A generalized bidirectional distribution function (BRDF) that relates the specific intensity of the scattered light from a semi-infinite medium to the specific intensity of the incident light is introduced in the framework of coherence theory. This derivation allows us to obtain from first principles several fundamental properties: First, it is established that the generalized BRDF takes the form of a nonlocal relation between the incident and the scattered specific intensities. This nonlocal structure allows us to account naturally for the lateral shift of a beam. Second, the generalized BRDF is the Fourier transform of the correlation function that describes the memory effect. Third, the Helmholtz principle for specific intensities is derived as a theorem from the reciprocity property of the scattering operator for wave fields. This result allows us to prove Kirchhoff’s law.
© 1998 Optical Society of America
(030.1640) Coherence and statistical optics : Coherence
(030.5630) Coherence and statistical optics : Radiometry
(120.5700) Instrumentation, measurement, and metrology : Reflection
(240.6700) Optics at surfaces : Surfaces
(290.0290) Scattering : Scattering
Jean-Jacques Greffet and Manuel Nieto-Vesperinas, "Field theory for generalized bidirectional reflectivity: derivation of Helmholtz’s reciprocity principle and Kirchhoff’s law," J. Opt. Soc. Am. A 15, 2735-2744 (1998)