Illuminating lens designed by extrinsic differential geometry

For use in providing an illumination system with a prescribed output pattern comprising a light source and an optical lens redirecting the light of said source into an output beam, said lens with a shape that is not a surface of revolution, said shape generated by the method that includes:

• a) on a Gaussian sphere of directions of said output beam exiting a surface of said lens, in accordance with said prescribed output pattern, establish a first grid of equal-flux zones of solid angle,
• b) on a portion of the Gaussian sphere of directions of the light emitted from said source into an interior of said lens, establish a grid with the same number of equal-flux zones of solid angle as said first grid, and with a coordinate system topology congruent with that of said first grid, such that the zones of said second grid are in one-to-one topological correspondence with the zones of said first grid, with the flux of each zone of said second grid in proportion to the flux of its corresponding zone of said first grid, according to a local transmittance of said lens, with either or both of said grids being rotationally non-symmetric,
• c) by use of said correspondence, define a flux-redistributing directional mapping function from said first Gaussian sphere to said second Gaussian sphere, whereby any light ray from said source is assigned a direction in said output beam, according to the zone of said second grid into which said ray falls, and so that the redirected ray also falls in the corresponding zone of said first grid,
• d) by the vector form of Snell's law of refraction, express said correspondence by establishing on said second grid an overlaying distribution of surface normal vectors,
• e) from an initial starting point, mathematically generate the surface coordinates of said lens by contact-integrating said distribution of said surface normal vectors, along an initial strip that follows a principal curvature of the surface, and then, by successive contact-integrations, orthogonally outwards from said initial strip, of said surface normals, generate adjacent characteristic geodesic strips that follow the other principal curvature of said lens surface, outward to a boundary of said second grid,
• f) perform successive integrations of adjacent characteristic geodesic strips, so as to fulfill an integrability condition dictating equality of crossed second derivatives of the surface of said lens, thereby to ensure that the surface of said lens possesses the surface normals necessary for it to transform the light from said source into an output beam substantially fulfilling said prescription,
• g) and determine an overall size of said lens relative to a size of said light source by selecting a distance of said initial point from said source so as to keep the blurring of said output beam below a level defined by an angular resolution of said prescription.

A luminaire comprising:

• a) a lens body having a forwardly dome-shaped inner portion, and an outer portion extending abut and spaced from said inner portion, said portions being light-transmitting, and integral,
• b) the inner portions extending non-circularly about a forwardly and upward axis,
• c) their being a reflector on said outer portion, whereby a light source in rearward alignment with said inner portion provides certain light rays that travel forwardly and are refracted by said dome-shaped inner portion to travel forwardly from said inner portion, and other light rays that travel in said outer portion and are reflected by said reflector to travel forwardly in said outer portion, and forwardly from said outer portion,
• d) said dome-shaped inner portion located above an integral base, said light source associated with said base, said base upwardly divergent relatively away from a recess, and wherein said light source means is embedded in a transparent mass of material received in the recess, said base and dome-shaped body being laterally elongated, said dome-shaped body overhanging said base, and said body being generally ellipsoidal in lateral horizontal planes above said base.