Light-emitting diodes (LEDs) come in many varieties and with a wide range of radiation patterns. We propose a general, simple but accurate analytic representation for the radiation pattern of the light emitted from an LED. To accurately render both the angular intensity distribution and the irradiance spatial pattern, a simple phenomenological model takes into account the emitting surfaces (chip, chip array, or phosphor surface), and the light redirected by both the reflecting cup and the encapsulating lens. Mathematically, the pattern is described as the sum of a maximum of two or three Gaussian or cosine-power functions. The resulting equation is widely applicable for any kind of LED of practical interest. We accurately model a wide variety of radiation patterns from several world-class manufacturers.

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A novel LED modeling algorithm for precise three-dimensional light pattern simulation is proposed and demonstrated. We propose to use normalized cross correlation to verify the validity of the simulation in one-dimensional intensity patterns as well as two-dimensional irradiance patterns in various midfield distances and to provide feedback to achieve a successful model. The model is demonstrated to obtain an average of 99% in normalized cross correlation between the simulation light pattern and experimental measurement for a truncated inverse pyramid LED.

Light extraction analysis of GaN-based light-emitting diodes (LEDs) with Monte Carlo ray tracing is presented. To obtain high light extraction efficiency, periodic structures introduced on the top surface and/or on the substrate of various types of LED are simulated, including wire bonding, flip chip and Thin GaN. Micro pyramid array with an apex angle from 20o to 70o is shown to effectively improve the light extraction efficiency. In addition, for an LED encapsulated within an epoxy lens, the patterned substrate with pyramid array is found to be a more effective way to increase light extraction efficiency than the surface texture.