TY - JOUR
T1 - A least-squares method for the inverse reflector problem in arbitrary orthogonal coordinates
AU - Beltman, René
AU - ten Thije Boonkkamp, Jan
AU - IJzerman, Wilbert
PY - 2018/8/15
Y1 - 2018/8/15
N2 - In this article we solve the inverse reflector problem for a light source emitting a parallel light bundle and a target in the far-field of the reflector by use of a least-squares method. We derive the Monge–Ampère equation, expressing conservation of energy, while assuming an arbitrary coordinate system. We generalize a Cartesian coordinate least-squares method presented earlier by Prins et al. [13] to arbitrary orthogonal coordinate systems. This generalized least-squares method provides us the freedom to choose a coordinate system suitable for the shape of the light source. This results in significantly increased numerical accuracy. Decrease of errors by factors up to 104 is reported. We present the generalized least-squares method and compare its numerical results with the Cartesian version for a disk-shaped light source.
AB - In this article we solve the inverse reflector problem for a light source emitting a parallel light bundle and a target in the far-field of the reflector by use of a least-squares method. We derive the Monge–Ampère equation, expressing conservation of energy, while assuming an arbitrary coordinate system. We generalize a Cartesian coordinate least-squares method presented earlier by Prins et al. [13] to arbitrary orthogonal coordinate systems. This generalized least-squares method provides us the freedom to choose a coordinate system suitable for the shape of the light source. This results in significantly increased numerical accuracy. Decrease of errors by factors up to 104 is reported. We present the generalized least-squares method and compare its numerical results with the Cartesian version for a disk-shaped light source.
KW - Inverse reflector problem
KW - Least-squares method
KW - Monge–Ampère equation
UR - http://www.scopus.com/inward/record.url?scp=85046479641&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2018.04.041
DO - 10.1016/j.jcp.2018.04.041
M3 - Article
AN - SCOPUS:85046479641
SN - 0021-9991
VL - 367
SP - 347
EP - 373
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -