Propagation of nonparaxial partially coherent fields across interfaces using generalized radiometry

A radiometric framework is described for modeling the propagation of nonparaxial scalar fields of any degree of coherence past planar boundaries (or composite interfaces) between homogeneous, isotropic nonabsorptive media in three dimensions. The transformation is shown to be, to lowest order, that predicted by classical radiometry but potentially including a Goos-Hänchen shift. Higher-order corrections take the form of coefficients multiplied by derivatives of the basic estimate. The accuracy of the radiometric term, along with second-order derivative corrections, are examined for Gaussian Schell-model fields of varying width and states of coherence. This technique is found to work well for most such fields but to fail in reflection for fields with significant total-internally-reflected components.