Direct design of aspherical lenses for extended non-Lambertian sources in two-dimensional geometry

Illumination design for extended sources is very important for practical applications. The existing direct methods that are all developed for extended Lambertian sources are not applicable to extended non-Lambertian sources whose luminance is a function of position and direction. What we present in this Letter is to our knowledge the first direct method for extended non-Lambertian sources. In this method, the edge rays and the interior rays are both used, and the output intensity at a given direction is calculated to be the integral of the luminance function of all the outgoing rays at this direction. No cumbersome iterative illuminance compensation is needed. Two examples are presented to demonstrate the elegance of this method in prescribed intensity design for extended non-Lambertian sources in two-dimensional geometry.