Abstract: Many illumination situations involve a flat surface and an oblique luminaire placement. Today's commercially available luminaires give very uneven illumination here. A novel injection-moldable segmented lens is presented that will uniformly illuminate a rectangular zone, such as a stair- step or a picture on a wall. Its design is a development of prior methods of lens-surface generation that derived the array of surface normal vectors required to match a source with a particular illumination prescription. This matching is done via grids on the unit sphere: one for the source and one for the prescription. The cells of these two grids are sized so that they have the same flux of lumens, according to the source intensity and the prescribed illumination, respectively. The first development is the use of an equi- flux polar grid for the target rectangle, because most light sources have circular symmetry. The second development is the radial segmentation of the lens surface in order to approximate the non-irrotational array of surface normal vectors derived from the two grids. Designs are presented for step-lighting by LEDs and fiber-optic billboard lighting. !3
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