TY - JOUR
T1 - Inverse reflector design for a point source and far-field target
AU - Romijn, Lotte B.
AU - ten Thije Boonkkamp, Jan H.M.
AU - IJzerman, Wilbert L.
PY - 2020/5/1
Y1 - 2020/5/1
N2 - We present a method for the design of a single freeform reflector that converts the light distribution of a point source to a desired light distribution in the far field. Using the geometrical-optics law of reflection and requiring energy conservation, this optical design problem can be represented by a generalized Monge–Ampère equation for the shape of the reflector with transport boundary condition. We use a generalized least-squares algorithm that can handle a logarithmic cost function in the corresponding optimal transport problem. The algorithm first computes the optical map and subsequently constructs the optical surface. We demonstrate that the algorithm can generate reflector surfaces for a number of complicated target distributions.
AB - We present a method for the design of a single freeform reflector that converts the light distribution of a point source to a desired light distribution in the far field. Using the geometrical-optics law of reflection and requiring energy conservation, this optical design problem can be represented by a generalized Monge–Ampère equation for the shape of the reflector with transport boundary condition. We use a generalized least-squares algorithm that can handle a logarithmic cost function in the corresponding optimal transport problem. The algorithm first computes the optical map and subsequently constructs the optical surface. We demonstrate that the algorithm can generate reflector surfaces for a number of complicated target distributions.
KW - Geometrical optics
KW - Optimal mass transport
KW - Logarithmic cost function
KW - Generalized Monge-Ampère equation
KW - Least-squares method
KW - Stereographic coordinates
KW - Generalized Monge–Ampère equation
UR - http://www.scopus.com/inward/record.url?scp=85078931182&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2020.109283
DO - 10.1016/j.jcp.2020.109283
M3 - Article
SN - 0021-9991
VL - 408
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 109283
ER -