Radiometric coherence tensors for thermal radiation emission from an opaque specular surface

Abstract

For the first time to the author's knowledge, the electric, magnetic, and mixed cross-spectral tensors are derived for the thermal radiation emitted into free space from an opaque, planar, specular surface of finite size, held at uniform temperature. The results are valid in the asymptotic limit in which the mean-field energy density and energy flux are in agreement with the laws of classical radiometry, while at the same time field correlation effects are included in the description of the radiated field. Furthermore, the results are applicable to both wide and narrow angular diameter sources. The derivation is based on the generalized Kirchhoff radiation law, and the coherence tensor components can be viewed as a generalization to electromagnetic waves of the van Cittert–Zernike theorem in the radiometric limit.