Abstract: A linear Fresnel lens for LED illumination is configured initially by using a meridional flux-assignment method and is then corrected by assessing the three-dimensional flux distribution of individual facets. The facet angles are slightly altered as required to produce uniformity. A variety of specialized lens shapes are generated, such as for illuminating shelves in commercial refrigerator food-display cases. The lens shapes are suitably thin for economical production by extrusion.

Abstract: A light source emits light into a solid angle exceeding pi steradians with a known intensity distribution. An illumination lens has a first surface that receives at least 90% of the light of the known intensity distribution and has a shape that transforms the known intensity distribution into an intermediate intensity distribution within the transparent material of the lens. A second surface receives the intermediate intensity distribution and is shaped to transform the intermediate intensity distribution into a final intensity distribution that produces a prescribed illumination distribution upon a rectangular target zone. At least one of the shapes of the first and second surfaces is non-rotationally symmetric and is approximated by a super-ellipsoid.