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

VL - 367

SP - 347

EP - 373

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -