Abstract
Designing freeform optical surfaces that control the redistribution of light from a particular source distribution to a target irradiance poses challenging problems in the field of illumination optics. There exists a wide variety of strategies in academia and industry, and there is an interesting link with optimal transport theory. Many freeform optical design problems can be formulated as a generalized Monge-Ampère equation. In this paper, we consider the design of a single freeform lens that converts the light from an ideal point source into a far-field target. We derive the generalized Monge-Ampère equation and numerically solve it using a generalized least-squares algorithm. The algorithm first computes the optical map and subsequently constructs the optical surface. We show that the numerical algorithm is capable of computing a lens surface that produces a projection of a painting on a screen in the far field.
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Acknowledgements
This work is part of the research program NWO-TTW Perspectief with project number P15-36, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO).
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Romijn, L.B., Boonkkamp, J.H. .t.T., IJzerman, W.L. (2021). A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_82
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DOI: https://doi.org/10.1007/978-3-030-55874-1_82
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