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 -