A Monge–Ampère problem with non-quadratic cost function to compute freeform lens surfaces

N.K. Yadav (Corresponding author), J.H.M. ten Thije Boonkkamp, W.L. IJzerman

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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Uittreksel

In this article, we present a least-squares method to compute freeform surfaces of a lens with parallel incoming and outgoing light rays, which is a transport problem corresponding to a non-quadratic cost function. The lens can transfer a given emittance of the source into a desired illuminance at the target. The freeform lens design problem can be formulated as a Monge–Ampère type differential equation with transport boundary condition, expressing conservation of energy combined with the law of refraction. Our least-squares algorithm is capable to handle a non-quadratic cost function, and provides two solutions corresponding to either convex or concave lens surfaces.

Originele taal-2Engels
Pagina's (van-tot)475-499
Aantal pagina's25
TijdschriftJournal of Scientific Computing
Volume80
Nummer van het tijdschrift1
Vroegere onlinedatum27 mrt 2019
DOI's
StatusGepubliceerd - 15 jul 2019

Vingerafdruk

Cost functions
Lens
Cost Function
Lenses
Lens Design
Free-form Surface
Least Square Algorithm
Refraction
Least Square Method
Conservation
Half line
Differential equation
Boundary conditions
Target
Differential equations
Energy

Citeer dit

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A Monge–Ampère problem with non-quadratic cost function to compute freeform lens surfaces. / Yadav, N.K. (Corresponding author); ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.

In: Journal of Scientific Computing, Vol. 80, Nr. 1, 15.07.2019, blz. 475-499.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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