Freeform imaging systems: Fermat's principle unlocks "first time right" design

Fabian Duerr; Hugo Thienpont

doi:10.1038/s41377-021-00538-1

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Freeform imaging systems: Fermat's principle unlocks "first time right" design

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- Freeform imaging systems: Fermat's principle unlocks "first time right" design
- Freeform imaging systems: Fermat's principle unlocks "first time right" design
- LSA 2021年10卷第6期页码：1029-1040
- Affiliations：
  
  Brussels Photonics, Department of Applied Physics and Photonics (B-PHOT TONA) Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
- Author bio：
  
  Fabian Duerr (fduerr@b-phot.org)
- Funds：
- DOI：10.1038/s41377-021-00538-1
  中图分类号：
- 纸质出版日期：2021-06-30，
  
  网络出版日期：2021-05-06，
  
  收稿日期：2020-10-26，
  
  修回日期：2021-04-07，
  
  录用日期：2021-04-18
- Accepted：
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Freeform imaging systems: Fermat's principle unlocks "first time right" design[J]. LSA, 2021,10(6):1029-1040.

Duerr, F. & Thienpont, H. Freeform imaging systems: Fermat's principle unlocks "first time right" design. Light: Science & Applications, 10, 1029-1040 (2021).
Freeform imaging systems: Fermat's principle unlocks "first time right" design[J]. LSA, 2021,10(6):1029-1040. DOI： 10.1038/s41377-021-00538-1.

Duerr, F. & Thienpont, H. Freeform imaging systems: Fermat's principle unlocks "first time right" design. Light: Science & Applications, 10, 1029-1040 (2021). DOI： 10.1038/s41377-021-00538-1.

摘要

Abstract

For more than 150 years

scientists have advanced aberration theory to describe

analyze and eliminate imperfections that disturb the imaging quality of optical components and systems. Simultaneously

they have developed optical design methods for and manufacturing techniques of imaging systems with ever-increasing complexity and performance up to the point where they are now including optical elements that are unrestricted in their surface shape. These so-called optical freeform elements offer degrees of freedom that can greatly extend the functionalities and further boost the specifications of state-of-the-art imaging systems. However

the drastically increased number of surface coefficients of these freeform surfaces poses severe challenges for the optical design process

such that the deployment of freeform optics remained limited until today. In this paper

we present a deterministic direct optical design method for freeform imaging systems based on differential equations derived from Fermat's principle and solved using power series. The method allows calculating the optical surface coefficients that ensure minimal image blurring for each individual order of aberrations. We demonstrate the systematic

deterministic

scalable

and holistic character of our method with catoptric and catadioptric design examples. As such we introduce a disruptive methodology to design optical imaging systems from scratch

we largely reduce the "trial-and-error" approach in present-day optical design

and we pave the way to a fast-track uptake of freeform elements to create the next-generation high-end optics. We include a user application that allows users to experience this unique design method hands-on.

关键词

Keywords

references

Maddison, F. Early astronomical and mathematical instruments: a brief survey of sources and modern studies.Hist. Sci.2, 17–50 (1963)..

Turner, G. L. The history of optical instruments: a brief survey of sources and modern studies.Hist. Sci.8, 53–93 (1969)..

Johnson, R. B. A historical perspective on understanding optical aberrations.Proc. SPIE10263, (1992)..

Fang, F. Z. et al. Manufacturing and measurement of freeform optics.CIRP Ann.62, 823–846 (2013)..

Gissibl, T. et al. Two-photon direct laser writing of ultracompact multi-lens objectives.Nat. Photonics10, 554–560 (2016)..

Gissibl, T. et al. Sub-micrometre accurate free-form optics by three-dimensional printing on single-mode fibres.Nat. Commun.7, 11763 (2016)..

Hong, Z. H.&Liang, R. G. IR-laser assisted additive freeform optics manufacturing.Sci. Rep.7, 7145 (2017)..

Thompson, K. P.&Rolland, J. P. Freeform optical surfaces: a revolution in imaging optical design.Opt. Photonics N.23, 30–35 (2012)..

Reimers, J. et al. Freeform spectrometer enabling increased compactness.Light. : Sci. Appl.6, e17026 (2017)..

Jahn, W., Ferrari, M.&Hugot, E. Innovative focal plane design for large space telescope using freeform mirrors.Optica4, 1188–1195 (2017)..

West, G. J.&Howard, J. M. Application for freeform optics at NASA.https://ntrs.nasa.gov/search.jsp?R=20170010419https://ntrs.nasa.gov/search.jsp?R=20170010419(2017).

Zou, Y. C. et al. Miniature adjustable-focus endoscope with a solid electrically tunable lens.Opt. Express23, 20582–20592 (2015)..

Li, J. W. et al. Two-photon polymerisation 3D printed freeform micro-optics for optical coherence tomography fibre probes.Sci. Rep.8, 14789 (2018)..

Kress, B. C.Optical Architectures for Augmented-, Virtual-, and Mixed-Reality Headsets(SPIE Press, 2020).

Wagner, C.&Harned, N. EUV lithography: lithography gets extreme.Nat. Photonics4, 24–26 (2010)..

Williamson, D. M. Freeforms in EUV lithography projection optics. InProceedings of Freeform Optics 2015FM3B. 4 (Optical Society of America, 2015)https://www.osapublishing.org/abstract.cfm?uri=freeform-2015-FM3B.4https://www.osapublishing.org/abstract.cfm?uri=freeform-2015-FM3B.4..

Wills, S. Freeform optics: notes from the revolution.Opt. Photonics N.28, 34–41 (2017)..

The Scott Partnership. Optical simulation software.Nat. Photonics4, 256–257 (2010)..

Sahin, F. E. Open-source optimization algorithms for optical design.Optik178, 1016–1022 (2019)..

Feder, D. P. Automatic optical design.Appl. Opt.2, 1209–1226 (1963)..

van Turnhout, M.&Bociort, F. Instabilities and fractal basins of attraction in optical system optimization.Opt. Express17, 314–328 (2009)..

Shannon, R. R.The Art and Science of Optical Design(Cambridge University Press, 1997).

Gimenez-Benitez, P. et al. Simultaneous multiple surface optical design method in three dimensions.Optical Eng.43, 1489–1502 (2004)..

Liu, J. Y., Benítez, P.&Miñano, J. C. Single freeform surface imaging design with unconstrained object to image mapping.Opt. Express22, 30538–30546 (2014)..

Duerr, F. et al. Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces.Opt. Express20, 10839–10846 (2012)..

Duerr, F. et al. Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles.Opt. Express20, 5576–5585 (2012)..

Hicks, R. A. Controlling a ray bundle with a free-form reflector.Opt. Lett.33, 1672–1674 (2008)..

Yang, T. et al. Design method of freeform off-axis reflective imaging systems with a direct construction process.Opt. Express22, 9193–9205 (2014)..

Volatier, J. B.&Druart, G. Differential method for freeform optics applied to two-mirror off-axis telescope design.Opt. Lett.44, 1174–1177 (2019)..

Volatier, J. B., Duveau, L.&Druart, G. An exploration of the freeform two-mirror off-axis solution space.J. Phys. : Photonics2, 014004 (2020)..

Croke, C. B.&Hicks, R. A. Solution to the bundle-to-bundle mapping problem of geometric optics using four freeform reflectors.J. Optical Soc. Am. A31, 2097–2104 (2014)..

Yang, T., Jin, G. F.&Zhu, J. Automated design of freeform imaging systems.Light. : Sci. Appl.6, e17081 (2017)..

Xu, C. et al. Automatic optical path configuration variation in off-axis mirror system design.Opt. Express27, 15251–15261 (2019)..

Carneiro de Albuquerque, B. F., Luis de Sousa, F.&Montes, A. S. Multi-objective approach for the automatic design of optical systems.Opt. Express24, 6619–6643 (2016)..

Wu, R. M., Sasián, J.&Liang, R. G. Algorithm for designing free-form imaging optics with nonrational B-spline surfaces.Appl. Opt.56, 2517–2522 (2017)..

Chrisp, M. P., Primeau, B.&Echter, M. A. Imaging freeform optical systems designed with NURBS surfaces.Optical Eng.55, 071208 (2016)..

Houllier, T.&Lépine, T. Comparing optimization algorithms for conventional and freeform optical design.Opt. Express27, 18940–18957 (2019)..

Korsch, D.Reflective Optics207–259 (Academic Press, 1991).

Rakich, A.&Rumsey, N. Method for deriving the complete solution set for three-mirror anastigmatic telescopes with two spherical mirrors.J. Optical Soc. Am. A19, 1398–1405 (2002)..

Nie, Y. F. et al. Freeform optical design for a nonscanning corneal imaging system with a convexly curved image.Appl. Opt.56, 5630–5638 (2017)..

González-Acuña, R. G., Chaparro-Romo, H. A.&Gutiérrez-Vega, J. C. Analytic solution of the Eikonal for a stigmatic singlet lens.Phys. Scr.95, 085201 (2020)..

Howard, J. M.&Stone, B. D. Imaging with three spherical mirrors.Appl. Opt.39, 3216–3231 (2000)..

Howard, J. M.&Stone, B. D. Imaging with four spherical mirrors.Appl. Opt.39, 3232–3242 (2000)..

Thompson, K. Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry.J. Optical Soc. Am. A22, 1389–1401 (2005)..

Thompson, K. P. Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: spherical aberration.J. Optical Soc. Am. A26, 1090–1100 (2009)..

Thompson, K. P. Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the comatic aberrations.J. Optical Soc. Am. A27, 1490–1504 (2010)..

Fuerschbach, K., Rolland, J. P.&Thompson, K. P. Extending Nodal Aberration Theory to include mount-induced aberrations with application to freeform surfaces.Opt. Express20, 20139–20155 (2012)..

Yang, T., Zhu, J.&Jin, G. F. Nodal aberration properties of coaxial imaging systems using Zernike polynomial surfaces.J. Optical Soc. Am. A32, 822–836 (2015)..

Shi, H. D. et al. Analysis of nodal aberration properties in off-axis freeform system design.Appl. Opt.55, 6782–6790 (2016)..

Bauer, A., Schiesser, E. M.&Rolland, J. P. Starting geometry creation and design method for freeform optics.Nat. Commun.9, 1756 (2018)..

Zhong, Y.&Gross, H. Initial system design method for non-rotationally symmetric systems based on Gaussian brackets and Nodal aberration theory.Opt. Express25, 10016–10030 (2017)..

Duerr, F.&Thienpont, H. Optical design methods for imaging systems and optical systems designed therewith. Patent No. WO/2019/129872 (2019).

Barakat, R.&Houston, A. The aberrations of non-rotationally symmetric systems and their diffraction effects.Opt. Acta. : Int. J. Opt.13, 1–30 (1966)..

Gross, H. et al.Handbook of Optical Systems: Volume 3: Aberration Theory and Correction of Optical Systems(Wiley-VCH, 2007).

Said-Houari, B. inDifferential Equations: Methods and Applications(ed Said-Houari, B. ) 125–140 (Springer, 2015).

Lawson, C. L.&Hanson, R. J.Solving Least Squares Problems(Society for Industrial and Applied Mathematics, 1995),https://doi.org/10.1137/1.9781611971217https://doi.org/10.1137/1.9781611971217..

Kiontke, S. R. Monolithic freeform element.Proc. SPIE9575, 95750G (2015)..

Fuchs, U.&Kiontke, S. R.Proc. SPIE9948, 99480L (2016)..

Reshidko, D.&Sasián, J. Method for the design of nonaxially symmetric optical systems using free-form surfaces.Opt. Eng.57, 101704 (2018)..

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