Reflectors for uniform far-field irradiance: Fundamental limits and example of an axi-symmetric solution

We establish a fundamental bound on the field of view over which strictly uniform far-field irradiance can be achieved in symmetric 2D (trough-like) and 3D (cone-like) 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 disc light source and a prescribed uniform cone region half-angle (theta) _c, no more than tan²((theta) _c) 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. Being 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.