  Virtually all light-emitting diodes (LEDs) are encapsulated with a
transparent epoxy or silicone-gel. In this paper we analyze the optical
efficiency of spherical encapsulants. We develop a quasi-radiometric equation
for the light transmission efficiency, which incorporates some ideas of
Monte-Carlo ray tracing into the context of radiometry. The approach includes
the 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 of
the package, and also of several chip parameters such as shape, size, radiance,
and location inside the package. To illustrate the use of this equation, we
analyze several packaging configurations of practical interest; for example, a
hemispherical dome with multiple chips, a flat encapsulation as a special case
of the spherical package, and approximate calculations of an encapsulant with a
photonic crystal LED or with a photonic quasi crystal LED. These calculations
are compared with Monte-Carlo ray-tracing, giving almost identical values.
