Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design

A.H. van Roosmalen; Martijn J.H. Anthonissen; Wilbert L. IJzerman; Jan H.M. ten Thije Boonkkamp

doi:10.1007/978-3-031-86169-7_31

Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design

A.H. van Roosmalen (Corresponding author), Martijn J.H. Anthonissen, Wilbert L. IJzerman, Jan H.M. ten Thije Boonkkamp

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

We present an inverse method to design freeform optical systems. This method is based on combining a generated Jacobian equation with a geometric equation. These are then solved using an iterative least-squares method. We evaluate the behavior of the algorithm using the example of a lens with a point source and a far-field target.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2
Subtitle of host publication	European Conference, September 4-8, Lisbon, Portugal
Editors	Adélia Sequeira, Ana Silvestre, Svilen S. Valtchev, João Janela
Place of Publication	Cham
Publisher	Springer
Pages	302-309
Number of pages	8
ISBN (Electronic)	978-3-031-86169-7
ISBN (Print)	978-3-031-86168-0, 978-3-031-86171-0
DOIs	https://doi.org/10.1007/978-3-031-86169-7_31
Publication status	Published - 28 Apr 2025
Event	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2023 - Lisbon, Portugal Duration: 4 Sept 2023 → 8 Sept 2023

Publication series

Name	Lecture Notes in Computational Science and Engineering (LNCSE)
Volume	154
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2023
Country/Territory	Portugal
City	Lisbon
Period	4/09/23 → 8/09/23

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10.1007/978-3-031-86169-7_31

Cite this

van Roosmalen, A. H., Anthonissen, M. J. H., IJzerman, W. L., & ten Thije Boonkkamp, J. H. M. (2025). Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design. In A. Sequeira, A. Silvestre, S. S. Valtchev, & J. Janela (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2: European Conference, September 4-8, Lisbon, Portugal (pp. 302-309). (Lecture Notes in Computational Science and Engineering (LNCSE); Vol. 154). Springer. https://doi.org/10.1007/978-3-031-86169-7_31

van Roosmalen, A.H. ; Anthonissen, Martijn J.H. ; IJzerman, Wilbert L. et al. / Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design. Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2: European Conference, September 4-8, Lisbon, Portugal. editor / Adélia Sequeira ; Ana Silvestre ; Svilen S. Valtchev ; João Janela. Cham : Springer, 2025. pp. 302-309 (Lecture Notes in Computational Science and Engineering (LNCSE)).

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abstract = "We present an inverse method to design freeform optical systems. This method is based on combining a generated Jacobian equation with a geometric equation. These are then solved using an iterative least-squares method. We evaluate the behavior of the algorithm using the example of a lens with a point source and a far-field target.",

author = "\{van Roosmalen\}, A.H. and Anthonissen, \{Martijn J.H.\} and IJzerman, \{Wilbert L.\} and \{ten Thije Boonkkamp\}, \{Jan H.M.\}",

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van Roosmalen, AH, Anthonissen, MJH , IJzerman, WL & ten Thije Boonkkamp, JHM 2025, Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design. in A Sequeira, A Silvestre, SS Valtchev & J Janela (eds), Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2: European Conference, September 4-8, Lisbon, Portugal. Lecture Notes in Computational Science and Engineering (LNCSE), vol. 154, Springer, Cham, pp. 302-309, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2023, Lisbon, Portugal, 4/09/23. https://doi.org/10.1007/978-3-031-86169-7_31

Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design. / van Roosmalen, A.H. (Corresponding author); Anthonissen, Martijn J.H.; IJzerman, Wilbert L. et al.
Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2: European Conference, September 4-8, Lisbon, Portugal. ed. / Adélia Sequeira; Ana Silvestre; Svilen S. Valtchev; João Janela. Cham: Springer, 2025. p. 302-309 (Lecture Notes in Computational Science and Engineering (LNCSE); Vol. 154).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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van Roosmalen AH, Anthonissen MJH , IJzerman WL , ten Thije Boonkkamp JHM. Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design. In Sequeira A, Silvestre A, Valtchev SS, Janela J, editors, Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2: European Conference, September 4-8, Lisbon, Portugal. Cham: Springer. 2025. p. 302-309. (Lecture Notes in Computational Science and Engineering (LNCSE)). doi: 10.1007/978-3-031-86169-7_31

Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design

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