A lighting apparatus for providing uniform irradiance is provided. The lighting apparatus includes a light source configured to emit rays toward a polygonal target region, and a lens configured to uniformize irradiance from the light source to the target region, wherein sag of the lens and normals along a boundary of the lens are arranged so as to illuminate a perimeter of the target region based on an edge-ray mapping, wherein a lens surface is formed based on polyharmonic spline interpolations so as to smoothly illuminate an interior of the target region, wherein the irradiance is uniformized by argumenting light field tailoring of the lens, wherein the light field tailoring is augmented to maintain to maintain the irradiance perimeter.
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