Sensitivity evaluation of measurement uncertainty contributions of spectral data for calculated integral quantities

Integrating spectral data (spectral responsivities of photometers or spectral distributions of light sources) to calculate integrated quantities such as tristimulus values is straightforward at first sight. However, estimating the measurement uncertainty of these integrated quantities is challenging. When calculating integrated photometric quantities, some uncertainty contributions from the spectral data transfer to the final results, some ‘cancel out’, some ‘average out’ and others increase or decrease their weight by correlation. The spectral data are usually assumed to be uncorrelated when deriving other quantities by integration, which is typically not justified. A method called the framework approach, applying orthogonal basis functions and Monte Carlo simulations, is introduced. This approach shows that neglecting partial spectral correlations may lead to a significant underestimation of the measurement uncertainty of integrated quantities. Furthermore, this paper shows how information about spectral error correlation structures can be used to obtain better estimations of the measurement uncertainty.