Spline-based variational method with constraints for spectrophotometric data correction

The raw results of spectrophotometric measurements are subject to systematic errors of an instrumental type which may be reduced provided a mathematical model of the instrumental imperfections is identified. It is assumed that this model has the form of an integral, convolution-type equation of the first kind. The correction of the spectrometric data consists in numerically solving this equation on the basis of the raw results of measurements. An algorithm of correction is proposed which is based on the approximation of the solution with a spline function whose parameters are determined using a variational method with the positivity constraint imposed on the set of feasible solutions. The efficiency of the incorporation of this constraint into the algorithm of correction is demonstrated using synthetic data. The possibility of improving resolution of spectrometric data is shown on a set of real spectrophotometric measurements