Abstract

Two design approaches (multicell and addition of phase resets in single cell) are introduced to optimize the performances of tunable refractive liquid crystal lenses, including improvements on the switching speed, optical power, and the off-axis, wide-angle imaging performance. Key parameters and advantages for each method are discussed, and their effects on the performance are demonstrated in detail with numerical calculations.

© 2014 Optical Society of America

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References

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  1. S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6, 471–485 (1999).
    [CrossRef]
  2. S. T. Kowel, D. S. Cleverly, and P. G. Kornreich, “Focusing by electrical modulation of refraction in a liquid crystal cell,” Appl. Opt. 23, 278–289 (1984).
    [CrossRef]
  3. H. Ren and S. T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14, 11292–11298 (2006).
    [CrossRef]
  4. 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, 2010, http://www.laserfocusworld.com/articles/2010/12/liquid-crystals-promise-compact-lenses-with-variablefocus.html .
  5. A. F. Naumov, M. Y. Loktev, I. R. Guralnik, and G. Vdovin, “Liquid-crystal adaptive lenses with modal control,” Opt. Lett. 23, 992–994 (1998).
    [CrossRef]
  6. L. Li, L. Shi, D. Bryant, T. V. 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]
  7. 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]
  8. M. Ye, B. Wang, M. Uchida, S. Yanase, S. Takahashi, and S. Sato, “Focus tuning by liquid crystal lens in imaging system,” Appl. Opt. 51, 7630–7635 (2012).
    [CrossRef]
  9. K. Asatryan, V. Presnyakov, A. Tork, A. Zohrabyan, A. Bagramyan, and T. Galstian, “Optical lens with electrically variable focus using an optically hidden dielectric structure,” Opt. Express 18, 13981–13992 (2010).
    [CrossRef]
  10. M. Kawamura, K. Nakamura, and S. Sato, “Liquid-crystal micro-lens array with two-divided and tetragonally hole-patterned electrodes,” Opt. Express 21, 26520–26526 (2013).
    [CrossRef]
  11. Y.-H. Lin and H.-S. Chen, “Electrically tunable-focusing and polarizer-free liquid crystal lenses for ophthalmic applications,” Opt. Express 21, 9428–9436 (2013).
    [CrossRef]
  12. H.-S. Chen and Y.-H. Lin, “An endoscopic system adopting a liquid crystal lens with an electrically tunable depth-of-field,” Opt. Express 21, 18079–18088 (2013).
    [CrossRef]
  13. V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97, 103101 (2005).
    [CrossRef]
  14. L. Lu, V. Sergan, T. V. Heugten, D. Duston, A. Bhowmik, and P. J. Bos, “Surface localized polymer aligned liquid crystal lens,” Opt. Express 21, 7133–7138 (2013).
    [CrossRef]
  15. H. Ren, S. Xu, Y. Liu, and S. T. Wu, “Switchable focus using a polymeric lenticular microlens array and a polarization rotator,” Opt. Express 21, 7916–7925 (2013).
    [CrossRef]
  16. Y. Li, Y. Liu, Q. Li, and S. T. Wu, “Polarization independent blue-phase liquid crystal cylindrical lens with a resistive film,” Appl. Opt. 51, 2568–2572 (2012).
    [CrossRef]
  17. C. T. Lee, Y. Li, H. Y. Lin, and S. T. Wu, “Design of polarization-insensitive multi-electrode GRIN lens with a blue-phase liquid crystal,” Opt. Express 19, 17402–17407 (2011).
    [CrossRef]
  18. H. T. Dai, Y. J. Liu, X. W. Sun, and D. Luo, “A negative-positive tunable liquid-crystal microlens array by printing,” Opt. Express 17, 4317–4323 (2009).
    [CrossRef]
  19. P. Valley, N. Savidis, J. Schwiegerling, M. R. Dodge, G. Peyman, and N. Peyghambarian, “Adjustable hybrid diffractive/refractive achromatic lens,” Opt. Express 19, 7468–7479 (2011).
    [CrossRef]
  20. G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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]
  21. L. Li, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Near-diffraction-limited tunable liquid crystal lens with simplified design,” Opt. Eng. 52, 035007 (2013).
    [CrossRef]
  22. L. Li, D. Bryant, T. V. Heugten, and P. J. Bos, “Near-diffraction-limited and low-haze electro-optical tunable liquid crystal lens with floating electrodes,” Opt. Express 21, 8371–8381 (2013).
    [CrossRef]
  23. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1988).
  24. D. Voelz, Computational Fourier Optics: A Matlab Tutorial (SPIE, 2011).
  25. L. Li, D. Bryant, T. V. Heugten, and P. J. Bos, “Physical limitations and fundamental factors affecting performance of liquid crystal tunable lenses with concentric electrode rings,” Appl. Opt. 52, 1978–1986 (2013).
    [CrossRef]
  26. H. P. Herzig, Micro-optics: Elements, Systems and Applications (Taylor & Francis, 1997).
  27. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  28. C. Gu and P. Yeh, “Extended Jones matrix method. II,” J. Opt. Soc. Am. A 10, 966–973 (1993).
    [CrossRef]
  29. G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” (Lincoln Laboratory, MIT, 1989).

2013

M. Kawamura, K. Nakamura, and S. Sato, “Liquid-crystal micro-lens array with two-divided and tetragonally hole-patterned electrodes,” Opt. Express 21, 26520–26526 (2013).
[CrossRef]

Y.-H. Lin and H.-S. Chen, “Electrically tunable-focusing and polarizer-free liquid crystal lenses for ophthalmic applications,” Opt. Express 21, 9428–9436 (2013).
[CrossRef]

H.-S. Chen and Y.-H. Lin, “An endoscopic system adopting a liquid crystal lens with an electrically tunable depth-of-field,” Opt. Express 21, 18079–18088 (2013).
[CrossRef]

L. Lu, V. Sergan, T. V. Heugten, D. Duston, A. Bhowmik, and P. J. Bos, “Surface localized polymer aligned liquid crystal lens,” Opt. Express 21, 7133–7138 (2013).
[CrossRef]

H. Ren, S. Xu, Y. Liu, and S. T. Wu, “Switchable focus using a polymeric lenticular microlens array and a polarization rotator,” Opt. Express 21, 7916–7925 (2013).
[CrossRef]

L. Li, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Near-diffraction-limited tunable liquid crystal lens with simplified design,” Opt. Eng. 52, 035007 (2013).
[CrossRef]

L. Li, D. Bryant, T. V. Heugten, and P. J. Bos, “Near-diffraction-limited and low-haze electro-optical tunable liquid crystal lens with floating electrodes,” Opt. Express 21, 8371–8381 (2013).
[CrossRef]

L. Li, D. Bryant, T. V. Heugten, and P. J. Bos, “Physical limitations and fundamental factors affecting performance of liquid crystal tunable lenses with concentric electrode rings,” Appl. Opt. 52, 1978–1986 (2013).
[CrossRef]

2012

2011

2010

2009

2006

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

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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

V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97, 103101 (2005).
[CrossRef]

2004

1999

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

1998

1993

1984

Asatryan, K.

Ayräs, P.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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]

Bagramyan, A.

Bhowmik, A.

Born, M.

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

Bos, P. J.

Bryant, D.

L. Li, D. Bryant, T. V. Heugten, and P. J. Bos, “Physical limitations and fundamental factors affecting performance of liquid crystal tunable lenses with concentric electrode rings,” Appl. Opt. 52, 1978–1986 (2013).
[CrossRef]

L. Li, D. Bryant, T. V. Heugten, and P. J. Bos, “Near-diffraction-limited and low-haze electro-optical tunable liquid crystal lens with floating electrodes,” Opt. Express 21, 8371–8381 (2013).
[CrossRef]

L. Li, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Near-diffraction-limited tunable liquid crystal lens with simplified design,” Opt. Eng. 52, 035007 (2013).
[CrossRef]

L. Li, L. Shi, D. Bryant, T. V. 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]

Chen, H.-S.

Cleverly, D. S.

Dai, H. T.

Dodge, M. R.

Duston, D.

L. Lu, V. Sergan, T. V. Heugten, D. Duston, A. Bhowmik, and P. J. Bos, “Surface localized polymer aligned liquid crystal lens,” Opt. Express 21, 7133–7138 (2013).
[CrossRef]

L. Li, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Near-diffraction-limited tunable liquid crystal lens with simplified design,” Opt. Eng. 52, 035007 (2013).
[CrossRef]

L. Li, L. Shi, D. Bryant, T. V. 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]

Galstian, T.

Galstian, T. V.

V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97, 103101 (2005).
[CrossRef]

Giridhar, M. S.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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).

Gu, C.

Guralnik, I. R.

Haddock, J. N.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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]

Herzig, H. P.

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

Heugten, T. V.

Honkanen, S.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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]

Kawamura, M.

Kippelen, B.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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]

Kornreich, P. G.

Kowel, S. T.

Lee, C. T.

Li, G.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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]

Li, L.

L. Li, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Near-diffraction-limited tunable liquid crystal lens with simplified design,” Opt. Eng. 52, 035007 (2013).
[CrossRef]

L. Li, D. Bryant, T. V. Heugten, and P. J. Bos, “Near-diffraction-limited and low-haze electro-optical tunable liquid crystal lens with floating electrodes,” Opt. Express 21, 8371–8381 (2013).
[CrossRef]

L. Li, D. Bryant, T. V. Heugten, and P. J. Bos, “Physical limitations and fundamental factors affecting performance of liquid crystal tunable lenses with concentric electrode rings,” Appl. Opt. 52, 1978–1986 (2013).
[CrossRef]

L. Li, L. Shi, D. Bryant, T. V. 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]

Li, Q.

Li, Y.

Lin, H. Y.

Lin, Y.-H.

Liu, Y.

Liu, Y. J.

Loktev, M. Y.

Lu, L.

Luo, D.

Mathine, D. L.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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]

Meredith, G. R.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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]

Nakamura, K.

Naumov, A. F.

Peyghambarian, N.

P. Valley, N. Savidis, J. Schwiegerling, M. R. 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. Ayräs, 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]

Peyman, G.

Presnyakov, V.

Presnyakov, V. V.

V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97, 103101 (2005).
[CrossRef]

Ren, H.

Sato, S.

Savidis, N.

Schwiegerling, J.

P. Valley, N. Savidis, J. Schwiegerling, M. R. 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. Ayräs, 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]

Sergan, V.

Shi, L.

L. Li, L. Shi, D. Bryant, T. V. 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]

Sun, X. W.

Swanson, G. J.

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” (Lincoln Laboratory, MIT, 1989).

Takahashi, S.

Tork, A.

Uchida, M.

Valley, P.

P. Valley, N. Savidis, J. Schwiegerling, M. R. 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. Ayräs, 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]

Vdovin, G.

Voelz, D.

D. Voelz, Computational Fourier Optics: A Matlab Tutorial (SPIE, 2011).

Wang, B.

Williby, G.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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.

Xu, S.

Yanase, S.

Ye, M.

Yeh, P.

Zohrabyan, A.

Appl. Opt.

J. Appl. Phys.

V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97, 103101 (2005).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

L. Li, D. Bryant, T. V. Heugten, D. Duston, and P. J. Bos, “Near-diffraction-limited tunable liquid crystal lens with simplified design,” Opt. Eng. 52, 035007 (2013).
[CrossRef]

Opt. Express

L. Li, D. Bryant, T. V. Heugten, and P. J. Bos, “Near-diffraction-limited and low-haze electro-optical tunable liquid crystal lens with floating electrodes,” Opt. Express 21, 8371–8381 (2013).
[CrossRef]

C. T. Lee, Y. Li, H. Y. Lin, and S. T. Wu, “Design of polarization-insensitive multi-electrode GRIN lens with a blue-phase liquid crystal,” Opt. Express 19, 17402–17407 (2011).
[CrossRef]

H. T. Dai, Y. J. Liu, X. W. Sun, and D. Luo, “A negative-positive tunable liquid-crystal microlens array by printing,” Opt. Express 17, 4317–4323 (2009).
[CrossRef]

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

K. Asatryan, V. Presnyakov, A. Tork, A. Zohrabyan, A. Bagramyan, and T. Galstian, “Optical lens with electrically variable focus using an optically hidden dielectric structure,” Opt. Express 18, 13981–13992 (2010).
[CrossRef]

M. Kawamura, K. Nakamura, and S. Sato, “Liquid-crystal micro-lens array with two-divided and tetragonally hole-patterned electrodes,” Opt. Express 21, 26520–26526 (2013).
[CrossRef]

Y.-H. Lin and H.-S. Chen, “Electrically tunable-focusing and polarizer-free liquid crystal lenses for ophthalmic applications,” Opt. Express 21, 9428–9436 (2013).
[CrossRef]

H.-S. Chen and Y.-H. Lin, “An endoscopic system adopting a liquid crystal lens with an electrically tunable depth-of-field,” Opt. Express 21, 18079–18088 (2013).
[CrossRef]

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

L. Lu, V. Sergan, T. V. Heugten, D. Duston, A. Bhowmik, and P. J. Bos, “Surface localized polymer aligned liquid crystal lens,” Opt. Express 21, 7133–7138 (2013).
[CrossRef]

H. Ren, S. Xu, Y. Liu, and S. T. Wu, “Switchable focus using a polymeric lenticular microlens array and a polarization rotator,” Opt. Express 21, 7916–7925 (2013).
[CrossRef]

Opt. Lett.

Opt. Rev.

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

Proc. Natl. Acad. Sci. USA

G. Li, D. L. Mathine, P. Valley, P. Ayräs, 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]

Proc. SPIE

L. Li, L. Shi, D. Bryant, T. V. 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]

Other

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, 2010, http://www.laserfocusworld.com/articles/2010/12/liquid-crystals-promise-compact-lenses-with-variablefocus.html .

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

D. Voelz, Computational Fourier Optics: A Matlab Tutorial (SPIE, 2011).

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” (Lincoln Laboratory, MIT, 1989).

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

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

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Figures (10)

Fig. 1.
Fig. 1.

Phase profiles of two component LC lenses and the resulting composite lens.

Fig. 2.
Fig. 2.

(a) LC lens diagram in 3D coordinate, (b) cross section of lens thickness in the xz plane and along the radial axis in the x direction, and (c) cross section of lens thickness in the yz plane and along the radial axis in the y direction.

Fig. 3.
Fig. 3.

Calculated OPD versus off-axis incident light.

Fig. 4.
Fig. 4.

(a) Calculated Strehl ratio for off-axis light, normalized to the peak irradiance for ideal lens and on-axis light and (b) calculated MTF for off-axis light.

Fig. 5.
Fig. 5.

Conceptual cross section of the (a) dual lenses with antiparallel alignment and (b) dual lenses with parallel alignment.

Fig. 6.
Fig. 6.

(a) Calculated Strehl ratio for dual lenses with antiparallel rubbing direction compared with other lens arrangements, normalized to the peak intensity for ideal lens and on-axis light and (b) calculated MTF for dual lenses with antiparallel rubbing direction compared with other lens arrangement with off-axis light.

Fig. 7.
Fig. 7.

Fresnel lens with 1λ and 3λ peak-to-peak phase difference in the reset.

Fig. 8.
Fig. 8.

Design of Fresnel lens f=440mm (total OPD 3 waves λ=543.5nm) with two and three subzones.

Fig. 9.
Fig. 9.

Calculated spot profile at z=440mm for Fresnel lens with two and three subzones with different wavelengths of light, compared with ideal refractive lens f=440mm.

Fig. 10.
Fig. 10.

Calculated MTF for Fresnel lens with two and three subzones with different wavelengths of light, compared with ideal refractive lens f=440mm.

Tables (1)

Tables Icon

Table 1. Calculated OPD Wavefront Error RMS for Off-axis Light and the Strehl Ratio

Equations (4)

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

OPD(r)r22f.
rn=2λfnfs,n=1,2,,N.
rm,n=2λf(m+M(n1))fs,m=1,2,,M,n=1,2,,N/M.
rm,(N/M)+1=R,m=1,2,,M1.

Metrics