next up previous

3.2.1 Local Spherical System--Directional Distribution     continued...

In Figure 7, is the ``cone'' angle and is the ``azimuthal'' angle. Emission occurs over the hemisphere defined from to and to . While angles are measured in radians, solid angles are measured in steradians. A hemisphere contains steradians, as follows:

The probability of emission of a particle at angle should properly be weighted by . As particles originate inside the solid, their probability of escaping from the solid and being emitted is inversely proportional to the path length s they must travel through the material to escape. In Figure 8, we depict this conceptually for particles originating a depth d beneath the surface. Thus, emission at angle is proportional to or . The emission from many real surfaces is well modelled in this fashion. Such surfaces are termed Lambertian or ``diffuse'' surfaces.

Figure 8: Emission from Within a Solid.