Using rational filters for digital correction of a spectrometric micro-transducer

The raw spectrometric data are subject to systematic errors of an instrumental type that may be reduced provided a mathematical model of the spectrometer, or its pseudoinverse, i.e. an operator of reconstruction is identified. The idea of identifying this operator, directly during calibration of the spectrometer, is developed in this paper. The applicability of an operator of reconstruction, having the form of a rational filter, is studied when it is used for correction of the instrumental errors introduced by a low-resolution spectrometric micro-transducer that is intended for designing a microspectrometer. Several algorithms of correction are developed and systematically studied using real-world spectra and the nonlinear mathematical model of the micro-transducer proposed by the authors in a previous publication.