We have proposed a method for rectangular illumination in a (u, v) coordinate system with high collection efficiency and favorable uniformity. In our proposed approach, with the target plane rotating at a certain angle around the z axis, one of the diagonals on the rectangular target plane moves to the coordinate axis; then, we partition the light source and target plane into grids. The intersection points of the grids are in one-to-one correspondence from the source to the target plane. This improved method will avoid the one-to-many correspondence topological relationship in the traditional (u, v) mapping method; uniformity of the illuminance pattern will be promoted. Based on this method, lenses are designed for rectangular target plane illumination; uniformity over 0.83 and efficiency of about 0.92 are obtained with a 1  mm×1  mm LED Lambertian source.

Lens for rectangular illumination has been designed in (u,v) coordinate system already. Because of light source in (u,v) coordinate system can be divided into two identical parts, we have found that it is possible to design lenses for illumination of specific shapes. Specific shapes include triangles, as well as quadrangles which can be divided into two equal-area parts by one of the diagonals. We partition two equal-area parts into grids separately with equivalent luminous flux as well as light source, after that we construct freeform lenses by ray mapping method. Simulation results show that lenses for illumination of specific shapes are obtained with a Lambertian point source and favorable efficiency is over 0.86.

We have designed a new TIR(Total Internal Reflection) structure for generating an LED lens which can produce a rectangular beam with small divergence angle in two perpendicular directions for an optical guidance system. The lens can control the divergence angle in the horizontal direction to be a small value of about 8° with a 1 mm × 1 mm LED source, also in the vertical direction it can be about 7°, with optical collection efficiency higher than 0.83. After the lens is manufactured, the work demonstrates that the lens is suitable for an optical guidance system.

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Based on a new ray mapping method in (u, v) coordinate system, we have designed a polymethyl methacrylate(PMMA) lens for indoor uniform illumination. The lighting area is 18m ×18m and has a distance of 8m to the light source. We have calculated the surface curves and lofted them into surface, then the lens three-dimensional model is constructed, the PMMA lens is with a refractive index of 1.4935, the size of the lens is 38mm × 38mm × 18mm. Since the new ray mapping method applies error control to constructing the lens surface, the surface is discontinuous and consists of 20 surface patches. With the lens model being inserted into the optical simulation software, we can process the lighting simulation by a LED source with 1 million rays. Simulation results show the minimum illuminance on the lighting area is 2.2lux and the average illuminance is about 2.6lux. After constructing arrays with 9 designed lenses, the simulation results show the minimum illuminance on the lighting area is about 21lux, which meets the requirement of indoor illumination. In order to prove the lens model can apply to the indoor lighting situation, we have manufactured a lens with PMMA on precision CNC machine tool. With the manufactured lens, we complete the lighting experiment and obtain the lighting pattern. But we have found dark fringes exist on the lighting pattern and the illuminance around two vertexes are not expected results, that is because the compact discontinuous part of the lens can't be manufactured precisely on precision CNC machine tool, and this bring manufacturing errors to the lens.