Inverse freeform design of a parallel-to-two-target reflector system

P.A. Braam; J.H.M. ten Thije Boonkkamp; M.J.H. Anthonissen; K. Mitra; R. Beltman; And W.L. Ijzerman

doi:10.1364/JOSAA.563099

Inverse freeform design of a parallel-to-two-target reflector system

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

We present an inverse method for transforming a given parallel light emittance to two light distributions at different parallel target planes using two freeform reflectors. The reflectors control both the spatial and directional target coordinates of light rays. To determine the shape and position of the reflectors, we derive generating functions and use Jacobian equations to find the optical mappings to the two targets. The model is solved numerically by a three-stage least-squares algorithm. A feasibility condition is derived, which ensures that the reflectors are not self-intersecting. Several examples validate this condition and demonstrate the algorithm’s capability of realizing complex distributions.

Original language	English
Pages (from-to)	1133-1143
Number of pages	11
Journal	Journal of the Optical Society of America A: Optics and Image Science, and Vision
Volume	42
Issue number	8
DOIs	https://doi.org/10.1364/JOSAA.563099
Publication status	Published - 1 Aug 2025

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© 2025 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.

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Cite this

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title = "Inverse freeform design of a parallel-to-two-target reflector system",

abstract = "We present an inverse method for transforming a given parallel light emittance to two light distributions at different parallel target planes using two freeform reflectors. The reflectors control both the spatial and directional target coordinates of light rays. To determine the shape and position of the reflectors, we derive generating functions and use Jacobian equations to find the optical mappings to the two targets. The model is solved numerically by a three-stage least-squares algorithm. A feasibility condition is derived, which ensures that the reflectors are not self-intersecting. Several examples validate this condition and demonstrate the algorithm{\textquoteright}s capability of realizing complex distributions.",

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note = "Publisher Copyright: {\textcopyright} 2025 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.",

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doi = "10.1364/JOSAA.563099",

language = "English",

volume = "42",

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journal = "Journal of the Optical Society of America A: Optics and Image Science, and Vision",

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Inverse freeform design of a parallel-to-two-target reflector system. / Braam, P.A. (Corresponding author); ten Thije Boonkkamp, J.H.M.; Anthonissen, M.J.H. et al.
In: Journal of the Optical Society of America A: Optics and Image Science, and Vision, Vol. 42, No. 8, 01.08.2025, p. 1133-1143.

Research output: Contribution to journal › Article › Academic › peer-review

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AU - Braam, P.A.

AU - ten Thije Boonkkamp, J.H.M.

AU - Anthonissen, M.J.H.

AU - Mitra, K.

AU - Beltman, R.

AU - Ijzerman, And W.L.

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AB - We present an inverse method for transforming a given parallel light emittance to two light distributions at different parallel target planes using two freeform reflectors. The reflectors control both the spatial and directional target coordinates of light rays. To determine the shape and position of the reflectors, we derive generating functions and use Jacobian equations to find the optical mappings to the two targets. The model is solved numerically by a three-stage least-squares algorithm. A feasibility condition is derived, which ensures that the reflectors are not self-intersecting. Several examples validate this condition and demonstrate the algorithm’s capability of realizing complex distributions.

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JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision

JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision

IS - 8

ER -

Inverse freeform design of a parallel-to-two-target reflector system

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