Uncertainty evaluation and propagation for spectral measurements

Abstract

The measurement of the spectral power distribution (SPD) of a radiation source by array spectroradiometers is a technique that is widely used. In many applications, quantities that are derived from the SPD by a weighted integral over a wavelength interval are of interest. These integral quantities ought to be accompanied by a reliable uncertainty statement, for example, to assess conformity with prescribed limits or in order to judge the consistency of results obtained at different laboratories. We have developed a generally applicable Monte Carlo procedure for evaluating the uncertainty of spectral measurements. The procedure naturally accounts for correlations in the SPD which turn out to be crucial. Means are provided to handle and transfer these large-scale correlation matrices easily. The proposed approach is illustrated by the determination of the SPD of colored LEDs from array spectroradiometer measurements, together with the derived CIE 1931 color coordinates. MATLAB TM software implementing the proposed analysis procedure is made available. K E Y W O R D Scolor coordinates, photometry, radiometry, spectral measurements, uncertainty 6 |

Calibrating spectrometers for measurements of the spectral irradiance caused by solar radiation

“…In the flow chart, this is represented by greek letters ρ, ν and τ . Having determined the specific values of all f -factors in Monte-Carlo iteration i, E DUT λ,i (λ) is calculated according to equation (14). Having finished the Monte-Carlo runs, a histogram is calculated from E DUT λ,i (λ).…”

“…The interpretation of measurement results is supported by substantiated estimates of the corresponding measurement uncertainty. Results of uncertainty analyses for spectral irradiance measurements have been presented in the literature [4][5][6][7][8][9][10][11][12][13][14][15][16]. However, these publications either focus on the characterization of specific instruments or only give a brief explanation of the underlying methodology.…”

Monte Carlo Evaluation of Uncertainties of UV Spectra Measured With Brewer Spectroradiometers

“…The Monte Carlo approach has been used to evaluate the uncertainty of spectral irradiance measurements obtained from both double monochromator‐based (Cordero, Seckmeyer, Pissulla, et al., 2008; Vaskuri et al., 2018) and CCD‐array‐based spectroradiometers (Cordero et al., 2012; Schinke et al., 2020; Schmähling et al., 2018). As for the Brewer spectrophotometer, this methodology was applied to estimate the uncertainty of its nitrogen dioxide measurements (Diémoz et al., 2014).…”