Field theory for generalized bidirectional reflectivity: derivation of Helmholtz's reciprocity principle and Kirchhoff's law

摘要

Received March 8, 1998; revised manuscript received June 15, 1998; accepted June 16, 1998 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 [S0740-3232(98)01210-1] OCIS codes: 120.5700, 290.0290, 240.6700, 030.1640, 030.5630,