On the cross-spectral tensors for black-body emission into space

The cross-spectral tensors for black-body emission into space are derived, and the results expressed in terms of Debye integrals which have recently been found to be important in the scalar theory of partial coherence. For the case of an infinite black-body surface, closed-form expressions can be obtained for the cross-spectral tensors which are exact within the constraints of the local thermodynamic equilibrium assumption and the idealization of a perfectly absorbing surface. The trace of the electric cross-spectral tensor agrees with the recent results in the scalar theory of emission from uniform planar Lambertian sources.