Generating-function approach for double freeform lens design

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Many LED lighting applications involve the design of multiple optical surfaces. A prime example is a single lens with two refractive surfaces. In this paper, we consider an LED light source approximated as a point and a far-field target intensity. Using Hamilton’s characteristic functions, the design problem is converted into two generalized Monge–Ampère equations by deriving a generating function for each optical surface. The generating function is a generalization of the cost function in optimal transport theory. The generalized Monge–Ampère equations are solved using an iterative least-squares algorithm. To compute the first optical surface, we choose an intermediate far-field target intensity. By choosing different intermediate target intensities based on the source and target intensity, we develop a “knob” to distribute the refractive power over both surfaces of the lens. We apply the algorithm on two example problems and show it is capable of producing complicated target distributions.
Originele taal-2Engels
Pagina's (van-tot)356-368
Aantal pagina's13
TijdschriftJournal of the Optical Society of America A, Optics, Image Science and Vision
Nummer van het tijdschrift3
StatusGepubliceerd - 1 mrt 2021

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