Ray selection for optimization of rotationally symmetric systems
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Greg W. Forbes
Greg W. Forbes is an Adjunct Professor in Physics at Macquarie University (Sydney) and the Director of Scisense Consulting Pty Ltd. Following his PhD in Theoretical Physics at the Australian National University, he was a Fulbright Fellow at the Optical Sciences Center (Tucson), a tenured faculty member of The Institute of Optics (Rochester, 1985–1994), a Research Professor at Macquarie University (Sydney, 1994–2000), and a Senior Scientist at QED Technologies (2000–2015). Throughout his career, optical modeling has remained one of his primary interests.
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Johannes Ruoff
Johannes Ruoff is a Senior Optical Designer at Carl Zeiss SMT GmbH. He holds a PhD in Physics from the University of Tübingen, Germany. His research interests are in EUV optics, high-NA imaging, electromagnetic diffraction theory, and polarization aspects in lithography.
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Andreas Flesch
Andreas Flesch is a staff member at the Corporate Research and Technology department at ZEISS in Oberkochen since 2013. His main research interests include optimization algorithms, mathematical surface descriptions, novel ray-based approaches for optical system modeling, and the efficient implementation of these methods in optical design software. He holds a PhD in Theoretical Physics from RWTH Aachen University, Germany.
Norbert Kerwien is the Director of the Optics Concepts group at Corporate Research and Technology of ZEISS. After his PhD on Polarization Effects in Microscopic Image Formation at the Institute of Applied Optics, University of Stuttgart, he joined the lithography division of ZEISS in 2006. Since 2010, he works at Corporate Research and Technology. Among his primary interests are physical optical image formation, computational imaging, and optical design.
Abstract
Efficient performance assessment is essential during the design of systems involving complex aspheres. We present new classes of pupil sampling schemes that, with a reduced number of rays, yield accurate estimates of the RMS wavefront aberration over a circular pupil. It turns out that the number of samples in the pupil can be reduced by a factor of about 0.7, and these ideas can also be expected to lead to a similar additional reduction factor when averaging over the field and color. Beyond that, analysis of a patented lens system is used to establish the path to further significant reductions.
About the authors
Greg W. Forbes is an Adjunct Professor in Physics at Macquarie University (Sydney) and the Director of Scisense Consulting Pty Ltd. Following his PhD in Theoretical Physics at the Australian National University, he was a Fulbright Fellow at the Optical Sciences Center (Tucson), a tenured faculty member of The Institute of Optics (Rochester, 1985–1994), a Research Professor at Macquarie University (Sydney, 1994–2000), and a Senior Scientist at QED Technologies (2000–2015). Throughout his career, optical modeling has remained one of his primary interests.
Johannes Ruoff is a Senior Optical Designer at Carl Zeiss SMT GmbH. He holds a PhD in Physics from the University of Tübingen, Germany. His research interests are in EUV optics, high-NA imaging, electromagnetic diffraction theory, and polarization aspects in lithography.
Andreas Flesch is a staff member at the Corporate Research and Technology department at ZEISS in Oberkochen since 2013. His main research interests include optimization algorithms, mathematical surface descriptions, novel ray-based approaches for optical system modeling, and the efficient implementation of these methods in optical design software. He holds a PhD in Theoretical Physics from RWTH Aachen University, Germany.
Norbert Kerwien is the Director of the Optics Concepts group at Corporate Research and Technology of ZEISS. After his PhD on Polarization Effects in Microscopic Image Formation at the Institute of Applied Optics, University of Stuttgart, he joined the lithography division of ZEISS in 2006. Since 2010, he works at Corporate Research and Technology. Among his primary interests are physical optical image formation, computational imaging, and optical design.
Acknowledgments
We are grateful to Alexander Epple for the helpful discussions.
Appendix
The details for one sector for each of the cubature schemes of Section 3.2 are given here. The weights are for integrating over just the first half of the sector, so they sum to π/2 divided by the number of sectors. These points and their weights must be replicated in order to fill either the semi-circle or the entire circle, so the weights for points on lines of symmetry get doubled while that for the origin is multiplied by up to twice the number of sectors. The sum of all the weights is then π/2 and π, respectively.
Top left in Figure 4 has six sectors:
Top right in Figure 4 has four sectors:
Bottom left in Figure 4 has four sectors:
Bottom right in Figure 4 has four sectors. In this case, increment the angles by π/4 to obtain the geometry shown in the figure, which was rotated for purely cosmetic reasons:
Configuration at the top in Figure 5 has two sectors:
Configuration at the bottom in Figure 5 has two sectors:
References
[1] G. W. Forbes, J. Opt. Soc. Am. A5, 1943–1956 (1988).10.1364/JOSAA.5.001943Search in Google Scholar
[2] R. Cools, Acta Numerica, 6, 1–54 (1997).10.1017/S0962492900002701Search in Google Scholar
[3] R. Cools and K. J. Kim, Korean J. Comput. Appl. Math. 7, 477–485 (2000).10.1007/BF03012263Search in Google Scholar
[4] R. Cools, J. Complexity 19, 445–453 (2003).10.1016/S0885-064X(03)00011-6Search in Google Scholar
[5] G. W. Forbes, Opt. Exp. 21, 19061–19081 (2013).10.1364/OE.21.019061Search in Google Scholar PubMed
[6] C. Menke and G. W. Forbes, Adv. Opt. Technol. 2, 97–109 (2012).10.1515/aot-2012-0072Search in Google Scholar
©2016 THOSS Media & De Gruyter
Articles in the same Issue
- Cover and Frontmatter
- Community
- News from the European Optical Society
- Conference Notes
- Conference Calendar
- Topical issue: Aspheric optics
- Editorial
- Aspheric optics: from design to manufacturing and aspheric metrology
- Tutorial
- Exploring the unlimited possibilities of modular aspheric Gauss to top-hat beam shaping
- Review Articles
- Metrology for the production process of aspheric lenses
- Breathing life into aspheric dreams
- Research Articles
- Ray selection for optimization of rotationally symmetric systems
- Simulation of imperfections in plastic lenses – transferring local refractive index changes into surface shape modifications
- Research Article
- Telecentric line scanning system based on a ring surface mirror for inline processes
Articles in the same Issue
- Cover and Frontmatter
- Community
- News from the European Optical Society
- Conference Notes
- Conference Calendar
- Topical issue: Aspheric optics
- Editorial
- Aspheric optics: from design to manufacturing and aspheric metrology
- Tutorial
- Exploring the unlimited possibilities of modular aspheric Gauss to top-hat beam shaping
- Review Articles
- Metrology for the production process of aspheric lenses
- Breathing life into aspheric dreams
- Research Articles
- Ray selection for optimization of rotationally symmetric systems
- Simulation of imperfections in plastic lenses – transferring local refractive index changes into surface shape modifications
- Research Article
- Telecentric line scanning system based on a ring surface mirror for inline processes
