Journal
OPTICS COMMUNICATIONS
Volume 439, Issue -, Pages 251-259Publisher
ELSEVIER
DOI: 10.1016/j.optcom.2019.01.069
Keywords
Laser beam shaping; Freeform optical surfaces; Monge-Ampere equation; Least-squares method
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In this article, we present a formulation for the design of double freeform lens surfaces to control the intensity distribution of a laser beam with plane wavefronts. Double freefrom surfaces are utilized to shape collimated beams. Two different layouts of the freeform lens optical system are introduced, i.e., a single lens with double freeform surfaces, and two separate lenses with two flat and two freeform surfaces. The freeform lens design problem can be formulated as a Monge-Ampere type differential equation with transport boundary condition, expressing conservation of energy combined with the law of refraction and the constraint imposed on the optical path length between source and target planes. Numerical solutions are computed using a generalized least-squares algorithm which is presented by Yadav a al. (2018). The algorithm is capable to compute two solutions of the Monge-Ampere boundary value problem, corresponding to either c-convex or c-concave freeform surfaces for both layouts. The freeform surfaces are validated for several numerical examples using a ray-tracer based on Quasi-Monte Carlo simulation.
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