Abstract

A miniature solid-state varifocal lens based on Alvarez principle with lens elements having free-form surfaces is reported. The Alvarez lens elements are implemented with diamond-turning and replication molding processes. They are integrated with electrostatically-driven MEMS comb-drive actuators fabricated using SOI micromachining. Dynamic tuning of focal length more than 1.5 times (from 3 mm to 4.65 mm) is experimentally demonstrated with only small MEMS-driven lateral movements of 40 μm. Such varifocal lens may be useful in miniature cameras for autofocus and zooming due to its advantages including ease of packaging and fast tuning speed.

© 2013 OSA

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References

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2012

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng.51(1), 013006 (2012).
[CrossRef]

2010

H. M. Leung, G. Zhou, H. Yu, F. S. Chau, and A. S. Kumar, “Diamond turning and soft lithography processes for liquid tunable lenses,” J. Micromech. Microeng.20(2), 025021 (2010).
[CrossRef]

2009

2008

2006

H. Ren, D. Fox, P. A. Anderson, B. Wu, and S. T. Wu, “Tunable-focus liquid lens controlled using a servo motor,” Opt. Express14(18), 8031–8036 (2006).
[CrossRef] [PubMed]

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature442(7102), 551–554 (2006).
[CrossRef] [PubMed]

2004

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]

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

2003

T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett.82(3), 316–318 (2003).
[CrossRef]

2000

1999

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

1997

1995

1990

W. C. Tang, T. C. H. Nguyen, M. W. Judy, and R. T. Howe, “Electrostatic combdrive of lateral polysilicon resonators,” Sens. Actuators A Phys.21(1-3), 328–331 (1990).
[CrossRef]

1970

Agarwal, A. K.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature442(7102), 551–554 (2006).
[CrossRef] [PubMed]

Anderson, P. A.

Avicola, K.

Baer, E.

Barbero, S.

Barton, I. M.

Beadie, G.

Beebe, D. J.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature442(7102), 551–554 (2006).
[CrossRef] [PubMed]

Blough, C. G.

Chau, F. S.

H. M. Leung, G. Zhou, H. Yu, F. S. Chau, and A. S. Kumar, “Diamond turning and soft lithography processes for liquid tunable lenses,” J. Micromech. Microeng.20(2), 025021 (2010).
[CrossRef]

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive/refractive hybrid lens,” Opt. Lett.34(18), 2793–2795 (2009).
[CrossRef] [PubMed]

Choi, J.-M.

Davies, M. A.

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng.51(1), 013006 (2012).
[CrossRef]

Dixit, S. N.

Dong, L.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature442(7102), 551–554 (2006).
[CrossRef] [PubMed]

Dutterer, B. S.

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng.51(1), 013006 (2012).
[CrossRef]

Fan, Y. H.

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]

Fox, D.

Gauza, S.

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]

Hendriks, B. H. W.

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

Hiltner, A.

Howe, R. T.

W. C. Tang, T. C. H. Nguyen, M. W. Judy, and R. T. Howe, “Electrostatic combdrive of lateral polysilicon resonators,” Sens. Actuators A Phys.21(1-3), 328–331 (1990).
[CrossRef]

Huang, C.

C. Huang, L. Li, and A. Y. Yi, “Design and fabrication of a micro Alvarez lens array with a variable focal length,” Microsyst. Technol.15(4), 559–563 (2009).
[CrossRef]

Jiang, H.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature442(7102), 551–554 (2006).
[CrossRef] [PubMed]

Judy, M. W.

W. C. Tang, T. C. H. Nguyen, M. W. Judy, and R. T. Howe, “Electrostatic combdrive of lateral polysilicon resonators,” Sens. Actuators A Phys.21(1-3), 328–331 (1990).
[CrossRef]

Kazmierczak, T.

Krupenkin, T.

T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett.82(3), 316–318 (2003).
[CrossRef]

Kuiper, S.

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

Kumar, A. S.

H. M. Leung, G. Zhou, H. Yu, F. S. Chau, and A. S. Kumar, “Diamond turning and soft lithography processes for liquid tunable lenses,” J. Micromech. Microeng.20(2), 025021 (2010).
[CrossRef]

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive/refractive hybrid lens,” Opt. Lett.34(18), 2793–2795 (2009).
[CrossRef] [PubMed]

Lee, Y.-J.

Lepkowicz, R. S.

Leung, H. M.

H. M. Leung, G. Zhou, H. Yu, F. S. Chau, and A. S. Kumar, “Diamond turning and soft lithography processes for liquid tunable lenses,” J. Micromech. Microeng.20(2), 025021 (2010).
[CrossRef]

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive/refractive hybrid lens,” Opt. Lett.34(18), 2793–2795 (2009).
[CrossRef] [PubMed]

Li, L.

C. Huang, L. Li, and A. Y. Yi, “Design and fabrication of a micro Alvarez lens array with a variable focal length,” Microsyst. Technol.15(4), 559–563 (2009).
[CrossRef]

Lineberger, J. L.

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng.51(1), 013006 (2012).
[CrossRef]

Lohmann, A. W.

Mach, P.

T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett.82(3), 316–318 (2003).
[CrossRef]

Mack, S. K.

Mait, J. N.

Michaels, R. L.

Nguyen, T. C. H.

W. C. Tang, T. C. H. Nguyen, M. W. Judy, and R. T. Howe, “Electrostatic combdrive of lateral polysilicon resonators,” Sens. Actuators A Phys.21(1-3), 328–331 (1990).
[CrossRef]

Paleta-Toxqui, C.

Ponting, M.

Ren, H.

H. Ren, D. Fox, P. A. Anderson, B. Wu, and S. T. Wu, “Tunable-focus liquid lens controlled using a servo motor,” Opt. Express14(18), 8031–8036 (2006).
[CrossRef] [PubMed]

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]

Rossi, M.

Sandrock, M. L.

Sato, S.

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

Schwiegerling, J.

Shirk, J. S.

Smilie, P. J.

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng.51(1), 013006 (2012).
[CrossRef]

Son, H.-M.

Suleski, T. J.

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng.51(1), 013006 (2012).
[CrossRef]

Summers, L. J.

Tang, W. C.

W. C. Tang, T. C. H. Nguyen, M. W. Judy, and R. T. Howe, “Electrostatic combdrive of lateral polysilicon resonators,” Sens. Actuators A Phys.21(1-3), 328–331 (1990).
[CrossRef]

Werber, A.

A. Werber and H. Zappe, “Tunable pneumatic microoptics,” J. Microelectromech. Syst.17(5), 1218–1227 (2008).
[CrossRef]

Wiggins, M. J.

Wilhelmsen, J.

Wu, B.

Wu, S. T.

H. Ren, D. Fox, P. A. Anderson, B. Wu, and S. T. Wu, “Tunable-focus liquid lens controlled using a servo motor,” Opt. Express14(18), 8031–8036 (2006).
[CrossRef] [PubMed]

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]

Yang, S.

T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett.82(3), 316–318 (2003).
[CrossRef]

Yang, Y.

Yi, A. Y.

C. Huang, L. Li, and A. Y. Yi, “Design and fabrication of a micro Alvarez lens array with a variable focal length,” Microsyst. Technol.15(4), 559–563 (2009).
[CrossRef]

Yu, H.

H. M. Leung, G. Zhou, H. Yu, F. S. Chau, and A. S. Kumar, “Diamond turning and soft lithography processes for liquid tunable lenses,” J. Micromech. Microeng.20(2), 025021 (2010).
[CrossRef]

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive/refractive hybrid lens,” Opt. Lett.34(18), 2793–2795 (2009).
[CrossRef] [PubMed]

Zappe, H.

A. Werber and H. Zappe, “Tunable pneumatic microoptics,” J. Microelectromech. Syst.17(5), 1218–1227 (2008).
[CrossRef]

Zhou, G.

H. M. Leung, G. Zhou, H. Yu, F. S. Chau, and A. S. Kumar, “Diamond turning and soft lithography processes for liquid tunable lenses,” J. Micromech. Microeng.20(2), 025021 (2010).
[CrossRef]

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive/refractive hybrid lens,” Opt. Lett.34(18), 2793–2795 (2009).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett.82(3), 316–318 (2003).
[CrossRef]

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

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]

J. Microelectromech. Syst.

A. Werber and H. Zappe, “Tunable pneumatic microoptics,” J. Microelectromech. Syst.17(5), 1218–1227 (2008).
[CrossRef]

J. Micromech. Microeng.

H. M. Leung, G. Zhou, H. Yu, F. S. Chau, and A. S. Kumar, “Diamond turning and soft lithography processes for liquid tunable lenses,” J. Micromech. Microeng.20(2), 025021 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Microsyst. Technol.

C. Huang, L. Li, and A. Y. Yi, “Design and fabrication of a micro Alvarez lens array with a variable focal length,” Microsyst. Technol.15(4), 559–563 (2009).
[CrossRef]

Nature

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature442(7102), 551–554 (2006).
[CrossRef] [PubMed]

Opt. Eng.

P. J. Smilie, B. S. Dutterer, J. L. Lineberger, M. A. Davies, and T. J. Suleski, “Design and characterization of an infrared Alvarez lens,” Opt. Eng.51(1), 013006 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Rev.

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

Sens. Actuators A Phys.

W. C. Tang, T. C. H. Nguyen, M. W. Judy, and R. T. Howe, “Electrostatic combdrive of lateral polysilicon resonators,” Sens. Actuators A Phys.21(1-3), 328–331 (1990).
[CrossRef]

Other

MEMSCAP, Inc., http://www.memscap.com/products/mumps/soimumps .

G. T. A. Kovacs, Micromachined Transducers Sourcebook (McGraw-Hill, New York, 1998).

L. W. Alvarez, “Two-element variable-power spherical lens,” US 3305294, Feb. 1967.

Supplementary Material (1)

» Media 1: MOV (239 KB)     

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Figures (5)

Fig. 1
Fig. 1

(a) An Alvarez lens consists of two lens elements having free-form surfaces. (b) Schematic showing a MEMS-driven tunable Alvarez lens. (c) and (d) Free-form surface z(x,y) = 0.6(xy2 + x3/3)-0.2x + 0.35 viewed from different viewing angles.

Fig. 2
Fig. 2

Schematics showing (a) MEMS actuator fabrication and (b) Alvarez lens element fabrication and assembly.

Fig. 3
Fig. 3

(a) SOI micromachined electrostatic comb-drive actuator. (b) Diamond-turned master mold having the desired free-form surface. (c) Replicated transparent lens element. (d) MEMS-driven Alvarez lens element after finally assembly process.

Fig. 4
Fig. 4

(a) Measured static displacement as a function of DC driving voltage for a MEMS electrostatic comb-drive actuator used in our tunable Alvarez lens. (b) Its frequency response.

Fig. 5
Fig. 5

(a) Experimental setup for focal length measurement. (b) Focal length of the MEMS tunable Alvarez lens as a function of the offset between two constituent lens elements. (c) to (h) Captured images at various focal lengths as indicated in (b). A series of images from P1 to P2 are also combined to create a video showing an apparent “zoom-out” effect due to the focal length change of the MEMS-driven Alvarez lens (Media1).

Equations (4)

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

t 1 =A( x y 2 + 1 3 x 3 )+Dx+E,
t 2 =A( x y 2 + 1 3 x 3 )Dx+E,
f= 1 4Aδ( n1 ) ,
f= DM 1M .

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