A new approach to bandpass correction in spectrometer measurements using the Richardson-Lucy method

Abstract

Bandpass correction in spectrometer measurements using monochromators is often mandatory in order to obtain accurate measurement results. In this paper we propose a new approach based on the Richardson-Lucy method, which is an iterative deconvolution scheme well known in digital image processing. The method is proved to converge to the maximum-likelihood solution. However, since bandpass correction is an ill-posed problem, the maximum-likelihood solution is not appropriate and the iterations should be stopped before convergence. To this end, we propose an automatic stopping criterion which is based on the L-curve method used in classical regularization. Our studies show that the proposed stopping criterion is robust and leads to good results. Altogether the new approach is easy to implement, and it appears to be superior to classical approaches to spectrometer bandpass correction.