An Improved Criterion for Inverse-Model-Based Calibration of Spectrophotometric Transducers

The paper is on the variational methods for calibration of spectrophotometric transducers. A nonlinear operator of spectrum reconstruction is identified directly on the basis of higher-resolution and lower-resolution data representative of a reference spectrum. It is demonstrated that the criterion of optimization, most frequently applied for this purpose, viz. the Euclidian norm of the error of reconstruction, generates the operators of spectrum reconstruction that suffer an important drawback, viz. the spectral peaks are as a rule underestimated at their tops. As a remedy for this drawback, a modification of the criterion is proposed in this paper which consists in increasing the weight of reference data around the tops of spectral peaks using the first derivative of the reference spectrum. The effectiveness of this remedy is demonstrated using both synthetic and real-world data.