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This paper introduces an uncertainty analysis model and its experimental implementation for chromaticity coordinates and luminous flux measurements of light-emitting diode (LED) sources. The uncertainty model applies the theory of the numerical method to estimate both the chromaticity coordinates and luminous flux uncertainties. The modeling process follows the steps described in GUM for determining the uncertainties. First, the mathematical functions for chromaticity coordinates and luminous flux are expressed according to both the sphere calibration and the LED measurement procedures. Based on the functions, the uncertainty contributors are identified as the input quantities of the model, and luminous flux and chromaticity coordinates are the output quantities. Second, the uncertainty contributors are categorized as random variables and systematic variables. Contributors such as spectrometer wavelength and spectral value repeatability are random variables; thus, their standard uncertainties are analyzed with statistical methods. The other contributors, such as spectrometer wavelength offsets and stray light, are systematic variables; thus, their standard uncertainties are estimated with non-statistical methods. In order to measure these contributors, several simple methods are developed for spectrometers and source measure units (SMU). Third, the sensitivity coefficients for the uncertainty contributors are calculated based on the numerical approach by calculating the output quantities with a change of the input quantities. Fourth, the uncertainties caused by each contributor are calculated using their standard uncertainties and sensitivity coefficients, and then combined. Finally, the expanded uncertainty is obtained with a coverage factor (k=2). The calculation for each step is conducted by a Matlab program.
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