Abstract

A comprehensive analysis of fundamental factors and their effects on the performance of liquid crystal (LC)-based lenses is given. The analysis adopts numerical LC director and electric field simulation, as well as scalar diffraction theory for calculating the lens performance considering different variable factors. A high-efficiency LC lens with concentric electrode rings is fabricated for verifying and enriching the analysis. The measurement results are in close agreement with the analysis, and a summary of key factors is given with their quantitative contributions to the efficiency.

© 2013 Optical Society of America

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  5. P. Valley, N. Savidis, J. Schwiegerling, M. Reza Dodge, G. Peyman, and N. Peyghambarian, “Adjustable hybrid diffractive/refractive achromatic lens,” Opt. Express 19, 7468–7479 (2011).
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    [CrossRef]
  22. S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. H. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43, 7634 (2004).
    [CrossRef]
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    [CrossRef]
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2012 (1)

2011 (2)

P. Valley, N. Savidis, J. Schwiegerling, M. Reza Dodge, G. Peyman, and N. Peyghambarian, “Adjustable hybrid diffractive/refractive achromatic lens,” Opt. Express 19, 7468–7479 (2011).
[CrossRef]

L. Li, L. Shi, D. Bryant, T. V. van Heugten, D. Duston, and P. J. Bos, “Modeling and design of a tunable refractive lens based on liquid crystals,” Proc. SPIE 7944,79440S (2011).
[CrossRef]

2010 (1)

2007 (1)

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and performance limits of a large aperture high-resolution wavefront control system based on a liquid crystal spatial light modulator,” Opt. Eng. 46, 044001 (2007).
[CrossRef]

2006 (3)

H. Ren and S. T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14, 11292–11298 (2006).
[CrossRef]

G. Li, P. Valley, M. S. Giridhar, D. L. Mathine, G. Meredith, J. N. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode patterns,” Appl. Phys. Lett. 89, 141120 (2006).
[CrossRef]

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

2005 (1)

B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with stacked structure of liquid-crystal layers,” Opt. Commun. 250, 266–273 (2005).
[CrossRef]

2004 (2)

M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43, 6407–6412 (2004).
[CrossRef]

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. H. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43, 7634 (2004).
[CrossRef]

2003 (1)

M. Ye and S. Sato, “Liquid crystal lens with focus movable along and off axis,” Opt. Commun. 225, 277–280 (2003).
[CrossRef]

1999 (1)

S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6, 471–485 (1999).
[CrossRef]

1997 (1)

1988 (1)

1984 (1)

Albero, J.

Anderson, J. E.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and performance limits of a large aperture high-resolution wavefront control system based on a liquid crystal spatial light modulator,” Opt. Eng. 46, 044001 (2007).
[CrossRef]

Äyräs, P.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

Bennis, N.

Boreman, G. D.

G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Bos, P. J.

L. Li, L. Shi, D. Bryant, T. V. van Heugten, D. Duston, and P. J. Bos, “Modeling and design of a tunable refractive lens based on liquid crystals,” Proc. SPIE 7944,79440S (2011).
[CrossRef]

L. Shi, J. Shi, P. F. McManamon, and P. J. Bos, “Design considerations for high efficiency liquid crystal decentered microlens arrays for steering light,” Appl. Opt. 49, 409–421 (2010).
[CrossRef]

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and performance limits of a large aperture high-resolution wavefront control system based on a liquid crystal spatial light modulator,” Opt. Eng. 46, 044001 (2007).
[CrossRef]

L. Li, L. Shi, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Liquid crystal lenses: liquid crystals promise compact lenses with variable focus,” Laser Focus World, http://www.laserfocusworld.com/articles/2010/12/liquid-crystals-promise-compact-lenses-with-variable-focus.html .

Brinkley, P. F.

Bryant, D.

L. Li, L. Shi, D. Bryant, T. V. van Heugten, D. Duston, and P. J. Bos, “Modeling and design of a tunable refractive lens based on liquid crystals,” Proc. SPIE 7944,79440S (2011).
[CrossRef]

L. Li, L. Shi, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Liquid crystal lenses: liquid crystals promise compact lenses with variable focus,” Laser Focus World, http://www.laserfocusworld.com/articles/2010/12/liquid-crystals-promise-compact-lenses-with-variable-focus.html .

Cerrolaza, B.

Chan, W. W.

Chu, C.

Cleverly, D. S.

Davis, J. A.

Debevec, P. E.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in SIGGRAPH ’97 (ACM, 1997) pp. 369–378.

Dodge, M. Reza

Duston, D.

L. Li, L. Shi, D. Bryant, T. V. van Heugten, D. Duston, and P. J. Bos, “Modeling and design of a tunable refractive lens based on liquid crystals,” Proc. SPIE 7944,79440S (2011).
[CrossRef]

L. Li, L. Shi, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Liquid crystal lenses: liquid crystals promise compact lenses with variable focus,” Laser Focus World, http://www.laserfocusworld.com/articles/2010/12/liquid-crystals-promise-compact-lenses-with-variable-focus.html .

Garcia-Martinez, P.

Gauza, S.

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. H. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43, 7634 (2004).
[CrossRef]

Giridhar, M. S.

G. Li, P. Valley, M. S. Giridhar, D. L. Mathine, G. Meredith, J. N. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode patterns,” Appl. Phys. Lett. 89, 141120 (2006).
[CrossRef]

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1988).

Haddock, J. N.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

G. Li, P. Valley, M. S. Giridhar, D. L. Mathine, G. Meredith, J. N. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode patterns,” Appl. Phys. Lett. 89, 141120 (2006).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2001).

Herzig, H. P.

H. P. Herzig, Micro-optics: Elements, Systems and Applications (Taylor & Francis, 1997).

Heugten, T. V.

L. Li, L. Shi, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Liquid crystal lenses: liquid crystals promise compact lenses with variable focus,” Laser Focus World, http://www.laserfocusworld.com/articles/2010/12/liquid-crystals-promise-compact-lenses-with-variable-focus.html .

Honkanen, S.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

Hsu, C. H.

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. H. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43, 7634 (2004).
[CrossRef]

Janarthanan, N.

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. H. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43, 7634 (2004).
[CrossRef]

Kippelen, B.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

G. Li, P. Valley, M. S. Giridhar, D. L. Mathine, G. Meredith, J. N. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode patterns,” Appl. Phys. Lett. 89, 141120 (2006).
[CrossRef]

Kornreich, P. G.

Kowel, S. T.

Li, G.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

G. Li, P. Valley, M. S. Giridhar, D. L. Mathine, G. Meredith, J. N. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode patterns,” Appl. Phys. Lett. 89, 141120 (2006).
[CrossRef]

Li, L.

L. Li, L. Shi, D. Bryant, T. V. van Heugten, D. Duston, and P. J. Bos, “Modeling and design of a tunable refractive lens based on liquid crystals,” Proc. SPIE 7944,79440S (2011).
[CrossRef]

L. Li, L. Shi, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Liquid crystal lenses: liquid crystals promise compact lenses with variable focus,” Laser Focus World, http://www.laserfocusworld.com/articles/2010/12/liquid-crystals-promise-compact-lenses-with-variable-focus.html .

Malik, J.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in SIGGRAPH ’97 (ACM, 1997) pp. 369–378.

Mathine, D. L.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

G. Li, P. Valley, M. S. Giridhar, D. L. Mathine, G. Meredith, J. N. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode patterns,” Appl. Phys. Lett. 89, 141120 (2006).
[CrossRef]

McManamon, P. F.

L. Shi, J. Shi, P. F. McManamon, and P. J. Bos, “Design considerations for high efficiency liquid crystal decentered microlens arrays for steering light,” Appl. Opt. 49, 409–421 (2010).
[CrossRef]

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and performance limits of a large aperture high-resolution wavefront control system based on a liquid crystal spatial light modulator,” Opt. Eng. 46, 044001 (2007).
[CrossRef]

Meredith, G.

G. Li, P. Valley, M. S. Giridhar, D. L. Mathine, G. Meredith, J. N. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode patterns,” Appl. Phys. Lett. 89, 141120 (2006).
[CrossRef]

Meredith, G. R.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

Miranda, F. A.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and performance limits of a large aperture high-resolution wavefront control system based on a liquid crystal spatial light modulator,” Opt. Eng. 46, 044001 (2007).
[CrossRef]

Moreno, I.

Oton, E.

Peyghambarian, N.

P. Valley, N. Savidis, J. Schwiegerling, M. Reza Dodge, G. Peyman, and N. Peyghambarian, “Adjustable hybrid diffractive/refractive achromatic lens,” Opt. Express 19, 7468–7479 (2011).
[CrossRef]

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

G. Li, P. Valley, M. S. Giridhar, D. L. Mathine, G. Meredith, J. N. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode patterns,” Appl. Phys. Lett. 89, 141120 (2006).
[CrossRef]

Peyman, G.

Pouch, J. J.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and performance limits of a large aperture high-resolution wavefront control system based on a liquid crystal spatial light modulator,” Opt. Eng. 46, 044001 (2007).
[CrossRef]

Ren, H.

Sato, S.

B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with stacked structure of liquid-crystal layers,” Opt. Commun. 250, 266–273 (2005).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43, 6407–6412 (2004).
[CrossRef]

M. Ye and S. Sato, “Liquid crystal lens with focus movable along and off axis,” Opt. Commun. 225, 277–280 (2003).
[CrossRef]

S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6, 471–485 (1999).
[CrossRef]

Savidis, N.

Schwiegerling, J.

P. Valley, N. Savidis, J. Schwiegerling, M. Reza Dodge, G. Peyman, and N. Peyghambarian, “Adjustable hybrid diffractive/refractive achromatic lens,” Opt. Express 19, 7468–7479 (2011).
[CrossRef]

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

Shi, J.

Shi, L.

L. Li, L. Shi, D. Bryant, T. V. van Heugten, D. Duston, and P. J. Bos, “Modeling and design of a tunable refractive lens based on liquid crystals,” Proc. SPIE 7944,79440S (2011).
[CrossRef]

L. Shi, J. Shi, P. F. McManamon, and P. J. Bos, “Design considerations for high efficiency liquid crystal decentered microlens arrays for steering light,” Appl. Opt. 49, 409–421 (2010).
[CrossRef]

L. Li, L. Shi, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Liquid crystal lenses: liquid crystals promise compact lenses with variable focus,” Laser Focus World, http://www.laserfocusworld.com/articles/2010/12/liquid-crystals-promise-compact-lenses-with-variable-focus.html .

Valley, P.

P. Valley, N. Savidis, J. Schwiegerling, M. Reza Dodge, G. Peyman, and N. Peyghambarian, “Adjustable hybrid diffractive/refractive achromatic lens,” Opt. Express 19, 7468–7479 (2011).
[CrossRef]

G. Li, P. Valley, M. S. Giridhar, D. L. Mathine, G. Meredith, J. N. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode patterns,” Appl. Phys. Lett. 89, 141120 (2006).
[CrossRef]

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

van Heugten, T. V.

L. Li, L. Shi, D. Bryant, T. V. van Heugten, D. Duston, and P. J. Bos, “Modeling and design of a tunable refractive lens based on liquid crystals,” Proc. SPIE 7944,79440S (2011).
[CrossRef]

Wang, B.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and performance limits of a large aperture high-resolution wavefront control system based on a liquid crystal spatial light modulator,” Opt. Eng. 46, 044001 (2007).
[CrossRef]

B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with stacked structure of liquid-crystal layers,” Opt. Commun. 250, 266–273 (2005).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43, 6407–6412 (2004).
[CrossRef]

Wang, X.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and performance limits of a large aperture high-resolution wavefront control system based on a liquid crystal spatial light modulator,” Opt. Eng. 46, 044001 (2007).
[CrossRef]

Wen, C. H.

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. H. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43, 7634 (2004).
[CrossRef]

Williby, G.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Wu, S. T.

H. Ren and S. T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14, 11292–11298 (2006).
[CrossRef]

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. H. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43, 7634 (2004).
[CrossRef]

S. T. Wu and D. K. Yang, Fundamentals of Liquid Crystal Devices (Wiley, 2006).

H. Ren and S. T. Wu, Introduction to Adaptive Lenses (Wiley, 2012).

Yang, D. K.

S. T. Wu and D. K. Yang, Fundamentals of Liquid Crystal Devices (Wiley, 2006).

Ye, M.

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[CrossRef]

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[CrossRef]

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Appl. Phys. Lett. (1)

G. Li, P. Valley, M. S. Giridhar, D. L. Mathine, G. Meredith, J. N. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode patterns,” Appl. Phys. Lett. 89, 141120 (2006).
[CrossRef]

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[CrossRef]

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[CrossRef]

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Proc. Natl. Acad. Sci. USA (1)

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. USA 103, 6100–6104 (2006).
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Proc. SPIE (1)

L. Li, L. Shi, D. Bryant, T. V. van Heugten, D. Duston, and P. J. Bos, “Modeling and design of a tunable refractive lens based on liquid crystals,” Proc. SPIE 7944,79440S (2011).
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Figures (6)

Fig. 1.
Fig. 1.

Calculated MTF for the lens with noise in the OPD profile.

Fig. 2.
Fig. 2.

(a) Top view of lens areas (1 and 2) where a tangent to the electrodes is perpendicular or parallel to the rubbing direction. (b) LC director two-dimensional (2D) plane as a cross section of area 1, projection of LC directors on cell surface is perpendicular to the electrode axis. (c) LC director 2D plane as a cross section of area 2, projection of LC directors on cell surface is parallel to the electrode axis.

Fig. 3.
Fig. 3.

Calculated OPD profile as a good parabolic shape (in the director plane where electrodes are parallel to rubbing direction) when the gap is 3 μm.

Fig. 4.
Fig. 4.

(a) Calculated light distribution in focal plane (for display purpose, the contrast is boosted by taking the third root of the intensity before plotting) for ideal lens, and (b) LC lens with 10 phase steps per wave and 3 μm gaps. (c) Strehl ratio of LC lens (in the director plane where electrodes are parallel to rubbing direction), normalized to center lobe intensity peak of an ideal lens in its focal plane. (d) Calculated MTF for LC lens and ideal lens.

Fig. 5.
Fig. 5.

(a) Picture of the actual lens with flex connector. (b) Microscopic top view of the patterned substrate with reflected light. The bright lines are the Nickel bus lines with a width about 10 μm, and they are connected with ring electrodes through round vias (bright dots). The ring electrodes, inter-ring resistors, and gaps are shown as well. (c) Measured OPD of LC lens under optimized voltage profile. (d) Measured OPD of high-quality glass lens. (e) Original pictures captured by the CCD (22.2mm×14.8mm in size) in the focal plane with 15 s exposure time for LC lens f=400mm, and (f) glass lens f=400mm. (g) Measured intensity spot profile in LC lens’s and glass lens’s focal plane, normalized to the intensity peak in glass lens’s focal plane. (h) Measured MTF of LC lens with typical and modified normalization approach, compared to glass lens.

Fig. 6.
Fig. 6.

Original pictures (15 s exposure time) captured by the CCD in the focal plane of the glass lens (f=400mm), while the LC lens immediately behind it is applied with uniform: (a) 0, (b) 1, (c) 2, and (d) 4 V to all electrodes.

Tables (7)

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Table 1. Analytical Diffraction Efficiency and the Numerically Calculated Strehl Ratio for Different Phase Step Heights

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Table 2. Analytical Diffraction Efficiency for Different Gap Widths

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Table 3. Calculated Strehl Ratio of the LC Lens as a Function of Gap Width Including the Factor of 10 Phase Steps per Wave, for Director Plane with Electrodes Perpendicular to Rubbing Direction, Parallel to Rubbing Direction, and the Average

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Table 4. Calculated Voltages for each Addressed Ring Electrode

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Table 5. Measured Strehl Ratio in Glass Lens’ Focal Plane Z=400Mm, when an LC Lens is Added behind the Glass Lens and Applied with Different Uniform Voltages

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Table 6. Transmission Efficiency of the Phase Grating in Gaps when the LC Lens is under Uniform Voltages

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Table 7. Summary of Key Factors for Actual LC Lens

Equations (10)

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η(sin(π/q)/(π/q))2.
η(1ΛFΛ)2.
felastic=12K11(·n⃗)2+12K22(n⃗·×n⃗+q0)2+12K33(n⃗××n⃗)2.
fe=12E⃗·D⃗=12E⃗·[εoεE⃗+εoΔε(E⃗·n⃗)n⃗]=12εoεE212εoΔεEiEjninj,i,j=x,y,z.
ninew=nioldΔtγ[fG]ni,[fG]ni=δfGδni=fGnij=x,y,zddj[fG(dnidj)].
OPL(x)=0dneff(x,z)·dz,neff(x,z)=noneno2cos2θ(x,z)+ne2sin2θ(x,z).
OPD(r)r22f.
rn=2λfnfs,n=1,2,,N.
U2(x,y)=zjλΣU1(ξ,η)exp(jkr12)r122dξdη,r12=z2+(xξ)2+(yη)2.
U1=|U1|ej·OPD.

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