Design of two-dimensional reflective imaging systems: an approach based on inverse methods

Imaging systems are inherently prone to aberrations. We present an optimization method to design two-dimensional (2D) freeform reflectors that minimize aberrations for various parallel ray beams incident on the optical system. We iteratively design reflectors using inverse methods from non-imaging o...

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Bibliographic Details
Published in:Journal of mathematics in industry 2024-12, Vol.14 (1), p.25-21, Article 25
Main Authors: Verma, Sanjana, Anthonissen, Martijn J. H., ten Thije Boonkkamp, Jan H. M., IJzerman, Wilbert L.
Format: Article
Language:English
Subjects:
Aberration
Aberrations
Applications of Mathematics
Configuration management
Design optimization
Design techniques
Freeform design
Illumination optics
Imaging
Imaging optics
Inverse methods
Math. Appl. in Environmental Science
Mathematical and Computational Biology
Mathematical and Computational Engineering
Mathematical Methods in Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Methods
Nelder-Mead optimization
Numerical analysis
Optical components
Optics
Optimization techniques
Partial differential equations
Reflectors
Selected topics from 22nd ECMI Conference on Industrial and Applied Mathematics
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Summary:Imaging systems are inherently prone to aberrations. We present an optimization method to design two-dimensional (2D) freeform reflectors that minimize aberrations for various parallel ray beams incident on the optical system. We iteratively design reflectors using inverse methods from non-imaging optics and optimize them to obtain a system that produces minimal aberrations. This is done by minimizing a merit function that quantifies aberrations and is dependent on the energy distributions at the source and target of an optical system, which are input parameters essential for inverse freeform design. The proposed method is tested for two configurations: a single-reflector system and a double-reflector system. Classical designs consisting of aspheric elements are well-known for their ability to minimize aberrations. We compare the performance of our freeform optical elements with classical designs. The optimized freeform designs outperform the classical designs in both configurations.
ISSN:2190-5983
2190-5983
DOI:10.1186/s13362-024-00164-7