) 772-778 (1998)

Wavelength Shift of Spectrum Lines in Spark Spectra

A. Bardócz, U. M. Vanyek, and T. Voros
J. Opt. Soc. Am. 51(3) 283-288 (1961)

Wavelength calibration of Fourier-transform emission spectra with applications to Fe i

R. C. M. Learner and A. P. Thorne
J. Opt. Soc. Am. B 5(10) 2045-2059 (1988)

Wavelength calibration of spectra measured by the Global Ozone Monitoring Experiment by use of a high-resolution reference spectrum

Jos H. G. M. van Geffen and Roeland F. van Oss
Appl. Opt. 42(15) 2739-2753 (2003)