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Virtually all light-emitting diodes (LEDs) are encapsulated with atransparent epoxy or silicone-gel. In this paper we analyze the opticalefficiency of spherical encapsulants. We develop a quasi-radiometric equationfor the light transmission efficiency, which incorporates some ideas ofMonte-Carlo ray tracing into the context of radiometry. The approach includesthe extended source nature of the LED chip, and the chip radiance distribution.The equation is an explicit function of the size and the refractive index ofthe package, and also of several chip parameters such as shape, size, radiance,and location inside the package. To illustrate the use of this equation, weanalyze several packaging configurations of practical interest; for example, ahemispherical dome with multiple chips, a flat encapsulation as a special caseof the spherical package, and approximate calculations of an encapsulant with aphotonic crystal LED or with a photonic quasi crystal LED. These calculationsare compared with Monte-Carlo ray-tracing, giving almost identical values.

Light-emitting diode spherical packages: an equation for the light transmission efficiency