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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 9428–9436
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Electrically tunable-focusing and polarizer-free liquid crystal lenses for ophthalmic applications

Yi-Hsin Lin and Hung-Shan Chen  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 9428-9436 (2013)
http://dx.doi.org/10.1364/OE.21.009428


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Abstract

An electrically tunable-focusing and polarizer-free liquid crystal (LC) lens for ophthalmic applications is demonstrated. The optical mechanism of a LC lens used in human eye system is introduced. The polarizer-free LC lens for myopia-presbyopia based on artificial accommodation is demonstrated. The continuously tunable-focusing properties of the LC lenses are more practical in applications for different visional conditions of people. The concept we proposed can also be applied to another types of lenses as long as the focusing properties are tunable. The concept in this paper can also be extensively applied to imaging systems, and projection systems, such as cameras in cell phones, pico projectors, and endoscopes.

© 2013 OSA

1. Introduction

2. Mechanism and operating principles

The image system of a human eye with an ophthalmic lens can be simplified as depicted in Fig. 1 (a)
Fig. 1 Operating principles of an electrically tunable ophthalmic lens using a polarizer-free LC lens. (a)When the LC lens is off and the crystalline lens is relaxed (i.e., lens powers of both lenses are zero), the farthest point the eye can see is point A. (b) When the LC lens is still off, the eye can see near under the curvature change of the crystalline lens. The nearest point the eye can see is point B. (c) From (b), when the LC lens is turned on as a positive lens, the nearest point shifts to point C (i.e., d3>d4). (d) From (c), the eye can clearly see the object in a range between point A and point C. (i.e., d0>d5>d4) when we manipulate the lens powers of the positive LC lens and the crystalline lens. (e) When the LC lens is operated as a negative lens and the crystalline lens is relaxed, the farthest point eye can see is point E. (d6>d0).
. In Fig. 1(a), the system consists of a LC lens (ophthalmic lens), a cornea, a crystalline lens and a retina as an image sensor. The LC lens and the crystalline lens of the eye are tunable-focusing lenses. After light passes through the eye system, the image formations can be expressed as:
1do+1d'=PLC(V),
(1)
1dgd'+nd''=PC,
(2)
nd1d''+nd2=Pcryst
(3)
where do is the distance between the solid lens and object, dg is the distance between the LC lens and cornea, d1 is the distance between the cornea and the lens in the eye, and d2 is the distance between the retina and the lens in the eye. d’ is the image distance of the first image after light passes through the LC lens and d” is the second image after light passes through the cornea. n is the refractive index of the eye ball (~1.333 in average), Pc is the lens power (or the inverse of the focal length) of the cornea (~42.735 m−1) [5

5. D. A. Atchison and G. Smith, Optics of The Human Eyes (Elsevier Science Limited, 2002).

], Pcryst is the lens power of the crystalline lens in the eye, and PLC(V) is the voltage-dependent lens power of the LC lens. According to Eqs. (1)-(3), do can be solved as:
do=1PLC(V)+S(Pcryst),
(4)
where S(Pcryst)is the effective lens power of eyes which satisfies Eq. (5).
S(Pcryst)=1dg1S'(Pcryst),
(5)
In Eq. (5), S'(Pcryst) satisfies Eq. (6).

S'(Pcryst)=Pc1d1n1Pcrystnd2
(6)

The operating principles of an electrically tunable ophthalmic lens on a human eye system are illustrated in Figs. 1(a)-1(e). Here is an example using a double-layered LC lens which is polarization independent or polarizer-free. When the LC lens is off and the crystalline lens is relaxed (i.e. PLC(V) = 0 and S~0), the farthest point the eye can see is point A in Fig. 1(a). From Eq. (4), do is infinity. This means people with relaxed normal eyes (or emmetropia) can see clearly even though the object is at infinity. When the LC lens is still off, the eye can see closer under a curvature change of the crystalline lens (i.e. Pcryst ≠0 and then S≠0). The nearest point eye can see is point B in Fig. 1(b). From Figs. 1(a) and 1(b), when the crystalline lens changes the curvature, eyes can see objects clearly as the objects is located between point A and point B. This is so-called accommodation of eyes. We define the furthest and closest object points for the clear vision as the far point and the near point, respectively. In Figs. 1(a) and 1(b) the distance between the far and near points (i.e. point A and point B) is called the range of accommodation. The difference between 1/do and 1/d3 is defined as amplitude of accommodation.

For myopic people, do in Fig. 1(a) is no longer infinity, but a finite distance due to S≠0. In Fig. 1(b), d3 for the near point B depends on the maximum lens power of the crystalline lens. However, d3 for the near point B increases with the age [4

4. M. Jalie, Opthalmic lenses & Dispensing, 3rd. ed. (Elsevier/Butterworth Heinemann, 2008).

]. This means aging eyes cannot see clearly when the objects are too closed to the eyes. This is also called presbyopia. In order to compensate the degradation of accommodation originating from the aging crystalline lens, we can use a tunable focusing lens. In Fig. 1(c), when the crystalline lens has its maximum lens power and the LC lens is active as a positive lens (i.e. PLC(V)>0) by means of adjusting the distribution of refractive indices of the LC lens under applied electric fields, the nearest point shifts from point B to point C (i.e. d3>d4). This also means the eye can clearly see the object in a range between point A and point C (i.e. d0>d5>d4) by adjusting the lens powers of the positive LC lens and the crystalline lens in Fig. 1(d).

When the people suffer from presbyopia, the LC lens can assist people to see clearly as the object is nearby. Even though the crystalline lenses of eyes lose the function of accommodation, the LC lens can be an extra-artificial crystalline lens to help elderly to see objects close by. The lens power of the LC lens (PLC(V)) can be expressed as [13

13. H. C. Lin, M. S. Chen, and Y. H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011).

]:
PLC(V)=2δn(V)dr2
(7)
where d is the thickness of the LC layer (or cell gap), r is the radius of the aperture of the LC lens, and δn(V)is the difference of the refractive indices between the rim and the middle of the aperture. When the people suffer from not only presbyopia but also myopia, the LC lens can help people in correcting both visional problems. By manipulating the distribution of LC molecules, the LC lens can be operated as a negative lens as well (i.e.δn(V)<0 and PLC(V)<0). When the LC lens acts as a negative lens and the crystalline lens is relaxed (i.e. S~0), the far point is shifted from point A to point E, as shown in Fig. 1(e) (i.e. d6>d0). Therefore, by switching the lens power of the LC lens, we can realize an electrically tunable ophthalmic lens for presbyopia and even myopia-presbyopia owing to an artificial compensation of the accommodation of human eyes.

3. Experimental results and discussions

The structure of such a LC lens consists of Indium Tin Oxide (ITO) electrodes, an insulating layer of polymer NOA81(Norland), two glass substrates, alignment layers of polyvinyl alcohol (PVA), two LC layers and a separator of a polymeric layer to separate two LC layers. The function of the middle polymeric layer cannot only align LC directors, but also be a cell separator; meanwhile, the optical properties of the polymeric layer are also polarization independent. Compared to the conventional one using a glass substrate as a separator, the polymeric layer possesses the advantages of a thin thickness, no need of an extra-alignment layer, and easily to be embedded into the double-layered structure. The fabrication process of the polymeric layer is as follows. We filled nematic LC (Merck, MLC 2070, Δn = 0.26 for λ = 589.3 nm at 20°C), reactive mesogen (Merck, RM 257), and photoinitiator (Merck, IRG-184) at 20:79:1 wt% ratios into the gap between two ITO glass substrates coated with PVA layers whose rubbing directions were orthogonal to each other. The thickness between those two ITO glass substrates was 50 μm and then we applied voltages of 300 Vrms (frequency was 1kHz) on ITO electrodes in order to reorient LC directors along electric fields. Then the cell was exposed to UV light (~3mW/cm2) for 1 hour for photo-polymerization. After photopolymerization, we peeled off the glass substrates by a thermal releasing process and obtained the polymeric layer. After peeling, the polymeric layer was assembled with two coated glass substrates (thickness = 2.1mm), and nematic LC mixture of MLC-2070 to construct the structure of the LC lens depicted in Fig. 2(a). The thickness of each LC layer in Fig. 2(a) was 50 μm controlled by mylar films. The aperture size of the LC lens was 6 mm. In Fig. 2(a), the rubbing directions of two alignment layers were perpendicular to each other. Actually, we can also use homeotropic alignment of the polymeric layer before polymerization, but the LC materials in the LC layers should be chosen properly.

Without applied voltages, the lens power of the LC lens is zero (Fig. 2(a)). When the applied voltage V2> V1, the LC lens is a negative lens because the LC directors around the rim of the aperture are parallel to the glass substrates and the LC directors inside the aperture are more perpendicular to the glass substrates as shown in Fig. 2(c). Thus, an incident plane wave is converted to a diverging parabolic wave by the negative LC lens. Similarly, the LC lens is a positive lens when the applied voltage V2< V1, as shown in Fig. 2(b). An incident plane wave is then converted to a converging parabolic wave by the positive LC lens. By changing the magnitude of the voltages, the focal length of the LC lens is electrically switchable.

To demonstrate the concept of an electrically tunable ophthalmic lens for myopia-presbyopia and to measure the performance, we exploited the same camera to mimic a presbyopic eye with amplitude of accommodation of 2D, a common presbyopic vision for people at the age of 50, by means of adjusting the equivalent focal length of lens module of the camera. The LC lens was directly attached on the camera. Then we performed the similar measurement to record the objective distance. Figures 4(a)
Fig. 4 (a)The objective distance as a function of accommodation of camera at different lens power of the LC lens. The camera was set to mimic a myopic-presbyopic eye with amplitude of accommodation of 2 D. (b) The same Fig. 4(a) with different range of the objective distance.
and 4(b) show the objective distance as a function of accommodation of the camera at different lens power of the LC lens. Without the LC lens (i.e. 0D), eyes can see the objective clearly from 100 cm to 31.6 cm. (Black squares in Figs. 5(a)
Fig. 5 Image performances of the eyeglasses for myopia-presbyopia. Four pieces of objective papers with symbols are placed at 360 cm, 100 cm, 33 cm and 20 cm. (a) When the lens power of the LC lens is −1D, the objective at 360 cm is clear. (b) When the lens power of the LC lens is 0D, the objective at 100 cm is clear. (c) When the lens power of the LC lens is 2D, the objective at 33 cm is clear. The accommodation of camera = 0D in (a), (b), and (c). (d) The objective at 20 cm is also clear under both of the accommodation of camera = 2D and the lens power of the LC lens = 2D.
and 5(b))When the LC lens is switched to a negative lens with a lens power of −1D with applied voltages (V1, V2) = (20 Vrms,160 Vrms), eyes can see clearly from ~360 cm to ~49.3 cm. (Pink triangles in Figs. 4(a) and 4(b)) This means the eyes can see farther and it also indicates the correction of myopia. When the LC lens is switched to a positive lens with a lens power of + 1D with applied voltages (V1, V2) = (160 Vrms, 50 Vrms), eyes can see clearly from ~49.3 cm to ~23.5 cm. (Blue dots in Figs. 4(a) and 4(b)) This means people can see closer with adding + 1D lens power of LC lens. When the LC lens is switched to a positive lens with a lens power of + 2D with applied voltages (V1, V2) = (160 Vrms, 0 Vrms), eyes can see clearly from ~32.5 cm to ~19 cm. (Red diamonds in Figs. 4(a) and 4(b)) In Figs. 4(a) and 4(b), people can see nearer with an assistance of a positive lens power of the LC lens and people can see farther with an assistance of a negative lens power of the LC lens. This also means the LC lens can correct myopia and presbyopia together by changing the applied voltages of the LC lens. When people lost the ability of accommodation (i.e. 0D of accommodation of camera in Figs. 4(a) and 4(b)), they can still see the objective clear in a range from 360 to 32.5 cm with extra artificial accommodation of the LC lens whose lens power is electrically switchable. In our measurement, the errors mainly result from the depth-of-field of the image, especially large depth-of-field as the object is larger than 100 cm.

Figures 5(a)-5(d) show the image performances of the LC lens for myopia-presbyopia. The LC lens was still attached on the camera and took photos directly under an ambient white light. Four pieces of objective papers with symbols were placed at 360 cm, 100 cm, 33 cm and 20 cm away from the LC lens. We adjust the camera properly in order to mimic the human eyes with myopia-presbyopia. At first, the camera did not have any accommodation (i.e. 0D). When the lens power of the LC lens was 0D, the objective at 100 cm could be seen clearly. (Fig. 5(b)) That means the far point was 100 cm. When the lens power of the LC lens was −1D, the objective at 360 cm was clear.(Fig. 5(a)) The vision is corrected by the LC lens with a negative lens power. When the lens power of the LC lens was switched to 2D by adjusting applied voltages, the objective at 33 cm was clear. (Fig. 5(c)) The objective at 20 cm was also clear as both of the accommodation of camera and the lens power of the LC lens were 2D. (Fig. 5(d)) This means that under assistance of the accommodation of crystalline lenses of eyes and the lens power of the LC lens, people can see the object closer. As a result, people with myopia-presbyopia can see farther and see nearer when the LC lens was operated as a positive or a negative lens even though people possess only limit accommodation of the crystalline lens of eyes.

The LC lens as a positive lens can help to decide a new near point in vision in order to correct presbyopia, and the LC lens as a negative lens can help to decide a new far point in vision in order to correct myopia. Moreover, the LC lens can be operated as a positive and a negative lens at the same time to correct myopia-presbyopia. It looks that the LC lens only need to switch between on and off (focus and out of focus), instead of continuously tunable focusing properties of eyeglasses. However, the LC lens still needs continuously tunable focusing properties for practical applications. The reason is as follows. The eye conditions or visions are different for different people. The LC lens with continuously tunable focusing properties is suitable for different visions just by setting different applied voltage. Even though a person has the degradation of the vision with time, the person can electrically adjust the LC lens by himself. This is more practical for application. In comparison, the conventional diffractive type of tunable eyeglasses only has on and off states [16

16. G. Q. 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. U.S.A. 103(16), 6100–6104 (2006). [PubMed]

]. When people experience the degradation of presbyopia with age, they have to re-design the complicated and expensive diffractive pattern of the tunable eyeglasses. In spite of the improvement of 4-steps design of the diffractive type of eyeglasses, the tradeoff is the decrease of diffraction efficiency from ~98% to ~40% [19

19. 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). [PubMed]

]. Our design of LC lens has several advantages: a compact in-cell structure, reduction of the interfacial reflection, and no need extra alignment layer for the polymeric layer compared with the LC lens with 4 LC layers [15

15. M. Ye, B. Wang, and S. Sato, “Polarization-independent liquid crystal lens with four liquid crystal layers,” IEEE Photon. Technol. Lett. 3, 505–507 (2006).

]. To further enlarge the tunable range of the lens power and the aperture size of the LC lens, some methods should be adopted according to Eq. (6), such as large cell gap, high birefringence of LC materials or other LC modes [20

20. H. C. Lin and Y. H. Lin, “An electrically tunable-focusing liquid crystal lens with a low voltage and simple electrodes,” Opt. Express 20(3), 2045–2052 (2012). [PubMed]

23

23. A. N. Simonov, G. Vdovin, and M. Loktev, “Liquid-crystal intraocular adaptive lens with wireless control,” Opt. Express 15(12), 7468–7478 (2007). [PubMed]

]. The polarization independent LC lens we proposed in this paper provides good image performance and easy fabrication process compared to the diffractive-type LC lenses [16

16. G. Q. 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. U.S.A. 103(16), 6100–6104 (2006). [PubMed]

].

4. Conclusion

We demonstrated a tunable ophthalmic lens by using a polarizer-free LC lens. The myopia and presbyopia could be corrected. We also studied the optical principles of designing the tunable eyeglasses and also experimentally demonstrated the concepts. The concept we proposed can also be applied to another types of tunable focusing lenses, such as liquid lenses. The tunable range of the lens power of the LC lens can be improved by adding LC layers, increasing the thickness of the LC layer, and adopting LC materials with high birefringence [13

13. H. C. Lin, M. S. Chen, and Y. H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011).

]. To lower the driving voltage of the LC lens, we can coat a thin layer with high impedance on the electrodes or increase the relative permittivity (or dielectric constant) of the glass substrates [13

13. H. C. Lin, M. S. Chen, and Y. H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011).

]. Adding other polymeric layer with a distribution of the relative permittivity can also reduce the applied voltage (< 5Vrms) [20

20. H. C. Lin and Y. H. Lin, “An electrically tunable-focusing liquid crystal lens with a low voltage and simple electrodes,” Opt. Express 20(3), 2045–2052 (2012). [PubMed]

]. Moreover, multiple layers of the LC lens can be adopted to increase the phase of the LC lens in order to enlarge the aperture size with a large tunable range. Therefore, the LC lenses are able to provide a full corrected field of vision and are not dimensionally limited. In terms of future clinical ophthalmic use, the aspherical phase profile of the LC lenses, special aberrations for some diseases (e.g. astigmatism), chromatic properties, and optical properties for oblique light should also be considered in the designs of the LC lenses. We believe this study provides a guideline to help the researchers and engineers to develop the electrically tunable ophthalmic lenses. The concept in this paper can also be applied to cameras in cell phones, pico projectors, and endoscopes.

Acknowledgments

The authors are indebted to Mr. Ming-Syuan Chen and Mr. Yu-Shih Tsou for technical assistance. This research was supported mainly by Liqxtal Technology Inc and partially by the National Science Council (NSC) in Taiwan under the contract no. NSC 101-2112-M-009 −011 -MY3.

References and links

1.

L. Werner, F. Trindade, F. Pereira, and L. Werner, “Physiology of accommodation and presbyopia,” Arq. Bras. Oftalmol. 63, 503–509 (2000).

2.

E. Hermans, M. Dubbelman, R. van der Heijde, and R. Heethaar, “The shape of the human lens nucleus with accommodation,” J. Vis. 7(10), 16, 1–10 (2007). [PubMed]

3.

G.-Y. Yoon and D. R. Williams, “Visual performance after correcting the monochromatic and chromatic aberrations of the eye,” J. Opt. Soc. Am. A 19(2), 266–275 (2002). [PubMed]

4.

M. Jalie, Opthalmic lenses & Dispensing, 3rd. ed. (Elsevier/Butterworth Heinemann, 2008).

5.

D. A. Atchison and G. Smith, Optics of The Human Eyes (Elsevier Science Limited, 2002).

6.

H. Ren and S. T. Wu, Introduction to adaptive lenses (John Wiley & Sons, 2012).

7.

E. J. Fernandez, L. Vabre, B. Hermann, A. Unterhuber, B. Povazay, and W. Drexler, “Adaptive optics with a magnetic deformable mirror: applications in the human eye,” Opt. Express 14(20), 8900–8917 (2006). [PubMed]

8.

C. A. López and A. H. Hirsa, “Fast focusing using a pinned-contact oscillating liquid lens,” Nat. Photonics 2(10), 610–613 (2008).

9.

H. C. Lin and Y. H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97(6), 063505 (2010).

10.

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).

11.

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).

12.

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).

13.

H. C. Lin, M. S. Chen, and Y. H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011).

14.

M. Ye and S. Sato, “Liquid Crystal Lens with Insulator Layers for Focusing Light Waves of Arbitrary Polarizations,” Jpn. J. Appl. Phys. 42(Part 1, No. 10), 6439–6440 (2003).

15.

M. Ye, B. Wang, and S. Sato, “Polarization-independent liquid crystal lens with four liquid crystal layers,” IEEE Photon. Technol. Lett. 3, 505–507 (2006).

16.

G. Q. 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. U.S.A. 103(16), 6100–6104 (2006). [PubMed]

17.

Y. H. Lin, H. Ren, Y. H. Wu, Y. Zhao, J. Fang, Z. Ge, and S. T. Wu, “Polarization-independent liquid crystal phase modulator using a thin polymer-separated double-layered structure,” Opt. Express 13(22), 8746–8752 (2005). [PubMed]

18.

Y. H. Lin, H. S. Chen, H. C. Lin, Y. S. Tsou, H. K. Hsu, and W. Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).

19.

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). [PubMed]

20.

H. C. Lin and Y. H. Lin, “An electrically tunable-focusing liquid crystal lens with a low voltage and simple electrodes,” Opt. Express 20(3), 2045–2052 (2012). [PubMed]

21.

A. F. Naumov, G. D. Love, M. Y. Loktev, and F. L. Vladimirov, “Control optimization of spherical modal liquid crystal lenses,” Opt. Express 4(9), 344–352 (1999). [PubMed]

22.

A. N. Simonov, G. Vdovin, and M. C. Rombach, “Cubic optical elements for an accommodative intraocular lens,” Opt. Express 14(17), 7757–7775 (2006). [PubMed]

23.

A. N. Simonov, G. Vdovin, and M. Loktev, “Liquid-crystal intraocular adaptive lens with wireless control,” Opt. Express 15(12), 7468–7478 (2007). [PubMed]

OCIS Codes
(230.2090) Optical devices : Electro-optical devices
(230.3720) Optical devices : Liquid-crystal devices

ToC Category:
Optical Devices

History
Original Manuscript: February 1, 2013
Revised Manuscript: March 6, 2013
Manuscript Accepted: April 2, 2013
Published: April 9, 2013

Virtual Issues
Vol. 8, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Yi-Hsin Lin and Hung-Shan Chen, "Electrically tunable-focusing and polarizer-free liquid crystal lenses for ophthalmic applications," Opt. Express 21, 9428-9436 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-9428


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References

  1. L. Werner, F. Trindade, F. Pereira, and L. Werner, “Physiology of accommodation and presbyopia,” Arq. Bras. Oftalmol.63, 503–509 (2000).
  2. E. Hermans, M. Dubbelman, R. van der Heijde, and R. Heethaar, “The shape of the human lens nucleus with accommodation,” J. Vis.7(10), 16, 1–10 (2007). [PubMed]
  3. G.-Y. Yoon and D. R. Williams, “Visual performance after correcting the monochromatic and chromatic aberrations of the eye,” J. Opt. Soc. Am. A19(2), 266–275 (2002). [PubMed]
  4. M. Jalie, Opthalmic lenses & Dispensing, 3rd. ed. (Elsevier/Butterworth Heinemann, 2008).
  5. D. A. Atchison and G. Smith, Optics of The Human Eyes (Elsevier Science Limited, 2002).
  6. H. Ren and S. T. Wu, Introduction to adaptive lenses (John Wiley & Sons, 2012).
  7. E. J. Fernandez, L. Vabre, B. Hermann, A. Unterhuber, B. Povazay, and W. Drexler, “Adaptive optics with a magnetic deformable mirror: applications in the human eye,” Opt. Express14(20), 8900–8917 (2006). [PubMed]
  8. C. A. López and A. H. Hirsa, “Fast focusing using a pinned-contact oscillating liquid lens,” Nat. Photonics2(10), 610–613 (2008).
  9. H. C. Lin and Y. H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett.97(6), 063505 (2010).
  10. 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).
  11. 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).
  12. S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys.18(9), 1679–1684 (1979).
  13. H. C. Lin, M. S. Chen, and Y. H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater.12(6), 234–240 (2011).
  14. M. Ye and S. Sato, “Liquid Crystal Lens with Insulator Layers for Focusing Light Waves of Arbitrary Polarizations,” Jpn. J. Appl. Phys. 42(Part 1, No. 10), 6439–6440 (2003).
  15. M. Ye, B. Wang, and S. Sato, “Polarization-independent liquid crystal lens with four liquid crystal layers,” IEEE Photon. Technol. Lett.3, 505–507 (2006).
  16. G. Q. 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. U.S.A.103(16), 6100–6104 (2006). [PubMed]
  17. Y. H. Lin, H. Ren, Y. H. Wu, Y. Zhao, J. Fang, Z. Ge, and S. T. Wu, “Polarization-independent liquid crystal phase modulator using a thin polymer-separated double-layered structure,” Opt. Express13(22), 8746–8752 (2005). [PubMed]
  18. Y. H. Lin, H. S. Chen, H. C. Lin, Y. S. Tsou, H. K. Hsu, and W. Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett.96(11), 113505 (2010).
  19. 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). [PubMed]
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