Advancements in Spectral Power Distribution Modeling of Light-Emitting Diodes

The unique radiative, photometric and colorimetric characteristic of a light-emitting diode is derived from its spectral power distribution. Modeling such characteristics with respect to the forward current, temperature or operating time has been subject of various studies. Deriving a simple analytical model, however, is not trivial due to the unique emission pattern varying with different types and technologies of light emitting diodes. For this purpose, curve fitting multiple superimposed Gaussian probability density functions to the spectral power distribution is a common approach. Despite excellent $R^{2}$ goodness of fit results, significant deviations within the photometric and colorimetric parameters, such as luminous flux or chromaticity coordinates, are observed. In addition, most studies were conducted on a small sample set of very few different spectral power distributions. This work provides a comprehensive comparison and evaluation of 19 different (superimposed) probability density function based models provided by the literature tested on a total of 15 different spectral power distributions of monochromatic blue, green and red light-emitting diode as well as phosphor-converted spectra of lime, purple and white samples with different correlated color temperatures. All models were evaluated by means of their coefficient of determination, radiant flux, chromaticity coordinate deviation and Bayesian Information Criterion. This study shows that a superimposed (split) Pearson VII model is able to outperform the commonly used Gaussian model approach by far. In addition, an application example in regard of forward current dependence is given to prove the proposed approach.