Abstract

In this paper, we propose a framework of starting points generation for freeform reflective triplet using back-propagation neural network based deep-learning. The network is trained using various system specifications and the corresponding surface data obtained by system evolution as the data set. Good starting points of specific system specifications for further optimization can be generated immediately using the obtained network in general. The feasibility of this design process is validated by designing the Wetherell-configuration freeform off-axis reflective triplet. The amount of time and human effort as well as the dependence on advanced design skills are significantly reduced. These results highlight the powerful ability of deep learning in the field of freeform imaging optical design.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  16. T. Yang, J. Zhu, X. Wu, and G. Jin, “Direct design of freeform surfaces and freeform imaging systems with a point-by-point three-dimensional construction-iteration method,” Opt. Express 23(8), 10233–10246 (2015).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  21. Z. Cao, N. Guo, M. Li, K. Yu, and K. Gao, “Back propagation neutral network based signal acquisition for Brillouin distributed optical fiber sensors,” Opt. Express 27(4), 4549–4561 (2019).
    [Crossref] [PubMed]
  22. https://en.wikipedia.org/wiki/Artificial_neural_network
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  24. https://en.wikipedia.org/wiki/Feedforward_neural_network
  25. https://en.wikipedia.org/wiki/Backpropagation
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  27. W. B. Wetherell and D. A. Womble, “All-reflective three element objective,” U.S. Patent 4,240,707 (23 December, 1980).
  28. CODE V Documentation Library, Synopsys Inc. (2018).

2019 (1)

2018 (5)

A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9(1), 1756 (2018).
[Crossref] [PubMed]

D. Reshidko and J. Sasian, “Method for the design of nonaxially symmetric optical systems using free-form surfaces,” Opt. Eng. 57(10), 1 (2018).
[Crossref]

X. Liu, T. Gong, G. Jin, and J. Zhu, “Design method for assembly-insensitive freeform reflective optical systems,” Opt. Express 26(21), 27798–27811 (2018).
[Crossref] [PubMed]

R. Horisaki, R. Takagi, and J. Tanida, “Deep-learning-generated holography,” Appl. Opt. 57(14), 3859–3863 (2018).
[Crossref] [PubMed]

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

2017 (4)

2016 (1)

2015 (4)

2013 (1)

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

2012 (2)

2011 (1)

2010 (1)

D. Cheng, Y. Wang, and H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849, 78490Q (2010).
[Crossref]

2009 (1)

Bauer, A.

A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9(1), 1756 (2018).
[Crossref] [PubMed]

Beale, M. H.

M. T. Hagan, H. B. Demuth, M. H. Beale, and Neural Network Design, (PWS Publishing, 1996).

Beier, M.

Benítez, P.

Cao, Z.

Cheng, D.

D. Cheng, Y. Wang, and H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849, 78490Q (2010).
[Crossref]

Damm, C.

Demuth, H. B.

M. T. Hagan, H. B. Demuth, M. H. Beale, and Neural Network Design, (PWS Publishing, 1996).

Duerr, F.

Eberhardt, R.

Evans, C.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Fang, F.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Flügel-Paul, T.

Froustey, E.

M. T. McCann, E. Froustey, M. Unser, M. Unser, and Kyong Hwan Jin, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26(9), 4509–4522 (2017).
[Crossref] [PubMed]

Fuerschbach, K.

Gao, K.

Gebhardt, A.

Gong, T.

Gross, H.

Günaydin, H.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

Guo, N.

Hagan, M. T.

M. T. Hagan, H. B. Demuth, M. H. Beale, and Neural Network Design, (PWS Publishing, 1996).

Hartung, J.

Horisaki, R.

Hou, W.

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

Hua, H.

D. Cheng, Y. Wang, and H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849, 78490Q (2010).
[Crossref]

Infante, J.

Ji, Z.

Jin, G.

Jin, G. F.

T. Yang, G. F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6(10), e17081 (2017).
[Crossref] [PubMed]

Li, M.

Lin, W.

Liu, C.

Liu, X.

McCann, M. T.

M. T. McCann, E. Froustey, M. Unser, M. Unser, and Kyong Hwan Jin, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26(9), 4509–4522 (2017).
[Crossref] [PubMed]

Meng, Q.

Meuret, Y.

Miñano, J. C.

Muñoz, F.

Nie, Y.

Ozcan, A.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

Peschel, T.

Reshidko, D.

D. Reshidko and J. Sasian, “Method for the design of nonaxially symmetric optical systems using free-form surfaces,” Opt. Eng. 57(10), 1 (2018).
[Crossref]

Risse, S.

Rivenson, Y.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

Rolland, J. P.

A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9(1), 1756 (2018).
[Crossref] [PubMed]

K. P. Thompson and J. P. Rolland, “Freeform optical surfaces: a revolution in imaging optical design,” Opt. Photonics News 23(6), 30–35 (2012).
[Crossref]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19(22), 21919–21928 (2011).
[Crossref] [PubMed]

Santamaría, A.

Sasian, J.

D. Reshidko and J. Sasian, “Method for the design of nonaxially symmetric optical systems using free-form surfaces,” Opt. Eng. 57(10), 1 (2018).
[Crossref]

Scheiding, S.

Schiesser, E. M.

A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9(1), 1756 (2018).
[Crossref] [PubMed]

Straif, C.

Stumpf, D.

Surman, P.

Takagi, R.

Tanida, J.

Teng, D.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

Thibault, S.

Thienpont, H.

Thompson, K. P.

K. P. Thompson and J. P. Rolland, “Freeform optical surfaces: a revolution in imaging optical design,” Opt. Photonics News 23(6), 30–35 (2012).
[Crossref]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19(22), 21919–21928 (2011).
[Crossref] [PubMed]

Tünnermann, A.

Unser, M.

M. T. McCann, E. Froustey, M. Unser, M. Unser, and Kyong Hwan Jin, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26(9), 4509–4522 (2017).
[Crossref] [PubMed]

M. T. McCann, E. Froustey, M. Unser, M. Unser, and Kyong Hwan Jin, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26(9), 4509–4522 (2017).
[Crossref] [PubMed]

Wang, D.

Wang, H.

Wang, K.

Wang, Y.

Weckenmann, A.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Wu, X.

Yang, T.

Yu, K.

Zeitner, U. D.

Zhang, G.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Zhang, X.

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Zhang, Y.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

Zhu, J.

Zhuang, Z.

Appl. Opt. (5)

CIRP Ann. (1)

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

IEEE Trans. Image Process. (1)

M. T. McCann, E. Froustey, M. Unser, M. Unser, and Kyong Hwan Jin, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26(9), 4509–4522 (2017).
[Crossref] [PubMed]

J. Opt. (1)

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

Light Sci. Appl. (2)

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7(2), 17141 (2018).
[Crossref] [PubMed]

T. Yang, G. F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6(10), e17081 (2017).
[Crossref] [PubMed]

Nat. Commun. (1)

A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9(1), 1756 (2018).
[Crossref] [PubMed]

Opt. Eng. (1)

D. Reshidko and J. Sasian, “Method for the design of nonaxially symmetric optical systems using free-form surfaces,” Opt. Eng. 57(10), 1 (2018).
[Crossref]

Opt. Express (7)

J. C. Miñano, P. Benítez, W. Lin, J. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17(26), 24036–24044 (2009).
[Crossref] [PubMed]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19(22), 21919–21928 (2011).
[Crossref] [PubMed]

F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles,” Opt. Express 20(5), 5576–5585 (2012).
[Crossref] [PubMed]

T. Yang, J. Zhu, X. Wu, and G. Jin, “Direct design of freeform surfaces and freeform imaging systems with a point-by-point three-dimensional construction-iteration method,” Opt. Express 23(8), 10233–10246 (2015).
[Crossref] [PubMed]

Y. Nie, H. Thienpont, and F. Duerr, “Multi-fields direct design approach in 3D: calculating a two-surface freeform lens with an entrance pupil for line imaging systems,” Opt. Express 23(26), 34042–34054 (2015).
[Crossref] [PubMed]

X. Liu, T. Gong, G. Jin, and J. Zhu, “Design method for assembly-insensitive freeform reflective optical systems,” Opt. Express 26(21), 27798–27811 (2018).
[Crossref] [PubMed]

Z. Cao, N. Guo, M. Li, K. Yu, and K. Gao, “Back propagation neutral network based signal acquisition for Brillouin distributed optical fiber sensors,” Opt. Express 27(4), 4549–4561 (2019).
[Crossref] [PubMed]

Opt. Photonics News (1)

K. P. Thompson and J. P. Rolland, “Freeform optical surfaces: a revolution in imaging optical design,” Opt. Photonics News 23(6), 30–35 (2012).
[Crossref]

Proc. SPIE (1)

D. Cheng, Y. Wang, and H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849, 78490Q (2010).
[Crossref]

Other (7)

https://en.wikipedia.org/wiki/Artificial_neural_network

C. Gannon and R. Liang, “Using machine learning to create high-efficiency freeform illumination design tools,” arXiv preprint arXiv: 1903.11166v1 (2018).

https://en.wikipedia.org/wiki/Feedforward_neural_network

https://en.wikipedia.org/wiki/Backpropagation

M. T. Hagan, H. B. Demuth, M. H. Beale, and Neural Network Design, (PWS Publishing, 1996).

W. B. Wetherell and D. A. Womble, “All-reflective three element objective,” U.S. Patent 4,240,707 (23 December, 1980).

CODE V Documentation Library, Synopsys Inc. (2018).

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Figures (5)

Fig. 1
Fig. 1 Illustration of the design framework.
Fig. 2
Fig. 2 Topology diagram of the BP network in the design framework.
Fig. 3
Fig. 3 Design of the initial base system BaseSys1. (a) The initial planar system. (b) The system generate by the CI method and the structure constraints used in the optimization. (c) Final design result of BaseSys1.
Fig. 4
Fig. 4 (a) The average RMS spot diameter of the six sample fields of each system. (b) The maximum absolute distortion among the sample fields of each system.
Fig. 5
Fig. 5 Output systems of several typical system specifications generated by the network.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

{ Half- X F O V min Half- X F O V Half- X F O V max Half- Y F O V min Half- Y F O V Half- Y F O V max E F L min E F L E F L max F # min F # F # max .
I N P U T m 1 = b m 1 + j 4 w j m 1 S S P ( j ) ,
O U T P U T m 1 = f m 1 ( b m 1 + j 4 w j m 1 S S P ( j ) ) ,
z ( x , y ) = A 3 x 2 + A 5 y 2 + A 7 x 2 y + A 9 y 3 + A 10 x 4 + A 12 x 2 y 2 + A 14 y 4 ,

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