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

The quantity is typically measured, although it may be accurately calculated in some situations. Note that, we have specified that may be a function of and not of . This is a common assumption, as only biases in surface finish (such as may be caused by specific machining practices) cause a dependence upon , and these are rarely significant. However, variations in molecular structure of emitting surfaces cause a dependence upon , and this must in general be accounted for.

Then, over the entire hemisphere,

Since has a maximum of 1, has a maximum of 1. We term the total hemispherical emittance, as characteristic of the emission into the entire hemisphere above the point. Henceforth, we shall neglect all angular dependences in this introductory treatment, and proceed by examining emission from ``perfect'' surfaces, where is 1.

Thus, the directional distribution for emission is what we actually seek. This is given by the argument of the integral in equation (15), i.e., particles are emitted from perfect surfaces according to , as shown in Figure 9. As we see, per unit degree of cone angle-, the greatest number of particles are emitted at an angle of from the surface normal (over all in ). As tends to (normal to the surface), the solid angle tends to 0, and as tends to (grazing), the projected area tends to zero. The balance between these two factors results in a maximum for emission per unit cone angle from a ``perfect'' surface at .

Figure 9: Probability of Emission in dq.

In Monte Carlo simulation, it is often required to emit particles according to a directional distribution such as shown in Figure 9. In effect, we emit many particles to establish a directional distribution such as shown in Figure 9. One way to do this is termed the accept/reject method.