Radiance Theorem with Partially Coherent Light

The transmission of a generalized radiance across a planar boundary separating two homogeneous media is considered. It is assumed that the optical field remains continuous at the interface and reflection is neglected. A result is obtained which may be regarded as a generalization of the conventional radiance theorem for fields of any state of coherence. This result differs from the conventional theorem by a factor that depends, in general, both on the optical intensity and on the degree of coherence of the field. However, over a wide range of circumstances the generalized radiance theorem is shown to be in good agreement with the conventional theorem.