Simple function for intensity distribution from LEDs

Since its beginnings, light-emitting diode (LED) has progressed toward greater performance. Today, LEDs are everywhere, in many shapes, and with a wide range of radiation patterns. We propose a general analytic representation for the angular intensity distribution of the light emitted from an LED. The radiation pattern equation is determined by adding a Gaussian or a power cosine expression for contributions from the emitting surfaces (chip, chip arrays, or for some cases a phosphor surface), and the light redirected by the reflecting cup and the encapsulating lens. Mathematically, the pattern is described as a sum of Gaussian or of cosine-power functions. The resulting equation is widely applicable for any kind of LED of practical interest. We successfully model the radiation patterns from several manufacturer datasheets.