Analysis of the Relationship Between Spectral and Color Uncertainty

Abstract

An approach is proposed for an approximate estimate of the relation between the uncertainties of spectral and color measurements. The approach is based on replacing the entire diversity of the spectra with simple models: a constant over all wavelengths, a pronounced peak, a sharp decrease and a sharp increase. The Monte-Carlo method was used for calculations. Small distortions were introduced to the model spectra at each wavelength, the standard deviation of these distortions was calculated, after which the chromaticity coordinates were calculated in the system (x, y, Y). The value of Y, as related to light measurements, was not further analyzed. The standard deviation of the distances between the chromaticity coordinates of the initial spectrum and the chromaticity coordinates of the distorted spectra in space (x, y) was used as a measure of the uncertainty of color measurements. The ratio of these standard devia­tions was considered to be a link between the uncertainties of the spectral and color measurements. The influence of the uncertainties of the spectral measurements, the effect of the spectral width of the model spectra in the form of a peak, a sharp decrease and a sharp increase on the axis of the wavelengths were analyzed. The ran­ges of the corresponding values are chosen taking into account the valid documents and the most common spectra. The influence of a stan­dard illuminator selected was considered: all calculations were carried out for both type A and D65 sources. The results of the calculations are provided in the form of graphs, which allow one to approximately determine the required level of accuracy of the spectral equipment before the measurements, in order to provide the necessary uncertainty of chromaticity measurements. The analysis of the results obtained.