A least-squares method for the inverse reflector problem in arbitrary orthogonal coordinates

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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.

Originele taal-2Engels
Pagina's (van-tot)347-373
Aantal pagina's27
TijdschriftJournal of Computational Physics
Volume367
DOI's
StatusGepubliceerd - 15 aug 2018

Vingerafdruk

Reflector
least squares method
Least Square Method
reflectors
Light sources
light sources
Generalized Least Squares
Arbitrary
Cartesian
Numerical Accuracy
Cartesian coordinates
conservation equations
Conservation
Far Field
bundles
far fields
Bundle
Choose
Numerical Results
Decrease

Citeer dit

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title = "A least-squares method for the inverse reflector problem in arbitrary orthogonal coordinates",
abstract = "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–Amp{\`e}re 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.",
keywords = "Inverse reflector problem, Least-squares method, Monge–Amp{\`e}re equation",
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A least-squares method for the inverse reflector problem in arbitrary orthogonal coordinates. / Beltman, René; ten Thije Boonkkamp, Jan; IJzerman, Wilbert.

In: Journal of Computational Physics, Vol. 367, 15.08.2018, blz. 347-373.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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

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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.

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