For many tasks in illumination and collection the acceptance angle is required to vary along the reflector. If the acceptance angle function is known, then the reflector profile can be calculated as a function 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 necessary to produce a certain flux distribution and thereby construct the reflector profile. We demonstrate the method for several examples, including finite size sources with reflectors directly joining the source.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.