Abstract

Traditional imaging design methods can often be ineffective when designing aspheric systems because of the large number of optimization parameters and lack of a good starting point. They are often trapped in a poor local minimum and it can be highly time-consuming to find a good solution in a bumpy design landscape. The simultaneous multiple surface (SMS) method can significantly shorten the time and effort needed to find a desired solution by providing a starting point to optimize close to a good local minimum. We investigate here two design examples and compare them with similar designs obtained via traditional design approaches, as well as global optimization. In the examples considered here, the SMS method combined with a shorter optimization leads to an optimal design.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  5. J. Nagar, S. D. Campbell, and D. H. Werner, “Apochromatic Singlets Enabled by Metasurface-Augmented GRIN Lenses,” Optica 5(2), 99–102 (2018).
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  6. C. Menke, “Application of particle swarm optimization to the automatic design of optical systems,” Proc. SPIE 10690, 106901A (2018).
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    [Crossref]
  8. F. Bociort and M. van Turnhout, “Finding new local minima in lens design landscapes by constructing saddle points,” Opt. Eng. 48(6), 063001 (2009).
    [Crossref]
  9. Z. Hou, I. Livshits, and F. Bociort, “One-dimensional searches for finding new lens design solutions efficiently,” Appl. Opt. 55(36), 10449–10456 (2016).
    [Crossref] [PubMed]
  10. L. Wang, “Advances in the simultaneous multiple surface optical design method for imaging and non-imaging applications,” Doctoral thesis, Universidad Politécnica de Madrid (2012).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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  21. CODE V® Optimization Reference Manual, Synopsys, inc., www.synopsis.com .

2018 (2)

J. Nagar, S. D. Campbell, and D. H. Werner, “Apochromatic Singlets Enabled by Metasurface-Augmented GRIN Lenses,” Optica 5(2), 99–102 (2018).
[Crossref]

C. Menke, “Application of particle swarm optimization to the automatic design of optical systems,” Proc. SPIE 10690, 106901A (2018).

2016 (1)

2014 (1)

P. Benitez, J. C. Miñano, M. Nikolic, J. Liu, J. Infante, and F. Duerr, “Conditions for perfect focusing multiple point sources with the SMS design method,” Proc. SPIE 9191, 919102 (2014).
[Crossref]

2013 (1)

2012 (2)

2011 (1)

L. Wang, P. Benítez, J. C. Miñano, J. Infante, and G. Biot, “Progress in the SMS design method for imaging optics,” Proc. SPIE 8128, 81280F (2011).
[Crossref]

2009 (2)

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]

F. Bociort and M. van Turnhout, “Finding new local minima in lens design landscapes by constructing saddle points,” Opt. Eng. 48(6), 063001 (2009).
[Crossref]

2007 (1)

1999 (1)

K. E. Moore, “Algorithm for global optimization of optical systems based on genetic competition,” Proc. SPIE 3780, 40–47 (1999).
[Crossref]

1994 (1)

D. Shafer, “Global Optimization in Optical Design,” Comput. Phys. 8(2), 188–195 (1994).
[Crossref]

1993 (1)

T. G. Kuper and T. I. Harris, “Global optimization for lens design: an emerging technology,” Proc. SPIE 1781, 14–28 (1993).
[Crossref]

1991 (1)

G. W. Forbes and A. E. Jones, “Towards global optimization with adaptive simulated annealing,” Proc. SPIE 1354, 144–153 (1991).
[Crossref]

Benitez, P.

P. Benitez, J. C. Miñano, M. Nikolic, J. Liu, J. Infante, and F. Duerr, “Conditions for perfect focusing multiple point sources with the SMS design method,” Proc. SPIE 9191, 919102 (2014).
[Crossref]

Benítez, P.

Biot, G.

Bociort, F.

Z. Hou, I. Livshits, and F. Bociort, “One-dimensional searches for finding new lens design solutions efficiently,” Appl. Opt. 55(36), 10449–10456 (2016).
[Crossref] [PubMed]

F. Bociort and M. van Turnhout, “Finding new local minima in lens design landscapes by constructing saddle points,” Opt. Eng. 48(6), 063001 (2009).
[Crossref]

Campbell, S. D.

de la Fuente, M.

Duerr, F.

Forbes, G. W.

G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express 15(8), 5218–5226 (2007).
[Crossref] [PubMed]

G. W. Forbes and A. E. Jones, “Towards global optimization with adaptive simulated annealing,” Proc. SPIE 1354, 144–153 (1991).
[Crossref]

Harris, T. I.

T. G. Kuper and T. I. Harris, “Global optimization for lens design: an emerging technology,” Proc. SPIE 1781, 14–28 (1993).
[Crossref]

Hou, Z.

Infante, J.

P. Benitez, J. C. Miñano, M. Nikolic, J. Liu, J. Infante, and F. Duerr, “Conditions for perfect focusing multiple point sources with the SMS design method,” Proc. SPIE 9191, 919102 (2014).
[Crossref]

L. Wang, P. Benítez, J. C. Miñano, J. Infante, and G. Biot, “Progress in the SMS design method for imaging optics,” Proc. SPIE 8128, 81280F (2011).
[Crossref]

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]

Infante, J. M.

Jones, A. E.

G. W. Forbes and A. E. Jones, “Towards global optimization with adaptive simulated annealing,” Proc. SPIE 1354, 144–153 (1991).
[Crossref]

Kuper, T. G.

T. G. Kuper and T. I. Harris, “Global optimization for lens design: an emerging technology,” Proc. SPIE 1781, 14–28 (1993).
[Crossref]

Lin, W.

Liu, J.

P. Benitez, J. C. Miñano, M. Nikolic, J. Liu, J. Infante, and F. Duerr, “Conditions for perfect focusing multiple point sources with the SMS design method,” Proc. SPIE 9191, 919102 (2014).
[Crossref]

Livshits, I.

Menke, C.

C. Menke, “Application of particle swarm optimization to the automatic design of optical systems,” Proc. SPIE 10690, 106901A (2018).

Meuret, Y.

Miñano, J. C.

Moore, K. E.

K. E. Moore, “Algorithm for global optimization of optical systems based on genetic competition,” Proc. SPIE 3780, 40–47 (1999).
[Crossref]

Muñoz, F.

Nagar, J.

Nikolic, M.

P. Benitez, J. C. Miñano, M. Nikolic, J. Liu, J. Infante, and F. Duerr, “Conditions for perfect focusing multiple point sources with the SMS design method,” Proc. SPIE 9191, 919102 (2014).
[Crossref]

Santamaría, A.

Shafer, D.

D. Shafer, “Global Optimization in Optical Design,” Comput. Phys. 8(2), 188–195 (1994).
[Crossref]

Thienpont, H.

van Turnhout, M.

F. Bociort and M. van Turnhout, “Finding new local minima in lens design landscapes by constructing saddle points,” Opt. Eng. 48(6), 063001 (2009).
[Crossref]

Wang, L.

L. Wang, P. Benítez, J. C. Miñano, J. Infante, and G. Biot, “Progress in the SMS design method for imaging optics,” Proc. SPIE 8128, 81280F (2011).
[Crossref]

Werner, D. H.

Appl. Opt. (1)

Comput. Phys. (1)

D. Shafer, “Global Optimization in Optical Design,” Comput. Phys. 8(2), 188–195 (1994).
[Crossref]

Opt. Eng. (1)

F. Bociort and M. van Turnhout, “Finding new local minima in lens design landscapes by constructing saddle points,” Opt. Eng. 48(6), 063001 (2009).
[Crossref]

Opt. Express (5)

Optica (1)

Proc. SPIE (6)

C. Menke, “Application of particle swarm optimization to the automatic design of optical systems,” Proc. SPIE 10690, 106901A (2018).

G. W. Forbes and A. E. Jones, “Towards global optimization with adaptive simulated annealing,” Proc. SPIE 1354, 144–153 (1991).
[Crossref]

K. E. Moore, “Algorithm for global optimization of optical systems based on genetic competition,” Proc. SPIE 3780, 40–47 (1999).
[Crossref]

T. G. Kuper and T. I. Harris, “Global optimization for lens design: an emerging technology,” Proc. SPIE 1781, 14–28 (1993).
[Crossref]

L. Wang, P. Benítez, J. C. Miñano, J. Infante, and G. Biot, “Progress in the SMS design method for imaging optics,” Proc. SPIE 8128, 81280F (2011).
[Crossref]

P. Benitez, J. C. Miñano, M. Nikolic, J. Liu, J. Infante, and F. Duerr, “Conditions for perfect focusing multiple point sources with the SMS design method,” Proc. SPIE 9191, 919102 (2014).
[Crossref]

Other (6)

J. Chaves, Introduction to Nonimaging Optics, Second edition, Chapter 8 (CRC, 2015).

L. Wang, “Advances in the simultaneous multiple surface optical design method for imaging and non-imaging applications,” Doctoral thesis, Universidad Politécnica de Madrid (2012).

R. Kingslake, Lens Design Fundamentals (Academic, 1978).

W. J. Smith, Modern Optical Engineering, 3rd edition, (McGraw-Hill, 2000).

R. E. Fisher and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).

CODE V® Optimization Reference Manual, Synopsys, inc., www.synopsis.com .

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Figures (13)

Fig. 1
Fig. 1 An illustration of an optical design landscape in 2D (a) and 3D (b).
Fig. 2
Fig. 2 SMS 2D design introduced to CODE V after fitting the surfaces to Forbes Qcon polynomials. The change of the spot diameter through the fields is shown on the right side.
Fig. 3
Fig. 3 Flowchart for our different design approaches.
Fig. 4
Fig. 4 The strategy for stepwise optimization. The blue shapes represent the optical surfaces. Each cross represents a freedom on the surface described by the Qcon polynomial. The blue arrows indicate how the freedoms are added step by step up to the highest order coefficients used for Qcon polynomial.
Fig. 5
Fig. 5 System 1: the system shapes obtained using different design approaches.
Fig. 6
Fig. 6 RMS spot diameter distribution curves for different design approaches considered: complete curves (a); enlarged section (b). The RMS spot diameter values of the starting spherical system vary from 60 to 96 µm and are not presented in the graph.
Fig. 7
Fig. 7 An illustration of the design landscape for system 1. We have found three equally good local minima which form two groups. Solution A (MF 0.0301) forms the first group. Solution B (MF 0.0461) and Solution C (MF 0.0450) form the second group.
Fig. 8
Fig. 8 Comparison of the efficiency of different design methods analyzed, evaluated as the merit function value versus the number of cycles performed. The merit function value of the resulting system from GS is 0.0301.
Fig. 9
Fig. 9 System 2: the system shapes obtained using different design approaches.
Fig. 10
Fig. 10 RMS spot diameter curves for second system using different design approaches: complete curves (a); enlarged section (b). The RMS spot diameter values of the starting spherical system vary from 124 to 142 µm from the center to the full field and are not shown in the graph.
Fig. 11
Fig. 11 Comparison of the efficiency of different design methods. The starting points are shown at zero cycles and are connected with the straight lines with the results obtained using different design methods. The merit function value of the GS result is 1.03.
Fig. 12
Fig. 12 Evolution of the minima with the change of aspheric coefficients (system 1). Four minima are found with conic surfaces. They become three minima when optimized with aspheric coefficient up to 12th order. All three are found with the different approaches we used. M1-P and M3-P are the two solutions previously found with the different approaches(Fig. 5).
Fig. 13
Fig. 13 Evolution of the minima with the change of aspheric coefficients (system 2). Three minima are found with conic surfaces. Adding higher-order aspheric coefficients (up to 16th order) to these minima results in three different solutions. M1-P is the solutions found by the two-steps approach, and M2-P is the solution found by the SMS with optimization in Fig. 9.

Tables (3)

Tables Icon

Table 1 System specifications

Tables Icon

Table 2 Surface parameters in CODE V of system 1 constructed with SMS

Tables Icon

Table 3 Surface parameters in CODE V of system 2 constructed with SMS

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