TY - JOUR

T1 - Generating-function approach for double freeform lens design

AU - Romijn, Lotte B.

AU - ten Thije Boonkkamp, Jan H.M.

AU - Anthonissen, Martijn J.H.

AU - IJzerman, Wilbert L.

PY - 2021/3/1

Y1 - 2021/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85102819292&partnerID=8YFLogxK

U2 - 10.1364/JOSAA.411883

DO - 10.1364/JOSAA.411883

M3 - Article

C2 - 33690465

AN - SCOPUS:85102819292

SN - 1084-7529

VL - 38

SP - 356

EP - 368

JO - Journal of the Optical Society of America A, Optics, Image Science and Vision

JF - Journal of the Optical Society of America A, Optics, Image Science and Vision

IS - 3

ER -