Nondiffuse Radiative Transfer 2: Planar Area Sources and Receivers

The most common form of nondiffuse radiative transfer calculation in lighting is determining the initial flux from luminaires onto discrete elements of architectural surface. The fundamental expression for the flux transferred from emitter to receiver is a double area integral over the areas of emitter and receiver. In general, such integrals do not have an analytic solution and various approximations have been developed.

The first paper in this series derived a contour integral taken around the perimeter of a nondiffuse emitter, which gives the illuminance at a point from the emitter. This work extends this to an illuminated area; the result being a double contour integral, taken around the perimeters of emitter and receiver, which give the total flux transferred directly from emitter to receiver. This is similar to the double contour integral first obtained for diffuse emitter by Fock. The double contour integral expression for area receivers and diffuse area emitters is well known, though only recently has an analytic expression been obtained for polygonal emitters and receivers.

The present results are useful in the design and analysis of luminaires where the reflectance properties of material are not diffuse and the discrete elements that constitute reflecting surfaces must be treated as non-diffuse emitters. Additionally, the present results can be used to calculate non-diffuse form factors for use in non-diffuse radiative transfer analysis.