Abstract

A distortion aberration (DA) correction device is fabricated using a liquid crystal lens array (LCLA), which is placed at the intermediate image plane of the optical system. Without voltage, the LCLA does not work, the image is distorted due to the aberration from the optical system; with voltage, the incident light is focused by the LCLA and then the distorted image is corrected. The correction of distorted image by LCLA is attributed to the redirection of the off-axis propagated chief ray approaches the principal point of the lens element.

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References

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  1. M. Ye and S. Sato, “New method of voltage application for improving response time of a liquid crystal lens,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)433(1), 229–236 (2005).
    [CrossRef]
  2. M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys.41(Part 2, No. 5B), L571–L573 (2002).
    [CrossRef]
  3. P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Tunable-focus flat liquid-crystal diffractive lens,” Opt. Lett.35(3), 336–338 (2010).
    [CrossRef] [PubMed]
  4. H. C. Lin and Y. H. Lin, “An electrically tunable focusing pico-projector adopting a liquid crystal lens,” Jpn. J. Appl. Phys.49(10), 102502 (2010).
    [CrossRef]
  5. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).
  6. E. Hecht, Optics (Addison-Wesley, 2002).
  7. C. Y. Chen, W. C. Su, Y. F. Wang, and C. H. Chen, “Reduction of distortion aberration in imaging systems by using a microlens array,” Opt. Commun.283(14), 2798–2802 (2010).
    [CrossRef]
  8. W. C. Su, C. Y. Chen, Y. F. Wang, Y. W. Chen, and S. S. Yang, “Effect of a diffuser on distortion reduction for a virtual image projector,” J. Opt.13(10), 105401 (2011).
    [CrossRef]
  9. H. Ren and S. T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express14(23), 11292–11298 (2006).
    [CrossRef] [PubMed]
  10. S. T. Wu, U. Efron, and L. D. Hess, “Birefringence measurements of liquid crystals,” Appl. Opt.23(21), 3911–3915 (1984).
    [CrossRef] [PubMed]
  11. J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol.1(1), 51–61 (2005).
    [CrossRef]
  12. S. Gauza, H. Wang, C.-H. Wen, S.-T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys.42, 3463–3466 (2003).
    [CrossRef]
  13. S. Gauza, X. Zhu, P. Piecek, R. Dabrowski, and S. T. Wu, “Fast Switching Liquid Crystals for Color-Sequential LCDs,” J. Disp. Technol.3(3), 250–252 (2007).
    [CrossRef]

2011 (1)

W. C. Su, C. Y. Chen, Y. F. Wang, Y. W. Chen, and S. S. Yang, “Effect of a diffuser on distortion reduction for a virtual image projector,” J. Opt.13(10), 105401 (2011).
[CrossRef]

2010 (3)

H. C. Lin and Y. H. Lin, “An electrically tunable focusing pico-projector adopting a liquid crystal lens,” Jpn. J. Appl. Phys.49(10), 102502 (2010).
[CrossRef]

C. Y. Chen, W. C. Su, Y. F. Wang, and C. H. Chen, “Reduction of distortion aberration in imaging systems by using a microlens array,” Opt. Commun.283(14), 2798–2802 (2010).
[CrossRef]

P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Tunable-focus flat liquid-crystal diffractive lens,” Opt. Lett.35(3), 336–338 (2010).
[CrossRef] [PubMed]

2007 (1)

S. Gauza, X. Zhu, P. Piecek, R. Dabrowski, and S. T. Wu, “Fast Switching Liquid Crystals for Color-Sequential LCDs,” J. Disp. Technol.3(3), 250–252 (2007).
[CrossRef]

2006 (1)

2005 (2)

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol.1(1), 51–61 (2005).
[CrossRef]

M. Ye and S. Sato, “New method of voltage application for improving response time of a liquid crystal lens,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)433(1), 229–236 (2005).
[CrossRef]

2003 (1)

S. Gauza, H. Wang, C.-H. Wen, S.-T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys.42, 3463–3466 (2003).
[CrossRef]

2002 (1)

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys.41(Part 2, No. 5B), L571–L573 (2002).
[CrossRef]

1984 (1)

Chen, C. H.

C. Y. Chen, W. C. Su, Y. F. Wang, and C. H. Chen, “Reduction of distortion aberration in imaging systems by using a microlens array,” Opt. Commun.283(14), 2798–2802 (2010).
[CrossRef]

Chen, C. Y.

W. C. Su, C. Y. Chen, Y. F. Wang, Y. W. Chen, and S. S. Yang, “Effect of a diffuser on distortion reduction for a virtual image projector,” J. Opt.13(10), 105401 (2011).
[CrossRef]

C. Y. Chen, W. C. Su, Y. F. Wang, and C. H. Chen, “Reduction of distortion aberration in imaging systems by using a microlens array,” Opt. Commun.283(14), 2798–2802 (2010).
[CrossRef]

Chen, Y. W.

W. C. Su, C. Y. Chen, Y. F. Wang, Y. W. Chen, and S. S. Yang, “Effect of a diffuser on distortion reduction for a virtual image projector,” J. Opt.13(10), 105401 (2011).
[CrossRef]

Dabrowski, R.

S. Gauza, X. Zhu, P. Piecek, R. Dabrowski, and S. T. Wu, “Fast Switching Liquid Crystals for Color-Sequential LCDs,” J. Disp. Technol.3(3), 250–252 (2007).
[CrossRef]

S. Gauza, H. Wang, C.-H. Wen, S.-T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys.42, 3463–3466 (2003).
[CrossRef]

Dodge, M. R.

Efron, U.

Gauza, S.

S. Gauza, X. Zhu, P. Piecek, R. Dabrowski, and S. T. Wu, “Fast Switching Liquid Crystals for Color-Sequential LCDs,” J. Disp. Technol.3(3), 250–252 (2007).
[CrossRef]

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol.1(1), 51–61 (2005).
[CrossRef]

S. Gauza, H. Wang, C.-H. Wen, S.-T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys.42, 3463–3466 (2003).
[CrossRef]

Hess, L. D.

Li, J.

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol.1(1), 51–61 (2005).
[CrossRef]

Lin, H. C.

H. C. Lin and Y. H. Lin, “An electrically tunable focusing pico-projector adopting a liquid crystal lens,” Jpn. J. Appl. Phys.49(10), 102502 (2010).
[CrossRef]

Lin, Y. H.

H. C. Lin and Y. H. Lin, “An electrically tunable focusing pico-projector adopting a liquid crystal lens,” Jpn. J. Appl. Phys.49(10), 102502 (2010).
[CrossRef]

Lu, R.

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol.1(1), 51–61 (2005).
[CrossRef]

Mathine, D. L.

Peyghambarian, N.

Peyman, G.

Piecek, P.

S. Gauza, X. Zhu, P. Piecek, R. Dabrowski, and S. T. Wu, “Fast Switching Liquid Crystals for Color-Sequential LCDs,” J. Disp. Technol.3(3), 250–252 (2007).
[CrossRef]

Ren, H.

Sato, S.

M. Ye and S. Sato, “New method of voltage application for improving response time of a liquid crystal lens,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)433(1), 229–236 (2005).
[CrossRef]

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys.41(Part 2, No. 5B), L571–L573 (2002).
[CrossRef]

Schwiegerling, J.

Seed, A. J.

S. Gauza, H. Wang, C.-H. Wen, S.-T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys.42, 3463–3466 (2003).
[CrossRef]

Su, W. C.

W. C. Su, C. Y. Chen, Y. F. Wang, Y. W. Chen, and S. S. Yang, “Effect of a diffuser on distortion reduction for a virtual image projector,” J. Opt.13(10), 105401 (2011).
[CrossRef]

C. Y. Chen, W. C. Su, Y. F. Wang, and C. H. Chen, “Reduction of distortion aberration in imaging systems by using a microlens array,” Opt. Commun.283(14), 2798–2802 (2010).
[CrossRef]

Valley, P.

Wang, H.

S. Gauza, H. Wang, C.-H. Wen, S.-T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys.42, 3463–3466 (2003).
[CrossRef]

Wang, Y. F.

W. C. Su, C. Y. Chen, Y. F. Wang, Y. W. Chen, and S. S. Yang, “Effect of a diffuser on distortion reduction for a virtual image projector,” J. Opt.13(10), 105401 (2011).
[CrossRef]

C. Y. Chen, W. C. Su, Y. F. Wang, and C. H. Chen, “Reduction of distortion aberration in imaging systems by using a microlens array,” Opt. Commun.283(14), 2798–2802 (2010).
[CrossRef]

Wen, C. H.

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol.1(1), 51–61 (2005).
[CrossRef]

Wen, C.-H.

S. Gauza, H. Wang, C.-H. Wen, S.-T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys.42, 3463–3466 (2003).
[CrossRef]

Wu, S. T.

S. Gauza, X. Zhu, P. Piecek, R. Dabrowski, and S. T. Wu, “Fast Switching Liquid Crystals for Color-Sequential LCDs,” J. Disp. Technol.3(3), 250–252 (2007).
[CrossRef]

H. Ren and S. T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express14(23), 11292–11298 (2006).
[CrossRef] [PubMed]

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol.1(1), 51–61 (2005).
[CrossRef]

S. T. Wu, U. Efron, and L. D. Hess, “Birefringence measurements of liquid crystals,” Appl. Opt.23(21), 3911–3915 (1984).
[CrossRef] [PubMed]

Wu, S.-T.

S. Gauza, H. Wang, C.-H. Wen, S.-T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys.42, 3463–3466 (2003).
[CrossRef]

Yang, S. S.

W. C. Su, C. Y. Chen, Y. F. Wang, Y. W. Chen, and S. S. Yang, “Effect of a diffuser on distortion reduction for a virtual image projector,” J. Opt.13(10), 105401 (2011).
[CrossRef]

Ye, M.

M. Ye and S. Sato, “New method of voltage application for improving response time of a liquid crystal lens,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)433(1), 229–236 (2005).
[CrossRef]

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys.41(Part 2, No. 5B), L571–L573 (2002).
[CrossRef]

Zhu, X.

S. Gauza, X. Zhu, P. Piecek, R. Dabrowski, and S. T. Wu, “Fast Switching Liquid Crystals for Color-Sequential LCDs,” J. Disp. Technol.3(3), 250–252 (2007).
[CrossRef]

Appl. Opt. (1)

J. Disp. Technol. (2)

S. Gauza, X. Zhu, P. Piecek, R. Dabrowski, and S. T. Wu, “Fast Switching Liquid Crystals for Color-Sequential LCDs,” J. Disp. Technol.3(3), 250–252 (2007).
[CrossRef]

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol.1(1), 51–61 (2005).
[CrossRef]

J. Opt. (1)

W. C. Su, C. Y. Chen, Y. F. Wang, Y. W. Chen, and S. S. Yang, “Effect of a diffuser on distortion reduction for a virtual image projector,” J. Opt.13(10), 105401 (2011).
[CrossRef]

Jpn. J. Appl. Phys. (3)

H. C. Lin and Y. H. Lin, “An electrically tunable focusing pico-projector adopting a liquid crystal lens,” Jpn. J. Appl. Phys.49(10), 102502 (2010).
[CrossRef]

S. Gauza, H. Wang, C.-H. Wen, S.-T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys.42, 3463–3466 (2003).
[CrossRef]

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys.41(Part 2, No. 5B), L571–L573 (2002).
[CrossRef]

Mol. Cryst. Liq. Cryst. (Phila. Pa.) (1)

M. Ye and S. Sato, “New method of voltage application for improving response time of a liquid crystal lens,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)433(1), 229–236 (2005).
[CrossRef]

Opt. Commun. (1)

C. Y. Chen, W. C. Su, Y. F. Wang, and C. H. Chen, “Reduction of distortion aberration in imaging systems by using a microlens array,” Opt. Commun.283(14), 2798–2802 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (2)

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

E. Hecht, Optics (Addison-Wesley, 2002).

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Figures (9)

Fig. 1
Fig. 1

Operation principle of the proposed optical system with the LCLA inserted at the intermediate image plane: (a) without voltage applied to the LCLA; (b) with voltage applied to the LCLA. In the figures, P indicates the principal point of lens 2.

Fig. 2
Fig. 2

Structure of the LCLA used in this experiment.

Fig. 3
Fig. 3

Apparatus for observing the DA correction effects in the optical system with LCLA.

Fig. 4
Fig. 4

Interference ring patterns of the LCLA at various voltages: (a) 0, (b) 2, (c) 2.5, (d) 3, (e) 3.5, and (f) 4 V.

Fig. 5
Fig. 5

Measured focal powers of the LCLA at various voltages.

Fig. 6
Fig. 6

Pincushion DA images of the object when the LCLA is supplied with (a) 0, (b) 1.5, (c) 2, (d) 2.5, (e) 3, and (f) 3.5 V.

Fig. 7
Fig. 7

Barrel DA images of the object when the LCLA is supplied with (a) 0, (b) 1.5, (c) 2, (d) 2.5, (e) 3, and (f) 3.5 V.

Fig. 8
Fig. 8

DA images of the object when the rubbing direction of the LCLA has an angle of (a) 0°, (b) 90°, (c) 0°, and (d) 90° with respect to the transmission axis of the polarizer. In (a) and (b), the DC is located 300 mm behind lens 2, whereas in (c) and (d), the DC is located 1060 mm behind lens 2. The voltage applied to the LCLA is 2 V. In each picture, R and P indicate rubbing direction of the LCLA and transmission axis of the polarizer, respectively.

Fig. 9
Fig. 9

DA images of the object: (a) with LCLA at zero voltage, and (b) with LCLA at 2 V. The DC is placed 400 mm behind lens 2.

Equations (1)

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f= r 2 2dδn

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