The typical illumination task is to redirecting the light of a known source by a mirror or a lens such as to achieve a desired irradiance / illuminance distribution on a given target surface. For small sources, such a task can be translated into a partial differential equation of Monge-Ampere type which can be solved numerically. This procedure is much more efficient and faster than an optimization approach. I general, the solution is a freeform optical surface which is exact except for discretization errors.<br /> Depending on the topological mapping and the boundary conditions there can be more than one solution.<br /> Particular challenges are multiple mappings and mappings with ring-topology. Additional requirements may be used to specify more than one surface. In particular more than one surface may allow extending the approach to extended sources.<br />

© 2015 Optical Society of America

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