Abstract

We present novel biconvex solid-body elastomer (polydimethylsiloxane) lenses, which can be tuned in focal length by using magnetic or mechanical actuation. The focal length change is induced by applying radial elastic strain and is investigated for different initial radii of curvature of the lenses and different actuation designs. In all cases, a linear correlation between induced strain and focal length tuning, in the range of about 10% (approximately 3mm), is found. These results compare favorably with finite element simulations.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: an application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
    [CrossRef]
  2. Y. Choi, J.-H. Park, J.-H. Kim, and S.-D. Lee, “Fabrication of a focal length variable microlens array based on a nematic liquid crystal,” Opt. Mater. 21, 643–646 (2003).
    [CrossRef]
  3. H. Ren, Y.-H. Fan, and S.-T. Wu, “Liquid-crystal microlens arrays using patterned polymer networks,” Opt. Lett. 29, 1608–1610 (2004).
    [CrossRef] [PubMed]
  4. C.-C. Cheng, C. A. Chang, and J. A. Yeh, “Variable focus dielectric liquid droplet lens,” Opt. Express 14, 4101–4106 (2006).
    [CrossRef] [PubMed]
  5. M. Agarwal, R. A. Gunasekaran, P. Coane, and K. Varahramyan, “Polymer-based variable focal length microlens system,” J. Micromech. Microeng. 14, 1665–1673 (2004).
    [CrossRef]
  6. A. Werber and H. Zappe, “Tunable microfluidic microlenses,” Appl. Opt. 44, 3238–3245 (2005).
    [CrossRef] [PubMed]
  7. D.-Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y.-H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82, 3171–3172 (2003).
    [CrossRef]
  8. F. Schneider, C. Muller, and U. Wallrabe, “Low-cost adaptive silicone membrane lens,” J. Opt. A 10, 044002(2008).
    [CrossRef]
  9. L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442, 551–554 (2006).
    [CrossRef] [PubMed]
  10. S.-Y. Lee, H.-W. Tung, W.-C. Chen, and W. Fang, “Thermal actuated solid tunable lens,” IEEE Photon. Technol. Lett. 18, 2191–2193 (2006).
    [CrossRef]
  11. T.Hahn, ed., International Tables for Crystallography, Vol.  A: Space-Group Symmetry (Springer, 2002)

2008 (1)

F. Schneider, C. Muller, and U. Wallrabe, “Low-cost adaptive silicone membrane lens,” J. Opt. A 10, 044002(2008).
[CrossRef]

2006 (3)

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

S.-Y. Lee, H.-W. Tung, W.-C. Chen, and W. Fang, “Thermal actuated solid tunable lens,” IEEE Photon. Technol. Lett. 18, 2191–2193 (2006).
[CrossRef]

C.-C. Cheng, C. A. Chang, and J. A. Yeh, “Variable focus dielectric liquid droplet lens,” Opt. Express 14, 4101–4106 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (2)

M. Agarwal, R. A. Gunasekaran, P. Coane, and K. Varahramyan, “Polymer-based variable focal length microlens system,” J. Micromech. Microeng. 14, 1665–1673 (2004).
[CrossRef]

H. Ren, Y.-H. Fan, and S.-T. Wu, “Liquid-crystal microlens arrays using patterned polymer networks,” Opt. Lett. 29, 1608–1610 (2004).
[CrossRef] [PubMed]

2003 (2)

Y. Choi, J.-H. Park, J.-H. Kim, and S.-D. Lee, “Fabrication of a focal length variable microlens array based on a nematic liquid crystal,” Opt. Mater. 21, 643–646 (2003).
[CrossRef]

D.-Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y.-H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82, 3171–3172 (2003).
[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, 159–163 (2000).
[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, 551–554 (2006).
[CrossRef] [PubMed]

Agarwal, M.

M. Agarwal, R. A. Gunasekaran, P. Coane, and K. Varahramyan, “Polymer-based variable focal length microlens system,” J. Micromech. Microeng. 14, 1665–1673 (2004).
[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, 551–554 (2006).
[CrossRef] [PubMed]

Berdichevsky, Y.

D.-Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y.-H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82, 3171–3172 (2003).
[CrossRef]

Berge, B.

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

Chang, C. A.

Chen, W.-C.

S.-Y. Lee, H.-W. Tung, W.-C. Chen, and W. Fang, “Thermal actuated solid tunable lens,” IEEE Photon. Technol. Lett. 18, 2191–2193 (2006).
[CrossRef]

Cheng, C.-C.

Choi, J.

D.-Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y.-H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82, 3171–3172 (2003).
[CrossRef]

Choi, Y.

Y. Choi, J.-H. Park, J.-H. Kim, and S.-D. Lee, “Fabrication of a focal length variable microlens array based on a nematic liquid crystal,” Opt. Mater. 21, 643–646 (2003).
[CrossRef]

Coane, P.

M. Agarwal, R. A. Gunasekaran, P. Coane, and K. Varahramyan, “Polymer-based variable focal length microlens system,” J. Micromech. Microeng. 14, 1665–1673 (2004).
[CrossRef]

Dong, L.

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

Fan, Y.-H.

Fang, W.

S.-Y. Lee, H.-W. Tung, W.-C. Chen, and W. Fang, “Thermal actuated solid tunable lens,” IEEE Photon. Technol. Lett. 18, 2191–2193 (2006).
[CrossRef]

Gunasekaran, R. A.

M. Agarwal, R. A. Gunasekaran, P. Coane, and K. Varahramyan, “Polymer-based variable focal length microlens system,” J. Micromech. Microeng. 14, 1665–1673 (2004).
[CrossRef]

Jiang, H.

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

Kim, J.-H.

Y. Choi, J.-H. Park, J.-H. Kim, and S.-D. Lee, “Fabrication of a focal length variable microlens array based on a nematic liquid crystal,” Opt. Mater. 21, 643–646 (2003).
[CrossRef]

Lee, S.-D.

Y. Choi, J.-H. Park, J.-H. Kim, and S.-D. Lee, “Fabrication of a focal length variable microlens array based on a nematic liquid crystal,” Opt. Mater. 21, 643–646 (2003).
[CrossRef]

Lee, S.-Y.

S.-Y. Lee, H.-W. Tung, W.-C. Chen, and W. Fang, “Thermal actuated solid tunable lens,” IEEE Photon. Technol. Lett. 18, 2191–2193 (2006).
[CrossRef]

Lien, V.

D.-Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y.-H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82, 3171–3172 (2003).
[CrossRef]

Lo, Y.-H.

D.-Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y.-H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82, 3171–3172 (2003).
[CrossRef]

Muller, C.

F. Schneider, C. Muller, and U. Wallrabe, “Low-cost adaptive silicone membrane lens,” J. Opt. A 10, 044002(2008).
[CrossRef]

Park, J.-H.

Y. Choi, J.-H. Park, J.-H. Kim, and S.-D. Lee, “Fabrication of a focal length variable microlens array based on a nematic liquid crystal,” Opt. Mater. 21, 643–646 (2003).
[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, 159–163 (2000).
[CrossRef]

Ren, H.

Schneider, F.

F. Schneider, C. Muller, and U. Wallrabe, “Low-cost adaptive silicone membrane lens,” J. Opt. A 10, 044002(2008).
[CrossRef]

Tung, H.-W.

S.-Y. Lee, H.-W. Tung, W.-C. Chen, and W. Fang, “Thermal actuated solid tunable lens,” IEEE Photon. Technol. Lett. 18, 2191–2193 (2006).
[CrossRef]

Varahramyan, K.

M. Agarwal, R. A. Gunasekaran, P. Coane, and K. Varahramyan, “Polymer-based variable focal length microlens system,” J. Micromech. Microeng. 14, 1665–1673 (2004).
[CrossRef]

Wallrabe, U.

F. Schneider, C. Muller, and U. Wallrabe, “Low-cost adaptive silicone membrane lens,” J. Opt. A 10, 044002(2008).
[CrossRef]

Werber, A.

Wu, S.-T.

Yeh, J. A.

Zappe, H.

Zhang, D.-Y.

D.-Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y.-H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82, 3171–3172 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D.-Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y.-H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82, 3171–3172 (2003).
[CrossRef]

Eur. Phys. J. E (1)

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

IEEE Photon. Technol. Lett. (1)

S.-Y. Lee, H.-W. Tung, W.-C. Chen, and W. Fang, “Thermal actuated solid tunable lens,” IEEE Photon. Technol. Lett. 18, 2191–2193 (2006).
[CrossRef]

J. Micromech. Microeng. (1)

M. Agarwal, R. A. Gunasekaran, P. Coane, and K. Varahramyan, “Polymer-based variable focal length microlens system,” J. Micromech. Microeng. 14, 1665–1673 (2004).
[CrossRef]

J. Opt. A (1)

F. Schneider, C. Muller, and U. Wallrabe, “Low-cost adaptive silicone membrane lens,” J. Opt. A 10, 044002(2008).
[CrossRef]

Nature (1)

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

Opt. Express (1)

Opt. Lett. (1)

Opt. Mater. (1)

Y. Choi, J.-H. Park, J.-H. Kim, and S.-D. Lee, “Fabrication of a focal length variable microlens array based on a nematic liquid crystal,” Opt. Mater. 21, 643–646 (2003).
[CrossRef]

Other (1)

T.Hahn, ed., International Tables for Crystallography, Vol.  A: Space-Group Symmetry (Springer, 2002)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic sketch of the lens geometry viewed along the optical axis. Strain is applied via four anchors that are (a) straight (T-shaped) or (b) curved (U-shaped).

Fig. 2
Fig. 2

Illustration of the lens fabrication process. (a) Positioning the first planoconcave master lens in a tubular mold and inserting the metallic anchors, (b) sealing the mold with second glass master lens and alignment of the anchors, (c) injecting PDMS and curing, (d) demolding.

Fig. 3
Fig. 3

Comparison of the measured focal length tuning (triangles) with FEM simulation (bullets). The purple shaded areas represent the level of uncertainty in the simulation prediction which would result, for example, from an uncertainty in the refractive index of 5‰. The orange and red shaded areas represent the calculated experimental error.

Fig. 4
Fig. 4

Surface profile for a lens with R 0 = 25.84 mm at 10% tetragonal strain, as obtained by FEM simulation. The contour lines are evenly spaced at 0.4 mm pitch. All scales are in millimeters and refer to the upper half of the lens, i. e., the total biconvex lens thickness at each point is twice the displayed value. The yellow circle indicates the effective aperture ( a eff = 14 mm ) of the lens, inside which the aberrations are expected to be low.

Fig. 5
Fig. 5

Change in focal length for tetragonal (symmetric), squares; and bidirectional (asymmetric), diamonds, strain. (a) Values derived from FEM simulation, (b) experimental results. Both graphs depict data for two lenses with initial focal lengths of 30 mm and 33 mm . The dashed lines in (b) represent a linear fit to the data. For the measurements, the error bars are derived from propagation of uncertainty.

Fig. 6
Fig. 6

Measured focal length as a function of electromagnet actuation current for bulk elastomeric lenses with magnetic bidirectional actuation. Results for both straight and curved anchors are shown and show the typical hyperbolic characteristic of magnetic pull actuation.

Fig. 7
Fig. 7

Schematic representation of the strain distribution inside the lens body for straight and curved anchors for uniaxially applied strain. Since the configuration is symmetric about the vertical axis, only one-half of the lens is sketched, with σ representing the symmetry plane. In case of the straight anchors, the strain distribution is uniform, while in case of the curved anchors, it peaks at the anchor edges.

Fig. 8
Fig. 8

Images through the lens taken by a CCD camera (Stingray 146B, Allied Vision Technologies GmbH, Germany) using incoherent Köhler illumination with a broadband white light source. (a) Object, (b) image at 0% strain, (c) image at 5% strain, (d) image at 10% strain. The image plane and the field stop are slightly out of plane, resulting in a blurred image of the field stop [visible in (a) and (b)]. All subfigures have the same scale. The lateral magnification is approximately 2 × with object distance, s o = 49 mm , and image distance s i = 100 mm for the lens in the relaxed state with f 0 = 32.8 mm .

Fig. 9
Fig. 9

Image of an advanced and miniaturized actuator with eightfold symmetry, designed to apply simultaneous strain along four axes. (a) Front view, (b) internal view with actuation disc, (c) internal view with adjustable fixation (brass) for anchors (not visible).

Tables (2)

Tables Icon

Table 1 Initial Properties of Fabricated Bulk Elastomeric Lenses

Tables Icon

Table 2 Focal Length Tuning Ranges Obtained by Experiment for Approx. 10% Strain for Lenses with Straight (T-shaped) and Curved (U-shaped) Anchors

Equations (2)

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

ϵ = Δ a a 0 = Δ a 16 mm ,
Φ ( ϵ ) = 1 f ( ϵ ) = ( n L n 0 n 0 ) · ( 2 R ( ϵ ) + ( n L n 0 ) · t ( ϵ ) n L R ( ϵ ) 2 ) ,

Metrics