We establish a fundamental bound on the field of view over which strictly uniform far-field irradiance can be achieved in symmetric two-dimensional (2D, troughlike) and three-dimensional (3D, conelike) illumination systems. Earlier results derived for particular 2D devices are shown to be special cases of the general formula. For a rotationally symmetric 3D luminaire with a Lambertian disk light source and a prescribed uniform core region half-angle θc, no more than tan2(θc) can be projected within a uniform core region. Hence the efficiency with which such illuminators can produce uniform flux is severely limited for many problems of practical interest. Guided by the tailored edge-ray device formalism for the design of 2D luminaires, we develop a 3D reflector that produces extremely uniform far-field illuminance.
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