Illumination variation under a freeform lens and misalignment of light source

Use of an optical lens with a freeform surface is a popular and flexible approach in the LED applications for uniform illumination. The lens topologies are flexible for design to achieve a desired illumination pattern. However, different topologies may have different powers against the misalignment of the light source. The misalignment problem was studied based on the ray-tracing simulation that is inefficient on the computer time. In this study, the problem of misalignment along the lens optical axis is analyzed and formulated by applying the perturbation analysis. The formulations developed are applicable for the problems with small misalignment and large misalignment as well. The superiority of the proposed analytical approach over the ray-tracing simulation approach is highlighted. The adequacy of the proposed formulations is confirmed by cross validation. Good consistency between the analysis and the simulation is demonstrated by examples.