Abstract

We report a complete theoretical model and supporting experimental results on the fabrication and characterization of macroscopic adaptive fluidic lenses with high dioptric power, tunable focal distance, and aperture shape. The lens is 17 mm wide and is made of an elastic polydimethylsiloxane (PDMS) polymer, which can adaptively restore accommodation distance within several cm according to the fluidic volume mechanically pumped in. Moreover, the lens can provide for magnification in the range of +25 diopter to +100 diopter with optical aberrations within a fraction of a wavelength, and overall lens weight of less than 2 g. The agreement between the non-linear theoretical model describing the elastic membrane deformation and the experimental results is apparent. We stress that these features make the proposed lenses appropriate for the low vision segment, as well as for applications in video magnifiers, camera zooms, telescope and microscopes objectives, and other machine vision applications where large magnification is required.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. A. Goss and R. W. West, Introduction to the Optics of the Eye (Butterworth-Hienemann, 2001).
  2. M. P. Keating, Geometric, Physical and Visual Optics (Butterworth-Hienemann, 2002).
  3. W. Tasman and E. A. Jaeger, Duane’s Ophtalmology (LLW, 2013).
  4. T. Callina and T. P. Reynolds, “Traditional methods for the treatment of presbyopia: spectacles, contact lenses, bifocal contact lenses,” Ophthalmol. Clin. North Am. 19, 25–33 (2006).
    [PubMed]
  5. Y. Lo and D. Zhang, “Fluidic adaptive lens,” WO patent application WO2006011937A2 (February2, 2006).
  6. N. Hazan, A. Banerjee, H. Kim, and C. Mastrangelo, “Tunable-focus lens for adaptive eyeglasses,” Opt. Express 25, 1221–1233 (2017).
    [Crossref]
  7. N. Hasan, M. Karkhanis, C. Ghosh, F. Khan, T. Ghosh, H. Kim, and C. H. Mastrangelo, “Lightweight smart autofocusing eyeglasses,” Proc. SPIE 10545, 1054507 (2018).
  8. G. Puentes, D. Voigt, A. Aiello, and J. P. Woerdman, “Experimental observation of depolarized light scattering,” Opt. Lett. 30, 3216–3219 (2005).
    [Crossref] [PubMed]
  9. G. Puentes and F. Minotti, ”Melt supply equipment, casting apparatus and casting method,” KR patent application 20170102760 (September12, 2017).
  10. K. Wei, H. Huang, Q. Wang, and Y. Zhao, “Focus-tunable liquid lens with an aspherical membrane for improved central and peripheral resolutions at high diopters,” Opt. Express 24, 3929–3939 (2016).
    [Crossref] [PubMed]
  11. P. Zhao, Ç. Ataman, and H. Zappe, “Spherical aberration free liquid-filled tunable lens with variable thickness membrane,” Opt. Express 23, 21264–21278 (2015).
    [Crossref] [PubMed]
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    [Crossref]
  13. T. Krupenking, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett. 82, 316–318 (2003).
    [Crossref]
  14. S. Kuiper and B. H. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85, 1128–1130 (2004).
    [Crossref]
  15. G. C. Knollman, J. L. Bellini, and J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1971).
    [Crossref]
  16. N. Sigiura and S. Morita, “Variable-docus liquid-filled optics lens,” Appl. Opt. 32, 4181–4186 (1993).
    [Crossref]
  17. D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptivelens with high focal length tenability,” App. Phys. Lett. 82, 3171–3172 (2003).
    [Crossref]
  18. K. H. Joeng, G. L. Liu, N. Chronis, and L. P. Lee, “Tunable microdoublets lens array,” Opt. Express 12, 2494–2500 (2004).
    [Crossref]
  19. J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable focusing microlens with microfluidic chip,” J. Micromech. Microeng. 14, 675–680 (2004).
    [Crossref]
  20. N. Chronis, G. L. Liu, K. H. Jeong, and L. P. Lee, “Tunable liquid filled micro-lens array integrated with microfludidic network,” Opt. Express 11, 2370–2378 (2003).
    [Crossref] [PubMed]
  21. P. M. Moran, s. Dharmatilleke, A. H. Khaw, and K. W. Tan, “Fluid lenses with variable focal length,” App. Phys. Lett. 88, 041120 (2006).
    [Crossref]
  22. H. Ren and S.-T. Wu, “Variable-focus liquid lens,” Opt. Express 15, 5931–5936 (2007).
    [Crossref] [PubMed]
  23. H. M. Beger, “A new approach to the analysis of large deflections of plates,” J. Appl. Mech. 22, 465–472 (1955).
  24. J. Mazumdar, “A method for solving problems of elastic plates of arbitrary shape,” J. Aust. Math. Soc. 11, 95–112 (1970).
    [Crossref]
  25. N. A. Polson and M. A. Hayes, “Microfluidics controllling fluids in small places,” Anal. Chem. 73, 312A–319A (2001).
    [Crossref]
  26. J. Mazumdar and R. Jones, “A simplified approach to the analysis of large deflections of plates,” J. Appl. Mech. 41, 523–524 (1974).
    [Crossref]
  27. E. Hetch, Optics, 2nd ed. (Addison Wesley, 2002).

2018 (1)

N. Hasan, M. Karkhanis, C. Ghosh, F. Khan, T. Ghosh, H. Kim, and C. H. Mastrangelo, “Lightweight smart autofocusing eyeglasses,” Proc. SPIE 10545, 1054507 (2018).

2017 (1)

2016 (1)

2015 (1)

2007 (1)

2006 (2)

P. M. Moran, s. Dharmatilleke, A. H. Khaw, and K. W. Tan, “Fluid lenses with variable focal length,” App. Phys. Lett. 88, 041120 (2006).
[Crossref]

T. Callina and T. P. Reynolds, “Traditional methods for the treatment of presbyopia: spectacles, contact lenses, bifocal contact lenses,” Ophthalmol. Clin. North Am. 19, 25–33 (2006).
[PubMed]

2005 (1)

2004 (3)

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

K. H. Joeng, G. L. Liu, N. Chronis, and L. P. Lee, “Tunable microdoublets lens array,” Opt. Express 12, 2494–2500 (2004).
[Crossref]

J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable focusing microlens with microfluidic chip,” J. Micromech. Microeng. 14, 675–680 (2004).
[Crossref]

2003 (3)

N. Chronis, G. L. Liu, K. H. Jeong, and L. P. Lee, “Tunable liquid filled micro-lens array integrated with microfludidic network,” Opt. Express 11, 2370–2378 (2003).
[Crossref] [PubMed]

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

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptivelens with high focal length tenability,” App. Phys. Lett. 82, 3171–3172 (2003).
[Crossref]

2001 (1)

N. A. Polson and M. A. Hayes, “Microfluidics controllling fluids in small places,” Anal. Chem. 73, 312A–319A (2001).
[Crossref]

1996 (1)

M. Vallet, B. Berge, and L. Vovelle, “Electrowetting of water and aqueos solutions on poly-ethilene-terephthalate insulating films,” Polymer 37, 2465–2470 (1996).
[Crossref]

1993 (1)

1974 (1)

J. Mazumdar and R. Jones, “A simplified approach to the analysis of large deflections of plates,” J. Appl. Mech. 41, 523–524 (1974).
[Crossref]

1971 (1)

G. C. Knollman, J. L. Bellini, and J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1971).
[Crossref]

1970 (1)

J. Mazumdar, “A method for solving problems of elastic plates of arbitrary shape,” J. Aust. Math. Soc. 11, 95–112 (1970).
[Crossref]

1955 (1)

H. M. Beger, “A new approach to the analysis of large deflections of plates,” J. Appl. Mech. 22, 465–472 (1955).

Aiello, A.

Ataman, Ç.

Banerjee, A.

Beger, H. M.

H. M. Beger, “A new approach to the analysis of large deflections of plates,” J. Appl. Mech. 22, 465–472 (1955).

Bellini, J. L.

G. C. Knollman, J. L. Bellini, and J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1971).
[Crossref]

Berdichevsky, Y.

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptivelens with high focal length tenability,” App. Phys. Lett. 82, 3171–3172 (2003).
[Crossref]

Berge, B.

M. Vallet, B. Berge, and L. Vovelle, “Electrowetting of water and aqueos solutions on poly-ethilene-terephthalate insulating films,” Polymer 37, 2465–2470 (1996).
[Crossref]

Callina, T.

T. Callina and T. P. Reynolds, “Traditional methods for the treatment of presbyopia: spectacles, contact lenses, bifocal contact lenses,” Ophthalmol. Clin. North Am. 19, 25–33 (2006).
[PubMed]

Chen, J.

J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable focusing microlens with microfluidic chip,” J. Micromech. Microeng. 14, 675–680 (2004).
[Crossref]

Choi, J.

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptivelens with high focal length tenability,” App. Phys. Lett. 82, 3171–3172 (2003).
[Crossref]

Chronis, N.

Dharmatilleke, s.

P. M. Moran, s. Dharmatilleke, A. H. Khaw, and K. W. Tan, “Fluid lenses with variable focal length,” App. Phys. Lett. 88, 041120 (2006).
[Crossref]

Fang, J.

J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable focusing microlens with microfluidic chip,” J. Micromech. Microeng. 14, 675–680 (2004).
[Crossref]

Ghosh, C.

N. Hasan, M. Karkhanis, C. Ghosh, F. Khan, T. Ghosh, H. Kim, and C. H. Mastrangelo, “Lightweight smart autofocusing eyeglasses,” Proc. SPIE 10545, 1054507 (2018).

Ghosh, T.

N. Hasan, M. Karkhanis, C. Ghosh, F. Khan, T. Ghosh, H. Kim, and C. H. Mastrangelo, “Lightweight smart autofocusing eyeglasses,” Proc. SPIE 10545, 1054507 (2018).

Goss, D. A.

D. A. Goss and R. W. West, Introduction to the Optics of the Eye (Butterworth-Hienemann, 2001).

Hasan, N.

N. Hasan, M. Karkhanis, C. Ghosh, F. Khan, T. Ghosh, H. Kim, and C. H. Mastrangelo, “Lightweight smart autofocusing eyeglasses,” Proc. SPIE 10545, 1054507 (2018).

Hayes, M. A.

N. A. Polson and M. A. Hayes, “Microfluidics controllling fluids in small places,” Anal. Chem. 73, 312A–319A (2001).
[Crossref]

Hazan, N.

Hendriks, B. H.

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

Hetch, E.

E. Hetch, Optics, 2nd ed. (Addison Wesley, 2002).

Huang, H.

Jaeger, E. A.

W. Tasman and E. A. Jaeger, Duane’s Ophtalmology (LLW, 2013).

Jeong, K. H.

Joeng, K. H.

Jones, R.

J. Mazumdar and R. Jones, “A simplified approach to the analysis of large deflections of plates,” J. Appl. Mech. 41, 523–524 (1974).
[Crossref]

Karkhanis, M.

N. Hasan, M. Karkhanis, C. Ghosh, F. Khan, T. Ghosh, H. Kim, and C. H. Mastrangelo, “Lightweight smart autofocusing eyeglasses,” Proc. SPIE 10545, 1054507 (2018).

Keating, M. P.

M. P. Keating, Geometric, Physical and Visual Optics (Butterworth-Hienemann, 2002).

Khan, F.

N. Hasan, M. Karkhanis, C. Ghosh, F. Khan, T. Ghosh, H. Kim, and C. H. Mastrangelo, “Lightweight smart autofocusing eyeglasses,” Proc. SPIE 10545, 1054507 (2018).

Khaw, A. H.

P. M. Moran, s. Dharmatilleke, A. H. Khaw, and K. W. Tan, “Fluid lenses with variable focal length,” App. Phys. Lett. 88, 041120 (2006).
[Crossref]

Kim, H.

N. Hasan, M. Karkhanis, C. Ghosh, F. Khan, T. Ghosh, H. Kim, and C. H. Mastrangelo, “Lightweight smart autofocusing eyeglasses,” Proc. SPIE 10545, 1054507 (2018).

N. Hazan, A. Banerjee, H. Kim, and C. Mastrangelo, “Tunable-focus lens for adaptive eyeglasses,” Opt. Express 25, 1221–1233 (2017).
[Crossref]

Knollman, G. C.

G. C. Knollman, J. L. Bellini, and J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1971).
[Crossref]

Krupenking, T.

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

Kuiper, S.

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

Lee, L. P.

Lien, V.

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptivelens with high focal length tenability,” App. Phys. Lett. 82, 3171–3172 (2003).
[Crossref]

Liu, G. L.

Lo, Y.

Y. Lo and D. Zhang, “Fluidic adaptive lens,” WO patent application WO2006011937A2 (February2, 2006).

Lo, Y. H.

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptivelens with high focal length tenability,” App. Phys. Lett. 82, 3171–3172 (2003).
[Crossref]

Mach, P.

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

Mastrangelo, C.

Mastrangelo, C. H.

N. Hasan, M. Karkhanis, C. Ghosh, F. Khan, T. Ghosh, H. Kim, and C. H. Mastrangelo, “Lightweight smart autofocusing eyeglasses,” Proc. SPIE 10545, 1054507 (2018).

Mazumdar, J.

J. Mazumdar and R. Jones, “A simplified approach to the analysis of large deflections of plates,” J. Appl. Mech. 41, 523–524 (1974).
[Crossref]

J. Mazumdar, “A method for solving problems of elastic plates of arbitrary shape,” J. Aust. Math. Soc. 11, 95–112 (1970).
[Crossref]

Minotti, F.

G. Puentes and F. Minotti, ”Melt supply equipment, casting apparatus and casting method,” KR patent application 20170102760 (September12, 2017).

Moran, P. M.

P. M. Moran, s. Dharmatilleke, A. H. Khaw, and K. W. Tan, “Fluid lenses with variable focal length,” App. Phys. Lett. 88, 041120 (2006).
[Crossref]

Morita, S.

Polson, N. A.

N. A. Polson and M. A. Hayes, “Microfluidics controllling fluids in small places,” Anal. Chem. 73, 312A–319A (2001).
[Crossref]

Puentes, G.

G. Puentes, D. Voigt, A. Aiello, and J. P. Woerdman, “Experimental observation of depolarized light scattering,” Opt. Lett. 30, 3216–3219 (2005).
[Crossref] [PubMed]

G. Puentes and F. Minotti, ”Melt supply equipment, casting apparatus and casting method,” KR patent application 20170102760 (September12, 2017).

Ren, H.

Reynolds, T. P.

T. Callina and T. P. Reynolds, “Traditional methods for the treatment of presbyopia: spectacles, contact lenses, bifocal contact lenses,” Ophthalmol. Clin. North Am. 19, 25–33 (2006).
[PubMed]

Sigiura, N.

Tan, K. W.

P. M. Moran, s. Dharmatilleke, A. H. Khaw, and K. W. Tan, “Fluid lenses with variable focal length,” App. Phys. Lett. 88, 041120 (2006).
[Crossref]

Tasman, W.

W. Tasman and E. A. Jaeger, Duane’s Ophtalmology (LLW, 2013).

Vallet, M.

M. Vallet, B. Berge, and L. Vovelle, “Electrowetting of water and aqueos solutions on poly-ethilene-terephthalate insulating films,” Polymer 37, 2465–2470 (1996).
[Crossref]

Varahramyan, K.

J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable focusing microlens with microfluidic chip,” J. Micromech. Microeng. 14, 675–680 (2004).
[Crossref]

Voigt, D.

Vovelle, L.

M. Vallet, B. Berge, and L. Vovelle, “Electrowetting of water and aqueos solutions on poly-ethilene-terephthalate insulating films,” Polymer 37, 2465–2470 (1996).
[Crossref]

Wang, Q.

Wang, W.

J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable focusing microlens with microfluidic chip,” J. Micromech. Microeng. 14, 675–680 (2004).
[Crossref]

Weaver, J. L.

G. C. Knollman, J. L. Bellini, and J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1971).
[Crossref]

Wei, K.

West, R. W.

D. A. Goss and R. W. West, Introduction to the Optics of the Eye (Butterworth-Hienemann, 2001).

Woerdman, J. P.

Wu, S.-T.

Yang, S.

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

Zappe, H.

Zhang, D.

Y. Lo and D. Zhang, “Fluidic adaptive lens,” WO patent application WO2006011937A2 (February2, 2006).

Zhang, D. Y.

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptivelens with high focal length tenability,” App. Phys. Lett. 82, 3171–3172 (2003).
[Crossref]

Zhao, P.

Zhao, Y.

Anal. Chem. (1)

N. A. Polson and M. A. Hayes, “Microfluidics controllling fluids in small places,” Anal. Chem. 73, 312A–319A (2001).
[Crossref]

App. Phys. Lett. (2)

P. M. Moran, s. Dharmatilleke, A. H. Khaw, and K. W. Tan, “Fluid lenses with variable focal length,” App. Phys. Lett. 88, 041120 (2006).
[Crossref]

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptivelens with high focal length tenability,” App. Phys. Lett. 82, 3171–3172 (2003).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

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

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

J. Acoust. Soc. Am. (1)

G. C. Knollman, J. L. Bellini, and J. L. Weaver, “Variable-focus liquid-filled hydroacoustic lens,” J. Acoust. Soc. Am. 49, 253–261 (1971).
[Crossref]

J. Appl. Mech. (2)

J. Mazumdar and R. Jones, “A simplified approach to the analysis of large deflections of plates,” J. Appl. Mech. 41, 523–524 (1974).
[Crossref]

H. M. Beger, “A new approach to the analysis of large deflections of plates,” J. Appl. Mech. 22, 465–472 (1955).

J. Aust. Math. Soc. (1)

J. Mazumdar, “A method for solving problems of elastic plates of arbitrary shape,” J. Aust. Math. Soc. 11, 95–112 (1970).
[Crossref]

J. Micromech. Microeng. (1)

J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable focusing microlens with microfluidic chip,” J. Micromech. Microeng. 14, 675–680 (2004).
[Crossref]

Ophthalmol. Clin. North Am. (1)

T. Callina and T. P. Reynolds, “Traditional methods for the treatment of presbyopia: spectacles, contact lenses, bifocal contact lenses,” Ophthalmol. Clin. North Am. 19, 25–33 (2006).
[PubMed]

Opt. Express (6)

Opt. Lett. (1)

Polymer (1)

M. Vallet, B. Berge, and L. Vovelle, “Electrowetting of water and aqueos solutions on poly-ethilene-terephthalate insulating films,” Polymer 37, 2465–2470 (1996).
[Crossref]

Proc. SPIE (1)

N. Hasan, M. Karkhanis, C. Ghosh, F. Khan, T. Ghosh, H. Kim, and C. H. Mastrangelo, “Lightweight smart autofocusing eyeglasses,” Proc. SPIE 10545, 1054507 (2018).

Other (6)

G. Puentes and F. Minotti, ”Melt supply equipment, casting apparatus and casting method,” KR patent application 20170102760 (September12, 2017).

Y. Lo and D. Zhang, “Fluidic adaptive lens,” WO patent application WO2006011937A2 (February2, 2006).

D. A. Goss and R. W. West, Introduction to the Optics of the Eye (Butterworth-Hienemann, 2001).

M. P. Keating, Geometric, Physical and Visual Optics (Butterworth-Hienemann, 2002).

W. Tasman and E. A. Jaeger, Duane’s Ophtalmology (LLW, 2013).

E. Hetch, Optics, 2nd ed. (Addison Wesley, 2002).

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Figures (10)

Fig. 1
Fig. 1 Lens profile profile according to the theoretical model for a single elastic membrane for the cases: (a) circular aperture of diameter 17 mm, and (b) elliptical aperture of axes 17 mm and 12 mm. This figure was made by using Wolfram Mathematica.
Fig. 2
Fig. 2 Scheme of fluidic lenses. By tuning the width of the elastic membrane it is possible to design (a) planar-convex and (b) bi-convex lenses. By changing the shape of the aperture between (c) spheric or (d) elliptical, it is possible to address different visual aberrations. (e) Photograph of circular aperture lens prototype exhibiting large dioptric power. (f) Color labels.
Fig. 3
Fig. 3 Transmission spectrum of PDMS membrane obtained by iluminating the elastic membrane with an compact stabilized broad-band Halogen Lamp (Model Thorlabs SLS201L), and measuring the transmitted spectrum with a compact spectrometer (Thorlabs CCS100), in the spectral range 350nm–700nm. The figure reveals that appart from attenuation losses the membrane is transparent in the visible region.
Fig. 4
Fig. 4 Measured response time using a fast oscilloscope (Model Rigol DG500). Typical values are within 43 ms, making them suitable for low-latency applications.
Fig. 5
Fig. 5 (a) Intensity probfile for an expanded beam, (b) intensity profile for a focused beam through a fluidic lens of focal distance 20mm.
Fig. 6
Fig. 6 Resolution power tested via calibrated targets. (a) Spherical lens has a resultion of at least 10 line-pairs/mm. These figures can be increased by increasing the fluid volume, making the fluidic lenses suitable for razor-sharp professional applications.
Fig. 7
Fig. 7 (a) Experimental scheme for measuring the focal distance of the fluidic lenses using a He-Ne laser source (Melles Griot 05-LHR-111, λ = 633 nm). (b) Experimental scheme for reconstruction of wave-front produced by fluidic lenses and characterization of optical aberration, using a LED source (λ = 633nm) and a Shack-Hartmann wave-front sensor (Thorlabs WFS150-5C).
Fig. 8
Fig. 8 Measured focal distance vs. fluidic volume for a lens with elliptic aperture (red triangles) and circular aperture (blue circles). Blue curve: Theoretical prediction for a spheric lens with 17mm diameter. Red curve: Theoretical prediction for an elliptic lens with mayor and minor axes 17 mm and 15 mm, respectively. Measured Optical Power (OP) dynamic range: 33D to 66D. The agreement between experiment and theory is apparent.
Fig. 9
Fig. 9 Wave-front reconstruction using wave-front sensor (Thorlabs WFS150-5C) for a fluidic lens with (a) spheric aperture, (b) elliptic aperture.
Fig. 10
Fig. 10 Measured typical aberrations (trefoil(X,Y), astigmatism(X,Y), spherical, and coma) in μm, in terms of Zernike polynomial (Zn,m) coefficients up to 4th order. Left column corresponds to Vmax = 6 ml (OP=50D), right column corresponds to Vmin = 4 ml (OP=36D). (a) Circular aperture (d = 17 mm), (b) elliptic aperture (axes a = 17 mm, b = 15mm), (c) elliptic aperture (axes a = 17 mm, b = 13mm). Typical aberrations are within a fraction of the wavelength λ = 633 nm.

Equations (12)

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

4 w α 2 2 w = q D ,
u x + v y + 1 2 ( w x ) 2 + 1 2 ( w x ) 2 = α 2 h 2 12 .
q D S ψ = d 3 w d ψ 3 ψ ( ψ x 2 + ψ y 2 ) 2 | d x | | ψ y | + d 2 w d ψ 2 ψ [ ( ψ x 2 + ψ y 2 ) 2 ψ + 2 ( ψ x 2 ψ x x + 2 ψ x ψ y ψ x y + ψ y 2 ψ y y ) ] | d x | | ψ y | + d w d ψ ψ ( ψ x 2 ψ x + ψ y 2 ψ y ) | d x | | ψ y | α 2 d w d ψ ψ ( ψ x 2 + ψ y 2 ) | d x | | ψ y | ,
α 2 h 2 6 S 0 = 0 1 d ψ ( d w d ψ ) 2 ψ ( ψ x 2 + ψ y 2 ) | d x | | ψ y | .
ψ ( x , y ) = 1 x 2 / a 2 y 2 / b 2 .
( ψ 1 ) d 3 w d ψ 3 + 2 d 2 w d ψ 2 + γ 2 d w d ψ = Q ,
γ 2 = α 2 a 2 b 2 ( a 2 + b 2 ) 3 a 4 + 2 a 2 b 2 + 3 b 4 ,
Q = a 4 b 4 3 a 4 + 2 a 2 b 2 + 3 b 4 q 2 D .
ς 2 = 1 ψ ,
w ( ς ) = Q γ 3 I 1 ( 2 γ ) [ γ ( 1 ς 2 ) I 1 ( 2 γ ) + I 0 ( 2 γ ς ) I 0 ( 2 γ ) ] ,
γ 2 = 6 h 2 ( a 2 + b 2 ) 2 3 a 4 + 2 a 2 b 2 + 3 b 4 0 1 ( d w d ς ) 2 ς d ς .
d = 2.44 λ f D ,

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