Abstract

A compact, high-speed variable-focus liquid lens using acoustic radiation force is proposed. The lens consists of an annular piezoelectric ultrasound transducer and an aluminum cell (height: 3 mm; diameter: 6 mm) filled with degassed water and silicone oil. The profile of the oil-water interface can be rapidly varied by applying acoustic radiation force from the transducer, allowing the liquid lens to be operated as a variable-focus lens. A theoretical model based on a spring-mass-dashpot model is proposed for the vibration of the lens. The sound pressure distribution in the lens was calculated by finite element analysis and it suggests that an acoustic standing wave is generated in the lens. The fastest response time of 6.7 ms was obtained with silicone oil with a kinematic viscosity of 100 cSt.

© 2010 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  24. Y. Wada, D. Koyama, and K. Nakamura, “Finite element analysis of acoustic streaming in an ultrasonic air pump,” Jpn. J. Appl. Phys. 49(7), 07HE15 (2010).
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  25. Y. Yamayoshi, J. Shiina, H. Tamura, and S. Hirose, “Sound field characteristics in air gaps of noncontact ultrasonic motor driven by two flexural standing wave vibration disks,” Jpn. J. Appl. Phys. 49(7), 07HE16 (2010).
    [CrossRef]
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    [CrossRef]

2010 (4)

D. Koyama and K. Nakamura, “Noncontact ultrasonic transportation of small objects over long distances in air using a bending vibrator and a reflector,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(5), 1152–1159 (2010).
[CrossRef] [PubMed]

D. Koyama and K. Nakamura, “Noncontact ultrasonic transportation of small objects in a circular trajectory in air by flexural vibrations of a circular disc,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(6), 1434–1442 (2010).
[CrossRef] [PubMed]

Y. Wada, D. Koyama, and K. Nakamura, “Finite element analysis of acoustic streaming in an ultrasonic air pump,” Jpn. J. Appl. Phys. 49(7), 07HE15 (2010).
[CrossRef]

Y. Yamayoshi, J. Shiina, H. Tamura, and S. Hirose, “Sound field characteristics in air gaps of noncontact ultrasonic motor driven by two flexural standing wave vibration disks,” Jpn. J. Appl. Phys. 49(7), 07HE16 (2010).
[CrossRef]

2009 (3)

D. Koyama and K. Nakamura, “Noncontact self-running ultrasonically levitated two-dimensional stage using flexural standing waves,” Jpn. J. Appl. Phys. 48(7), 07GM07 (2009).
[CrossRef]

Y. Yamayoshi, H. Tamura, and S. Hirose, “Optimum design for noncontact ultrasonic motor with flexurally vibrating disk using an equivalent circuit considering viscosity of air,” Jpn. J. Appl. Phys. 48(7), 07GM08 (2009).
[CrossRef]

H. Oku and M. Ishikawa, “High-speed liquid lens with 2 ms response and 80.3 nm root-mean-square wavefront error,” Appl. Phys. Lett. 94(22), 221108 (2009).
[CrossRef]

2008 (1)

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

2007 (1)

H. Takei, T. Hasegawa, K. Nakamura, and S. Ueha, “Measurement of intense ultraousound field in air using fiber optic probe,” Jpn. J. Appl. Phys. 46(No. 7B), 4555–4557 (2007).
[CrossRef]

2006 (2)

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442(7102), 551–554 (2006).
[CrossRef] [PubMed]

K. Sakai and Y. Yamamoto, “Electric field tweezers for characterization of liquid surface,” Appl. Phys. Lett. 89(21), 211911 (2006).
[CrossRef]

2005 (3)

C. A. López, C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87, 134102 (2005).
[CrossRef]

H. Ren and S. Wu, “Variable-focus liquid lens by changing aperture,” Appl. Phys. Lett. 86(21), 211107 (2005).
[CrossRef]

Y. Yoshitake, S. Mitani, K. Sakai, and K. Takagi, “Measurement of high viscosity with laser induced surface deformation technique,” J. Appl. Phys. 97(2), 024901 (2005).
[CrossRef]

2004 (1)

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

2002 (1)

K. Miyamoto, S. Nagatomo, Y. Matsui, and S. Shiokawa, “Nonlinear vibration of liquid droplet by surface acoustic wave excitation,” Jpn. J. Appl. Phys. 41(Part 1, No. 5B), 3465–3468 (2002).
[CrossRef]

2000 (1)

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000).
[CrossRef]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

1988 (1)

Y. Watanabe, “Free vibrations of a drop partial contact with a circular support,” Jpn. J. Appl. Phys. 27(Part 1, No. 12), 2409–2413 (1988).
[CrossRef]

1984 (1)

M. Strani and F. Sabetta, “Free vibration of a drop in partial contact with a solid support,” J. Fluid Mech. 141(-1), 233–247 (1984).
[CrossRef]

1982 (1)

B. Chu and E. Apfel, “Acoustic radiation pressure produced by a beam of sound,” J. Acoust. Soc. Am. 72(6), 1673–1687 (1982).
[CrossRef]

1978 (1)

M. H. Li and H. S. Fogler, “Acoustic emulsification. Part 2. Breakup of the large primary oil droplets in a water medium,” J. Fluid Mech. 88(03), 513–528 (1978).
[CrossRef]

1958 (1)

L. D. Rozenberg and L. O. Makarov, “On the causes of ultrasonic distension of liquid surfaces,” Sov. Phys. Dokl. 2, 230–231 (1958).

1939 (1)

G. Hertz and H. Mende, “Der Schallstrahlungsdruck in Flüssigkeiten,” Z. Phys. 114(5-6), 354–367 (1939).
[CrossRef]

Agarwal, A. K.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442(7102), 551–554 (2006).
[CrossRef] [PubMed]

Apfel, E.

B. Chu and E. Apfel, “Acoustic radiation pressure produced by a beam of sound,” J. Acoust. Soc. Am. 72(6), 1673–1687 (1982).
[CrossRef]

Beebe, D. J.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442(7102), 551–554 (2006).
[CrossRef] [PubMed]

Berge, B.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Chu, B.

B. Chu and E. Apfel, “Acoustic radiation pressure produced by a beam of sound,” J. Acoust. Soc. Am. 72(6), 1673–1687 (1982).
[CrossRef]

Dong, L.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442(7102), 551–554 (2006).
[CrossRef] [PubMed]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Fogler, H. S.

M. H. Li and H. S. Fogler, “Acoustic emulsification. Part 2. Breakup of the large primary oil droplets in a water medium,” J. Fluid Mech. 88(03), 513–528 (1978).
[CrossRef]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hasegawa, T.

H. Takei, T. Hasegawa, K. Nakamura, and S. Ueha, “Measurement of intense ultraousound field in air using fiber optic probe,” Jpn. J. Appl. Phys. 46(No. 7B), 4555–4557 (2007).
[CrossRef]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hendriks, B. H. W.

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

Hertz, G.

G. Hertz and H. Mende, “Der Schallstrahlungsdruck in Flüssigkeiten,” Z. Phys. 114(5-6), 354–367 (1939).
[CrossRef]

Hirose, S.

Y. Yamayoshi, J. Shiina, H. Tamura, and S. Hirose, “Sound field characteristics in air gaps of noncontact ultrasonic motor driven by two flexural standing wave vibration disks,” Jpn. J. Appl. Phys. 49(7), 07HE16 (2010).
[CrossRef]

Y. Yamayoshi, H. Tamura, and S. Hirose, “Optimum design for noncontact ultrasonic motor with flexurally vibrating disk using an equivalent circuit considering viscosity of air,” Jpn. J. Appl. Phys. 48(7), 07GM08 (2009).
[CrossRef]

Hirsa, A. H.

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

C. A. López, C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87, 134102 (2005).
[CrossRef]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Ishikawa, M.

H. Oku and M. Ishikawa, “High-speed liquid lens with 2 ms response and 80.3 nm root-mean-square wavefront error,” Appl. Phys. Lett. 94(22), 221108 (2009).
[CrossRef]

Jiang, H.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442(7102), 551–554 (2006).
[CrossRef] [PubMed]

Koyama, D.

D. Koyama and K. Nakamura, “Noncontact ultrasonic transportation of small objects in a circular trajectory in air by flexural vibrations of a circular disc,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(6), 1434–1442 (2010).
[CrossRef] [PubMed]

D. Koyama and K. Nakamura, “Noncontact ultrasonic transportation of small objects over long distances in air using a bending vibrator and a reflector,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(5), 1152–1159 (2010).
[CrossRef] [PubMed]

Y. Wada, D. Koyama, and K. Nakamura, “Finite element analysis of acoustic streaming in an ultrasonic air pump,” Jpn. J. Appl. Phys. 49(7), 07HE15 (2010).
[CrossRef]

D. Koyama and K. Nakamura, “Noncontact self-running ultrasonically levitated two-dimensional stage using flexural standing waves,” Jpn. J. Appl. Phys. 48(7), 07GM07 (2009).
[CrossRef]

Kuiper, S.

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

Lee, C.

C. A. López, C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87, 134102 (2005).
[CrossRef]

Li, M. H.

M. H. Li and H. S. Fogler, “Acoustic emulsification. Part 2. Breakup of the large primary oil droplets in a water medium,” J. Fluid Mech. 88(03), 513–528 (1978).
[CrossRef]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

López, C. A.

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

C. A. López, C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87, 134102 (2005).
[CrossRef]

Makarov, L. O.

L. D. Rozenberg and L. O. Makarov, “On the causes of ultrasonic distension of liquid surfaces,” Sov. Phys. Dokl. 2, 230–231 (1958).

Matsui, Y.

K. Miyamoto, S. Nagatomo, Y. Matsui, and S. Shiokawa, “Nonlinear vibration of liquid droplet by surface acoustic wave excitation,” Jpn. J. Appl. Phys. 41(Part 1, No. 5B), 3465–3468 (2002).
[CrossRef]

Mende, H.

G. Hertz and H. Mende, “Der Schallstrahlungsdruck in Flüssigkeiten,” Z. Phys. 114(5-6), 354–367 (1939).
[CrossRef]

Mitani, S.

Y. Yoshitake, S. Mitani, K. Sakai, and K. Takagi, “Measurement of high viscosity with laser induced surface deformation technique,” J. Appl. Phys. 97(2), 024901 (2005).
[CrossRef]

Miyamoto, K.

K. Miyamoto, S. Nagatomo, Y. Matsui, and S. Shiokawa, “Nonlinear vibration of liquid droplet by surface acoustic wave excitation,” Jpn. J. Appl. Phys. 41(Part 1, No. 5B), 3465–3468 (2002).
[CrossRef]

Nagatomo, S.

K. Miyamoto, S. Nagatomo, Y. Matsui, and S. Shiokawa, “Nonlinear vibration of liquid droplet by surface acoustic wave excitation,” Jpn. J. Appl. Phys. 41(Part 1, No. 5B), 3465–3468 (2002).
[CrossRef]

Nakamura, K.

Y. Wada, D. Koyama, and K. Nakamura, “Finite element analysis of acoustic streaming in an ultrasonic air pump,” Jpn. J. Appl. Phys. 49(7), 07HE15 (2010).
[CrossRef]

D. Koyama and K. Nakamura, “Noncontact ultrasonic transportation of small objects over long distances in air using a bending vibrator and a reflector,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(5), 1152–1159 (2010).
[CrossRef] [PubMed]

D. Koyama and K. Nakamura, “Noncontact ultrasonic transportation of small objects in a circular trajectory in air by flexural vibrations of a circular disc,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(6), 1434–1442 (2010).
[CrossRef] [PubMed]

D. Koyama and K. Nakamura, “Noncontact self-running ultrasonically levitated two-dimensional stage using flexural standing waves,” Jpn. J. Appl. Phys. 48(7), 07GM07 (2009).
[CrossRef]

H. Takei, T. Hasegawa, K. Nakamura, and S. Ueha, “Measurement of intense ultraousound field in air using fiber optic probe,” Jpn. J. Appl. Phys. 46(No. 7B), 4555–4557 (2007).
[CrossRef]

Oku, H.

H. Oku and M. Ishikawa, “High-speed liquid lens with 2 ms response and 80.3 nm root-mean-square wavefront error,” Appl. Phys. Lett. 94(22), 221108 (2009).
[CrossRef]

Peseux, J.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Ren, H.

H. Ren and S. Wu, “Variable-focus liquid lens by changing aperture,” Appl. Phys. Lett. 86(21), 211107 (2005).
[CrossRef]

Rozenberg, L. D.

L. D. Rozenberg and L. O. Makarov, “On the causes of ultrasonic distension of liquid surfaces,” Sov. Phys. Dokl. 2, 230–231 (1958).

Sabetta, F.

M. Strani and F. Sabetta, “Free vibration of a drop in partial contact with a solid support,” J. Fluid Mech. 141(-1), 233–247 (1984).
[CrossRef]

Sakai, K.

K. Sakai and Y. Yamamoto, “Electric field tweezers for characterization of liquid surface,” Appl. Phys. Lett. 89(21), 211911 (2006).
[CrossRef]

Y. Yoshitake, S. Mitani, K. Sakai, and K. Takagi, “Measurement of high viscosity with laser induced surface deformation technique,” J. Appl. Phys. 97(2), 024901 (2005).
[CrossRef]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Shiina, J.

Y. Yamayoshi, J. Shiina, H. Tamura, and S. Hirose, “Sound field characteristics in air gaps of noncontact ultrasonic motor driven by two flexural standing wave vibration disks,” Jpn. J. Appl. Phys. 49(7), 07HE16 (2010).
[CrossRef]

Shiokawa, S.

K. Miyamoto, S. Nagatomo, Y. Matsui, and S. Shiokawa, “Nonlinear vibration of liquid droplet by surface acoustic wave excitation,” Jpn. J. Appl. Phys. 41(Part 1, No. 5B), 3465–3468 (2002).
[CrossRef]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Strani, M.

M. Strani and F. Sabetta, “Free vibration of a drop in partial contact with a solid support,” J. Fluid Mech. 141(-1), 233–247 (1984).
[CrossRef]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Takagi, K.

Y. Yoshitake, S. Mitani, K. Sakai, and K. Takagi, “Measurement of high viscosity with laser induced surface deformation technique,” J. Appl. Phys. 97(2), 024901 (2005).
[CrossRef]

Takei, H.

H. Takei, T. Hasegawa, K. Nakamura, and S. Ueha, “Measurement of intense ultraousound field in air using fiber optic probe,” Jpn. J. Appl. Phys. 46(No. 7B), 4555–4557 (2007).
[CrossRef]

Tamura, H.

Y. Yamayoshi, J. Shiina, H. Tamura, and S. Hirose, “Sound field characteristics in air gaps of noncontact ultrasonic motor driven by two flexural standing wave vibration disks,” Jpn. J. Appl. Phys. 49(7), 07HE16 (2010).
[CrossRef]

Y. Yamayoshi, H. Tamura, and S. Hirose, “Optimum design for noncontact ultrasonic motor with flexurally vibrating disk using an equivalent circuit considering viscosity of air,” Jpn. J. Appl. Phys. 48(7), 07GM08 (2009).
[CrossRef]

Ueha, S.

H. Takei, T. Hasegawa, K. Nakamura, and S. Ueha, “Measurement of intense ultraousound field in air using fiber optic probe,” Jpn. J. Appl. Phys. 46(No. 7B), 4555–4557 (2007).
[CrossRef]

Wada, Y.

Y. Wada, D. Koyama, and K. Nakamura, “Finite element analysis of acoustic streaming in an ultrasonic air pump,” Jpn. J. Appl. Phys. 49(7), 07HE15 (2010).
[CrossRef]

Watanabe, Y.

Y. Watanabe, “Free vibrations of a drop partial contact with a circular support,” Jpn. J. Appl. Phys. 27(Part 1, No. 12), 2409–2413 (1988).
[CrossRef]

Wu, S.

H. Ren and S. Wu, “Variable-focus liquid lens by changing aperture,” Appl. Phys. Lett. 86(21), 211107 (2005).
[CrossRef]

Yamamoto, Y.

K. Sakai and Y. Yamamoto, “Electric field tweezers for characterization of liquid surface,” Appl. Phys. Lett. 89(21), 211911 (2006).
[CrossRef]

Yamayoshi, Y.

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Figures (14)

Fig. 1
Fig. 1

Compact liquid lens: (a) photograph, (b) schematic view, and (c) configuration.

Fig. 2
Fig. 2

Spring-mass-dashpot model for vibration of the liquid lens.

Fig. 3
Fig. 3

FEA model.

Fig. 4
Fig. 4

FEA results. (a) Schematic layout of distributions (b), (c) and (d). (b) Vibrational displacement amplitude in the radial direction on the bottom of the lens. Sound pressure distributions in the (c) rz and (d) rθ planes at z = 2 mm.

Fig. 5
Fig. 5

Radial profiles of the oil-water interface observed by OCT at five different driving voltages.

Fig. 6
Fig. 6

Relationship between the input voltage to the transducer and the interface displacement at the center relative to its position when no ultrasound radiation is applied.

Fig. 7
Fig. 7

Ray-tracing results for liquid lens excited by five different input voltages.

Fig. 8
Fig. 8

Computed beam widths as a function of axial distance for five different input voltages.

Fig. 9
Fig. 9

Relationship between the focal point and the radial position of a ray for input voltages of (a) 44 and (b) 51 V.

Fig. 10
Fig. 10

Radial intensity distributions of the transmitted laser beam produced by a liquid lens for input voltages of 0 and 35 V.

Fig. 11
Fig. 11

Transient responses of the oil−water interface for kinematic viscosities of 10, 100, and 1000 cSt when ultrasound radiation was switched (a) on and (b) off.

Fig. 12
Fig. 12

Relationship between the kinematic viscosity of the silicone oil and the time constant when ultrasound radiation is switched off.

Fig. 13
Fig. 13

Relationship between the kinematic viscosity of the silicone oil and the resistance in the free vibration model.

Fig. 14
Fig. 14

Relationship between the kinematic viscosity of the silicone oil and the response time of the lens when ultrasound radiation is switched on and off.

Equations (3)

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

m d 2 x d t 2 + γ d x d t + k x = 0   or   d 2 x d t 2 + 2 α d x d t + ω 0 2 x = 0 ,
x = A e α t sin ω t ,
m = m w + m o = 1 2 4 3 π R 3 ρ w + V o ρ o ,

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