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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 4738–4746
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Using photopolymerization to achieve tunable liquid crystal lenses with coaxial bifocals

Che Ju Hsu and Chia Rong Sheu  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 4738-4746 (2012)
http://dx.doi.org/10.1364/OE.20.004738


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Abstract

Liquid crystal (LC) lenses with circular hole-patterned electrodes possess the excellent capabilities of tunable focal lengths. In this paper, we demonstrate the performance of a specific LC lens with tunable coaxial bifocals (CB) synthesized via photopolymerization of LC cells. The characteristics of tunable CB are clearly exhibited when the voltage applied is continuously increased, eventually disappearing until only one focus is left when significantly higher voltages are applied. We simultaneously demonstrate two types of tunable CB LC lenses fabricated via different photocurable processes and determine their optical functions.

© 2012 OSA

1. Introduction

In general, LC lenses have electrically tunable focal lengths. Multi-focal lengths can be achieved by varying the applied voltages, with one focus corresponding to one applied voltage. Lenses with two coaxial focuses had been proposed and realized in liquid lenses [9

9. H. B. Yu, G. Y. Zhou, F. K. Chau, F. W. Lee, S. H. Wang, and H. M. Leung, “A liquid-filled tunable double-focus microlens,” Opt. Express 17(6), 4782–4790 (2009). [CrossRef] [PubMed]

, 10

10. F. C. Wippermann, P. Schreiber, A. Bräuer, and P. Craen, “Bifocal liquid lens zoom objective for mobile phone applications,” Proc. SPIE 6501, 650109, 650109-9 (2007). [CrossRef]

] and LC lenses [11

11. M. Hain, R. Glöckner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun. 188(5-6), 291–299 (2001). [CrossRef]

, 12

12. Y. J. Lee, Y. W. Kim, Y. K. Kim, C. J. Yu, J. S. Gwag, and J. H. Kim, “Microlens array fabricated using electrohydrodynamic instability and surface properties,” Opt. Express 19(11), 10673–10678 (2011). [CrossRef] [PubMed]

]. In the current study, they are referred to as the optical feature of coaxial bifocals (CB). Tunable CB LC lenses have potential applications in different fields. Single tunable CB LC lenses can be used in multi-layer [13

13. H. R. Stapert, S. del Valle, E. J. K. Verstegen, B. M. I. van der Zande, J. Lub, and S. Stallinga, “Photoreplicated anisotropic liquid-crystalline lenses for aberration control and dual-layer readout of optical discs,” Adv. Funct. Mater. 13(9), 732–738 (2003). [CrossRef]

] optical data storage because of its tunable focal lengths. For a microlens array composed of tunable CB LC lens units, the viewing depth in autostereoscopy, such as in integral photography [14

14. H. Choi, J. H. Park, J. Hong, and B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” Jpn. J. Appl. Phys. 43(8A), 5330–5336 (2004). [CrossRef]

], is largely improved. If these lenses are carefully designed and fabricated, suitable specifications can be achieved for more applications. In the present paper, we demonstrate a method of photopolymerization to obtain tunable CB LC lenses. Photopolymerization is a common process used to treat LC cells for certain applications, such as stabilization of LC molecules and improvement of the optical response time. Here, photopolymerization is used to modify properties in the central area of LC cells. Photopolymerized LCs located in the central area exhibit a reorientation behavior different from those located in the peripheral area without photopolymerization under applied voltages. If the central area is exposed to UV light for a significant length of time, the directions of LCs can be set to create an intrinsic focus. The peripheral area without UV exposure still retains the feature of tunable focal lengths. By contrast, if the UV-exposed area is treated for a short period of time, the slight change in the exposed area also affects the LC reorientation. Therefore, areas with and without UV exposure exhibit the characteristics of tunable focal lengths but have different properties.

2. Prior LC lens structure and tunable CB LC lens fabrication with photopolymerization

A material mixed with RM257 (Merck), a photoinitiator (Iragcure 651, Chiba), and LCs (E7, Merck) at a weight ratio (wt. %) of 3.0:0.14:96.86 was prepared. The completely mixed material was injected through capillary action into empty cells on the 100 °C hot plate. Voltages (from 0 Vrms to 100 Vrms) were applied to the completely injected LC at a slow increasing rate to prevent the occurrence of disclination lines. The applied voltages had a square waveform and a frequency of 1 kHz. The LC cells were further modified via special photopolymerization to fabricate tunable CB LC lenses. A homemade photo-mask from a printed slide film and with a clear circular area (~3.5 mm in diameter) over the cell was used and is schematically shown in Fig. 2
Fig. 2 Schemes of a photo-mask and the LC cell configuration for the fabrication of tunable CB LC lens via photopolymerization: (a) a homemade photo-mask from a printed slide film has a clear circular area approximately 3.5 mm in diameter; and (b) CB LC lens structure with a circularly patterned electrode. The photo-mask comes into contact with the cell during UV exposure under an applied voltage of 100 Vrms.
. The LC cells were exposed to UV light at a power of 6 mW/cm2 under applied voltages. The optical performance of the CB LC lenses differed at different UV exposure times. In this study, two LC lens types, namely, Type-A and Type-B, exposed in UV light for 2 and 2.5 minutes under 100 Vrms voltages, respectively, are reported. Both types exhibit the characteristics of tunable CB LC lenses, and their optical performances are demonstrated in the subsequent sections.

3. Optical characteristics of CB LC lenses with experimental measurements

The optical characteristics of the fabricated CB LC lenses were measured using a widely used experimental setup [16

16. S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35(Part 1, No. 9A), 4668–4672 (1996). [CrossRef]

] to observe the interference patterns in the LC cells, which were recorded with a charge-coupled device (CCD) camera. The experimental setup had a He-Ne laser collimated and expanded light beam (λ = 632.8 nm), which was a normal incident when the tunable CB LC lens was placed between a pair of crossed polarizers. The rubbing direction of the LC cells was 45° with respect to the polarization of both polarizers. Figure 3
Fig. 3 Interference patterns for Type-A and Type-B LC lenses. (a) Type-A LC lens after UV exposure for 2 minutes. No interference pattern was detected in the cell without an applied voltage. The dark circle in the center of the LC cell after UV exposure represents the boundary of the UV-exposed area. (b) Type-B LC lens after UV exposure for 2.5 minutes, with other cell conditions the same as in Fig. 3(a). An intrinsic interference pattern can be seen in the cell without an applied voltage, indicating the existence of an intrinsic focus. The symbol on the right side of the figure shows the rubbing direction (labeled R) in the cell and the polarization of a pair of crossed polarizers (labeled A and P) in the experimental setup.
shows the interference patterns of two typical CB LC lenses (i.e., Type-A and Type-B) without an applied voltage. Figure 3(a) shows the experimental observation of an optical interference in a Type-A LC lens, which was developed via UV exposure for 2 minutes and has a circular central area ~3.5 mm in diameter. No interference pattern was observed in the cell without an applied voltage. By contrast, Fig. 3(b) shows the results of a Type-B LC lens under cell conditions similar to that of the cell shown in Fig. 3(a), except for a longer UV exposure time (2.5 minutes). An intrinsic interference pattern occurred in the cell without the applied voltage, which resulted in an intrinsic focus.

3.1. Type-A LC lenses

Type-A LC lenses are processed with a shorter of photopolymerization time. No obvious fixed interference patterns occurred in the entire circular area of the cell (7 mm in diameter) with or without UV exposure. When the voltages in the cells were gradually increased, the directions of the LC molecules with positive dielectric anisotropy were reoriented along the electric field so that the ideally spatially quadratic distributions of the refractive indices occurred in the form of interference patterns. Figure 4
Fig. 4 Interference patterns for a Type-A LC lens under different applied voltages: (a) 0, (b) 40, (c) 100, and (d) 180 Vrms. The red circle indicates the boundary of the UV-exposed areas. The difference in interference patterns in the exposed and unexposed areas is significant. When the applied voltages were increased, the variations in the interference patterns in both areas were independent. When a higher voltage (140 Vrms) was used, the interference patterns in both areas gradually merged into a single interference pattern. The symbol on the right side of figure indicates the rubbing direction (labeled R) in the cell and the polarization of a pair of crossed polarizers (labeled A and P) in the experimental setup.
shows a sequence of interference patterns for a Type-A LC lens under different applied voltages. The difference in the interference patterns in the UV-exposed and unexposed areas are highly obvious and imply that the reorientations of the LCs in the exposed and unexposed areas suffer different degrees of constraints. The difference in the interference patterns for both areas was gradually reduced when a higher voltage (100 Vrms) was applied. Finally, only one smooth and continuous interference pattern was left in the cell when voltages above 140 Vrms were applied.

We also observed and measured the focusing properties of the Type-A LC lenses. An expanded and collimated He-Ne laser beam was normally incident to the cell, in front of which a polarizer with a polarization parallel to the rubbing direction of the cell was placed. When a 40 Vrms voltage was applied to the cell, two focuses located 33 and 80 cm away from the cell were observed. The results are shown in Fig. 5
Fig. 5 Optical focuses for a Type-A LC lens at 40 Vrms: (a) one focus located 33 cm away from the cell, and (b) the other focus located 80 cm away from the cell. The focal lengths were measured through experimental observations of the focal points of the expanded laser beam.
. The optical characteristics of the CB LC lens were clearly observed.

We measured the variations in the CB of the cell under different applied voltages to evaluate the tunable capabilities of the Type-A LC lenses. The experimental results are shown in Fig. 6
Fig. 6 Characteristics of tunable CB for a Type-A LC lens under different applied voltages. At applied voltages below 30 Vrms, one tunable focus from an inner laser light was out of the focal length of 80 cm. At 40 Vrms, the properties of CB were observed. At 140 Vrms, only one focus was left in the cell.
. The coaxial bifocals were individually formed from two areas. One was the UV-exposed circular area with 3.5 mm in diameter, and the other was the 7 mm diameter circular unexposed area. When an expanded He-Ne laser beam was normally incident to the LC lens, the inner and external light beams were individually focused to monitor the variations in the LC distributions in both areas under different applied voltages.

3.2. Type-B LC lenses

Figure 7
Fig. 7 Interference patterns for a Type-B LC lens under different applied voltages: (a) 0, (b) 30, (c) 100, and (d) 180 Vrms. The red circle indicates the boundary of the UV-exposed areas. An intrinsically fixed interference pattern is clearly seen in the exposed area after photopolymerization for 2.5 minutes. When the applied voltages increased, the interference patterns in the exposed area remained constant, whereas those in the unexposed area varied with the applied voltages. The symbol on the right side of the figure indicates the rubbing direction (labeled R) in the cell and the polarization of a pair of crossed polarizers (labeled A and P) in the experimental setup.
shows the variations in the optical interference patterns for a Type-B LC lens with increasing applied voltages. A polymer network was formed after a long photopolymerization time, which stabilized the reorientation of the LC molecules located in the exposed area. Therefore, an intrinsically fixed interference pattern was observed regardless of the applied voltages. On the other hand, LC molecules located in the unexposed area still varied with varying applied voltages, which contributed to the development of tunable focuses in the cell. In Fig. 7(a), the strange circular texture near the interface between the exposed and unexposed areas may have been caused by diffraction during UV exposure. At much higher applied voltages, this strange texture gradually faded.

Figure 8
Fig. 8 Optical focuses for a Type-B LC lens under an applied voltage of 30 Vrms: (a) one focus was located 42 cm away from the cell, and (b) the other was located 30 cm away from the cell. The focal lengths were measured through experimental observations of the focal points of the expanded laser beam.
shows that two coaxial bifocals, located 42 and 30 cm away from the cell, were formed in the Type-B LC lens under an applied voltage of 30 Vrms.

We also measured the characteristics of the tunable CB for the Type-B LC lenses as shown in Fig. 9
Fig. 9 Characteristics of a tunable CB for a Type-B LC lens under different applied voltages. An intrinsically fixed focus existed in the inner part of the cell after photopolymerization, regardless of the applied voltages. The variation in the other tunable focus with the applied voltages is similar to that of conventional tunable LC lenses.
. Initially, the two focuses were very different from each other, mainly because of the significant difference in the LC distributions of the exposed and unexposed areas in the cell. The two focuses gradually became closer as the applied voltages increased, and merged into one focus at 100 Vrms. At applied voltages higher than 100 Vrms, the two focuses gradually separated from each other. These results indicate that a smooth connection of interference patterns occurred when the cell was subjected to a 100 Vrms voltage.

Finally, we demonstrate the capabilities of a Type-B LC lens used in an imaging system. A polarizer was placed in front of the CCD camera, with the polarization parallel to the X-axis in the coordinate. A Type-B CB LC lens was placed in front of the polarizer, and the mechanical rubbing direction was also parallel to the X-axis. A real object of text was placed a suitable distance away from the Type-B LC lens. We observed and recorded the text images with respect to the different conditions in the imaging system. The conditions are as follows: without a Type-B LC lens, with a Type-B LC lens but without an applied voltage, and with a Type-B LC lens and an applied voltages of 100 Vrms. The imaging system is shown in Fig. 10
Fig. 10 Scheme of an imaging system used to evaluate the capabilities of tunable CB LC lenses.
.

Figure 11
Fig. 11 Comparisons of the imaging capabilities of a tunable Type-B LC lens in the imaging system: (a) without a Type-B LC lens; (b) with a Type-B LC lens but without an applied voltage; and (c) with a Type-B LC lens and an applied voltage of 100 Vrms. A blurred image was observed when no Type-B LC lens was used. When a Type-B LC lens was used but without an applied voltage, a clear image was observed in the central area. When a 100 Vrms voltage was applied with the Type-B LC lens, an overall clear image was obtained because the same focus was achieved in both areas.
shows the imaging performance of the tuning Type-B CB LC lens for an object of text words. Figure 11(a) shows a blurred text image when no Type-B LC lens was placed in the imaging system. When a Type-B LC lens was used in front of the CCD camera but without an applied voltage, a clearer image was obtained in the central area of the LC lens as shown in Fig. 11(b). This clearer text image resulted from the intrinsic focal length in the Type-B LC lens. The image outside red circle remained blurred. In Fig. 11(c), when a 100 Vrms applied voltage was used, the images in both areas became clearer because the same focal lengths were obtained. A small difference in the images in the central area with and without applied voltages was induced by changing the LC orientation. Some LC molecules were not fully aligned with the ideal directions after UV exposure, resulting in non-ideal intrinsic focus. When a 100 Vrms voltage was applied, the orientations of the LC molecules were modified, and a better focus was achieved.

4. Conclusion

We have demonstrated the development of tunable LC lenses via photopolymerization. Type-A and Type-B LC lenses are obtained when LC cells are exposed to UV radiation at different exposure times. For the Type-A LC lens, lens function is not possible without an applied voltage. When the applied voltage is increased, two tunable focal lengths are observed in the cell, which eventually merge into one focus at higher applied voltages. On the other hand, the Type-B LC lens possesses an intrinsically fixed focus without an applied voltage. When the applied voltage is increased, the intrinsic focus retains the same value, whereas the other focus is tunable with respect to various applied voltages. In the future, we will carefully design and fabricate a tunable CB LC lens array for use in integral photography to improve the viewing depth performance.

Acknowledgments

This work is supported by the National Science Council (NSC) in Taiwan under Contract No. 100-2221-E-006-167.

References and links

1.

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

2.

S. Somalingam, K. Dressbach, M. Hain, S. Stankovic, T. Tschudi, J. Knittel, and H. Richter, “Effective spherical aberration compensation by use of a nematic liquid-crystal device,” Appl. Opt. 43(13), 2722–2729 (2004). [CrossRef] [PubMed]

3.

M. Ye, B. Wang, M. Kawamura, and S. Sato, “Image formation using liquid crystal lens,” Jpn. J. Appl. Phys. 46(10A), 6776–6777 (2007). [CrossRef]

4.

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). [CrossRef]

5.

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39(Part 1, No. 2A), 480–484 (2000). [CrossRef]

6.

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, “Tunable-focus flat liquid crystal spherical lens,” Appl. Phys. Lett. 84(23), 4789–4791 (2004). [CrossRef]

7.

H. Ren and S. T. Wu, “Tunable electronic lens using a gradient polymer network liquid crystal,” Appl. Phys. Lett. 82(1), 22–24 (2003). [CrossRef]

8.

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]

9.

H. B. Yu, G. Y. Zhou, F. K. Chau, F. W. Lee, S. H. Wang, and H. M. Leung, “A liquid-filled tunable double-focus microlens,” Opt. Express 17(6), 4782–4790 (2009). [CrossRef] [PubMed]

10.

F. C. Wippermann, P. Schreiber, A. Bräuer, and P. Craen, “Bifocal liquid lens zoom objective for mobile phone applications,” Proc. SPIE 6501, 650109, 650109-9 (2007). [CrossRef]

11.

M. Hain, R. Glöckner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun. 188(5-6), 291–299 (2001). [CrossRef]

12.

Y. J. Lee, Y. W. Kim, Y. K. Kim, C. J. Yu, J. S. Gwag, and J. H. Kim, “Microlens array fabricated using electrohydrodynamic instability and surface properties,” Opt. Express 19(11), 10673–10678 (2011). [CrossRef] [PubMed]

13.

H. R. Stapert, S. del Valle, E. J. K. Verstegen, B. M. I. van der Zande, J. Lub, and S. Stallinga, “Photoreplicated anisotropic liquid-crystalline lenses for aberration control and dual-layer readout of optical discs,” Adv. Funct. Mater. 13(9), 732–738 (2003). [CrossRef]

14.

H. Choi, J. H. Park, J. Hong, and B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” Jpn. J. Appl. Phys. 43(8A), 5330–5336 (2004). [CrossRef]

15.

C. J. Hsu, C. Y. Huang, and C. R. Sheu, “Experimental analysis to avoid migrating zigzag lines occurring in homogeneously aligned liquid crystal lenses with a hole-patterned electrode,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 544(1), 185–191 (2011). [CrossRef]

16.

S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35(Part 1, No. 9A), 4668–4672 (1996). [CrossRef]

OCIS Codes
(160.3710) Materials : Liquid crystals
(220.3630) Optical design and fabrication : Lenses
(230.3720) Optical devices : Liquid-crystal devices

ToC Category:
Optical Devices

History
Original Manuscript: January 3, 2012
Revised Manuscript: February 5, 2012
Manuscript Accepted: February 6, 2012
Published: February 9, 2012

Citation
Che Ju Hsu and Chia Rong Sheu, "Using photopolymerization to achieve tunable liquid crystal lenses with coaxial bifocals," Opt. Express 20, 4738-4746 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4738


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References

  1. 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. U.S.A.103(16), 6100–6104 (2006). [CrossRef] [PubMed]
  2. S. Somalingam, K. Dressbach, M. Hain, S. Stankovic, T. Tschudi, J. Knittel, and H. Richter, “Effective spherical aberration compensation by use of a nematic liquid-crystal device,” Appl. Opt.43(13), 2722–2729 (2004). [CrossRef] [PubMed]
  3. M. Ye, B. Wang, M. Kawamura, and S. Sato, “Image formation using liquid crystal lens,” Jpn. J. Appl. Phys.46(10A), 6776–6777 (2007). [CrossRef]
  4. 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). [CrossRef]
  5. S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys.39(Part 1, No. 2A), 480–484 (2000). [CrossRef]
  6. H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, “Tunable-focus flat liquid crystal spherical lens,” Appl. Phys. Lett.84(23), 4789–4791 (2004). [CrossRef]
  7. H. Ren and S. T. Wu, “Tunable electronic lens using a gradient polymer network liquid crystal,” Appl. Phys. Lett.82(1), 22–24 (2003). [CrossRef]
  8. 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]
  9. H. B. Yu, G. Y. Zhou, F. K. Chau, F. W. Lee, S. H. Wang, and H. M. Leung, “A liquid-filled tunable double-focus microlens,” Opt. Express17(6), 4782–4790 (2009). [CrossRef] [PubMed]
  10. F. C. Wippermann, P. Schreiber, A. Bräuer, and P. Craen, “Bifocal liquid lens zoom objective for mobile phone applications,” Proc. SPIE6501, 650109, 650109-9 (2007). [CrossRef]
  11. M. Hain, R. Glöckner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun.188(5-6), 291–299 (2001). [CrossRef]
  12. Y. J. Lee, Y. W. Kim, Y. K. Kim, C. J. Yu, J. S. Gwag, and J. H. Kim, “Microlens array fabricated using electrohydrodynamic instability and surface properties,” Opt. Express19(11), 10673–10678 (2011). [CrossRef] [PubMed]
  13. H. R. Stapert, S. del Valle, E. J. K. Verstegen, B. M. I. van der Zande, J. Lub, and S. Stallinga, “Photoreplicated anisotropic liquid-crystalline lenses for aberration control and dual-layer readout of optical discs,” Adv. Funct. Mater.13(9), 732–738 (2003). [CrossRef]
  14. H. Choi, J. H. Park, J. Hong, and B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” Jpn. J. Appl. Phys.43(8A), 5330–5336 (2004). [CrossRef]
  15. C. J. Hsu, C. Y. Huang, and C. R. Sheu, “Experimental analysis to avoid migrating zigzag lines occurring in homogeneously aligned liquid crystal lenses with a hole-patterned electrode,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)544(1), 185–191 (2011). [CrossRef]
  16. S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys.35(Part 1, No. 9A), 4668–4672 (1996). [CrossRef]

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