ILLUMINATING LENS DESIGNED BY EXTRINSIC DIFFERENTIAL GEOMETRY

An illumination system with a prescribed output pattern comprising a light source and an optical lens redirecting the light of the source into an output beam, the lens with multiple surfaces (100, 130, 120) at leas t one of which has shape that is not a surface of revolution, the shape generated by the following method: the Gaussian sphere establishes a first grid (100) of equal-flux zones of solid angle; a second grid (130) with the same number of equal-flux zones of solid angles as the first grid, with a coordinate-system topology congruent with that of the first grid, such that the zones of the second grid are in one-to-one correspondence with the zones of the first grid (100), according to the local transmittance of the lens, with either of both of the grids bei ng rotationally non-symmetric; by this correspondence define a flux-redistributing directional mapping function from the first Gaussian sphere to the second Gaussian sphere, whereby any light ray from the source can be assigned a direction in the output beam, according to the zone of the second grid (130) into which the ray falls, so that the redirected ray falls in corresponding zone of the first grid.