Prediction of a statistical distribution of luminous flux for LED modules with an analytical model

In this paper, an analytical model is developed to predict the statistical distribution of the luminous flux of LED modules based on the statistical properties of their components. This proposed model has only one parameter C which can be easily extracted from a single test on an LED lighting module. To validate the proposed model, ray-tracing optical simulations were performed on a number of ideal LED modules. In each ideal LED module, the luminous flux of the LED package, the transmittance of the lens and reflectance of the substrate were assumed as some specific distributions. The results show great agreements between the simulation results and the model predictions on the luminous flux distribution of the ideal LED modules. Thus, this proposed model has the advantage of effectively predicting the luminous flux distribution of LED lighting modules, provided the statistical properties of their components are known.