Page 251 - Phase Space Optics Fundamentals and Applications

232 Chapter Seven

The total spectral radiant power is found to be
= AS BB ( ,T) (7.49)

The constant A is the area of the elementary hole in the blackbody
cavity to provide the radiation to escape. The spectral radiant exitance
evaluates to
M( s , 0, ) = S BB ( ,T) (7.50)
r
Finally, the spectral radiant intensity can be shown to be

J ( ˆ n, ) = cos AS BB ( ,T) (7.51)
We observe from Eqs. (7.48) to (7.51) that blackbody radiation is Lam-
bertian; see Eq. (7.10).

7.7.2 Non-coherent Source
The spatial coherence function for a noncoherent 3, 5 source is defined
by
2
1 1
ˆ
r s + r s12 , r s − r s12 , 0, = I 0 ( ) ( r s12 ) (7.52)
2 2
ˆ
In this expression, I 0 ( ) is the squared modulus of the optical field at
frequency .
The use of the Dirac delta function of Eq. (7.52) permits us to eval-
uate the spectral radiance function of Eq. (7.33); it gives

m 2 m
ˆ
r
B( s , 0, ˆ n, ) = I 0 ( ) = ˆ I 0 ( ) (7.53)

2
Since the noncoherent source is assumed to be spatially stationary,
r
the spectral radiance is independent of the average variable s .
The spectral radiant power is
2
ˆ
( ) = A· I 0 ( ) (7.54)
3
The spectral radiant exitance is given by
2 ˆ
r
M( s , 0, ) = I 0 ( ) (7.55)
3
Finally, the spectral radiant intensity takes the form
A
ˆ
2
J ( ˆ n, ) = m I 0 ( ) (7.56)