Comparison of the Richardson–Lucy method and a classical approach for spectrometer bandpass correction

Abstract

Bandpass correction in spectrometer measurements using monochromators is often necessary in order to obtain accurate measurement results. The classical approach of spectrometer bandpass correction is based on local polynomial approximations and the use of finite differences. Here we compare this approach with an extension of the Richardson-Lucy method, which is well known in image processing, but has not been applied to spectrum bandpass correction yet. Using an extensive simulation study and a practical example, we demonstrate the potential of the Richardson-Lucy method. In contrast to the classical approach, it is robust with respect to wavelength step size and measurement noise. In almost all cases the Richardson-Lucy method turns out to be superior to the classical approach both in terms of spectrum estimate and its associated uncertainties.

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

“…Note that the convolution of the estimated spectrum with the mirrored bandpass function requires that their wavelength step size is equal. Typically the step size in the calibration of the bandpass function is smaller than for the measurement of the spectrum and interpolating the measured spectrum is required [5].…”

“…In [16] the authors propose the weighted error of the estimated measurement as the criterion for the estimation quality. As in [5] we propose the application of the change in the estimated spectrum during one iteration as a criterion. Therefore we consider the progress measure…”

“…A deconvolution, based on the monochromator bandpass function, is therefore often applied to reconstruct the underlying spectrum of the light source from the measured data. Recently, the Richardson-Lucy deconvolution method, originating from image processing, has been proposed for bandpass correction [5]. The Richardson-Lucy method dates back to the 1970s and has been studied rigorously by many authors since then [6][7][8][9].…”

“…Moreover, positivity of the solution is ensured provided that the initial estimate is positive. The results in [5] suggested that the iterative RichardsonLucy method together with a suitable stopping criterion provides more accurate spectra and that it is less sensitive to noise in the measurements than classical approaches in this field. In this paper we demonstrate these findings by means of simulations.…”

Evaluation of measurement uncertainty for time-dependent quantities

“…The recently published Supplement 2 to the GUM extends this framework to multivariate quantities [2]. However, the GUM does not address the measurement of quantities whose values depend on a continuous quantity like time, space or wavelength [3][4][5]. We here mainly focus on timedependent "dynamic" measurands, although the proposed methodology is largely the same when the measurand depends on another continuous quantity such as space or wavelength.…”