In this article, we consider the design of a compact freeform optical surface that uniformly irradiates an arbitrary convex polygonal region from an extended light source, while controlling spill. This problem has attracted a large body of literature that has primarily covered highly symmetric special cases or cases where the solution is approximated by a zero-etendue design based on a point source. Practical versions of this illumination design problem will likely feature large asymmetric light-emitting diodes, compact lenses, and irregular targets on angled projection surfaces. For these settings, we develop a solution method based on an edge ray mapping that routes maximally off-axis rays from the edges of the source through the edge of the optic to the edges of the target polygon. This determines the sag and normals along the boundary of the freeform surface. A "spill-free" surface is then interpolated from the boundary information and optimized to uniformize the irradiance, while preserving the polygonal boundary. Highly uniformirradiances (relative standard deviation <.01) can be attained with good control of spill, even when the exit surface is less than three source diameters from the embedded source. (C) 2020 Optical Society of America
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