Nonimaging reflectors as functionals of the desired irradiance

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Abstract
For many tasks in illumination and collection it is necessary that the acceptance angle vary along the reflector. If the acceptance-angle function is known, then the reflector profile can be calculated as a functional of it. The total flux seen by an observer from a source of uniform brightness (radiance) is proportional to the sum of the view factor of the source and its reflection. This allows one to calculate the acceptance-angle function that one needs to produce a certain flux distribution and thereby to construct the reflector profile. We demonstrate the method for several examples, including finite-size sources with reflectors directly joining the source.