A method to measure the spectral responsivity of a photometer using optical excitations with arbitrary spectral distributions

Abstract

The spectral responsivity of a photometer is usually measured using very narrow optical excitations, provided by a monochromator or a tuneable laser. This article describes a technique to measure the spectral responsivity using an arbitrary number of optical excitations having any type of spectral distribution. The problem is formulated as an inverse problem which is solved using a probabilistic approach based on Bayes’ theorem. The method requires a prior knowledge of the spectral responsivity, which can be proportional to the standard photopic function, with an uncertainty level related to the spectral match index of the photometer. Using this method, the estimation can be performed from data provided by a simple experimental set-up. The numerical application provides a stable and unique solution to the inverse problem, along with the estimation uncertainties. Using a tuneable LED source, the method was applied to an illuminance measurement head, giving an estimation of its spectral responsivity from 380 to 780 nm with a step of 1 nm. The results were in good agreement with data obtained by a monochromator-based technique. Our measurement had larger uncertainties towards the red and blue limits of the spectrum as the light source provided very little light at these wavelengths.