Abstract

The paper presents a methodology of calculation of the inner structure of two- and three-component hybrid liquid-membrane lenses with variable focal length that have corrected spherical aberration and coma. Specifically, the formulas for calculation of initial-design inner parameters (radii of curvatures of individual surfaces, axial thickness, and refractive indices of a material of the lens) of a thin-lens system are derived for a hybrid two-component system (doublet) made by one glass and one liquid-membrane lens, and a hybrid three-component lens (triplet) made by one glass lens and two liquid-membrane lenses, which both have variable focal length and corrected spherical aberration and coma for an object at infinity. As optimization during the optical design process requires the starting point be very close to the optimal solution, the presented approach can be successfully used for its calculation, as it is based on fundamental proven formulas of optical aberrations.

© 2020 Optical Society of America

Full Article  |  PDF Article
More Like This
Design of zoom systems composed of lenses with variable focal length

Antonín Mikš and Petr Pokorný
Appl. Opt. 59(34) 10838-10845 (2020)

Double curvature membrane lens

Antonín Mikš and Petr Pokorný
Appl. Opt. 59(32) 9924-9930 (2020)

Fundamental design parameters of two-component optical systems: theoretical analysis

Antonín Mikš and Petr Pokorný
Appl. Opt. 59(7) 1998-2003 (2020)

References

  • View by:
  • |
  • |
  • |

  1. L. Guoqiang, “Adaptive lens,” in Progress in Optics (Elsevier, 2010), Vol. 55, pp. 199–283.
  2. H. Ren and S.-T. Wu, Introduction to Adaptive Lenses (Wiley, 2012).
  3. http://www.optotune.com .
  4. http://www.varioptic.com .
  5. A. H. Rawicz and I. Mikhailenko, “Modeling a variable-focus liquid-filled optical lens,” Appl. Opt. 35, 1587–1589 (1996).
    [Crossref]
  6. D.-Y. Zhang, N. Justis, V. Lien, Y. Berdichevsky, and Y.-H. Lo, “High-performance fluidic adaptive lenses,” Appl. Opt. 43, 783–787 (2004).
    [Crossref]
  7. N. Sugiura and S. Morita, “Variable-focus liquid-filled optical lens,” Appl. Opt. 32, 4181–4186 (1993).
    [Crossref]
  8. H. Ren, D. Fox, P. A. Anderson, B. Wu, and S.-T. Wu, “Tunable-focus liquid lens controlled using a servo motor,” Opt. Express 14, 8031–8036 (2006).
    [Crossref]
  9. Q. Yang, P. Kobrin, C. Seabury, S. Narayanaswamy, and W. Christian, “Mechanical modeling of fluid-driven polymer lenses,” Appl. Opt. 47, 3658–3668 (2008).
    [Crossref]
  10. G.-H. Feng and Y.-C. Chou, “Flexible meniscus/biconvex lens system with fluidic-controlled tunable-focus applications,” Appl. Opt. 48, 3284–3290 (2009).
    [Crossref]
  11. H. Ren and S.-T. Wu, “Variable-focus liquid lens,” Opt. Express 15, 5931–5936 (2007).
    [Crossref]
  12. D. Shaw and T. E. Sun, “Optical properties of variable-focus liquid-filled optical lenses with different membrane shapes,” Opt. Eng. 46, 024002 (2007).
    [Crossref]
  13. D. Shaw and C.-W. Lin, “Design and analysis of an asymmetrical liquid-filled lens,” Opt. Eng. 46, 123002 (2007).
    [Crossref]
  14. H. Choi, D. S. Han, and Y. H. Won, “Adaptive double-sided fluidic lens of polydimethylsiloxane membranes of matching thickness,” Opt. Lett. 36, 4701–4703 (2011).
    [Crossref]
  15. L. Li, Q.-H. Wang, and W. Jiang, “Liquid lens with double tunable surfaces for large power tunability and improved optical performance,” J. Opt. 13, 115503 (2011).
    [Crossref]
  16. F. Schneider, J. Draheim, R. Kamberger, P. Waibel, and U. Wallrabe, “Optical characterization of adaptive fluidic silicone-membrane lenses,” Opt. Express 17, 11813–11821 (2009).
    [Crossref]
  17. Y.-K. Fuh, M.-X. Lin, and S. Lee, “Characterizing aberration of a pressure-actuated tunable biconvex microlens with a simple spherically-corrected design,” Opt. Lasers Eng. 50, 1677–1682 (2012).
    [Crossref]
  18. A. Miks, J. Novak, and P. Novak, “Algebraic and numerical analysis of imaging properties of thin tunable-focus fluidic membrane lenses with parabolic surfaces,” Appl. Opt. 52, 2136–2144 (2013).
    [Crossref]
  19. A. Mikš and J. Novák, “Three-component double conjugate zoom lens system from tunable focus lenses,” Appl. Opt. 52, 862–865 (2013).
    [Crossref]
  20. A. Mikš and J. Novák, “Paraxial imaging properties of double conjugate zoom lens system composed of three tunable-focus lenses,” Opt. Lasers Eng. 53, 86–89 (2014).
    [Crossref]
  21. A. Mikš and P. Novák, “Double-sided telecentric zoom lens consisting of four tunable lenses with fixed distance between object and image plane,” Appl. Opt. 56, 7020–7023 (2017).
    [Crossref]
  22. L. Wang, H. Oku, and M. Ishikawa, “Development of variable-focus lens with liquid-membrane-liquid structure and 30 mm optical aperture,” Proc. SPIE 8617, 861706 (2013).
    [Crossref]
  23. L. Wang, H. Oku, and M. Ishikawa, “An improved low-optical-power variable focus lens with a large aperture,” Opt. Express 22, 19448–19456 (2014).
    [Crossref]
  24. S. T. Choi, B. S. Son, G. W. Seo, S.-Y. Park, and K.-S. Lee, “Opto-mechanical analysis of nonlinear elastomer membrane deformation under hydraulic pressure for variable-focus liquid-filled microlenses,” Opt. Express 22, 6133–6146 (2014).
    [Crossref]
  25. D. Liang and X.-Y. Wang, “A bio-inspired optical system with a polymer membrane and integrated structure,” Bioinsp. Biomim. 11, 066008 (2016).
    [Crossref]
  26. N. Hasan, A. Banerjee, H. Kim, and C. H. Mastrangelo, “Tunable-focus lens for adaptive eyeglasses,” Opt. Express 25, 1221–1233 (2017).
    [Crossref]
  27. A. Miks, J. Novak, and P. Novak, “Generalized refractive tunable-focus lens and its imaging characteristics,” Opt. Express 18, 9034–9047 (2010).
    [Crossref]
  28. A. Mikš and J. Novák, “Third-order aberrations of the thin refractive tunable-focus lens,” Opt. Lett. 35, 1031–1033 (2010).
    [Crossref]
  29. A. Mikš and P. Novák, “Calculation of a surface shape of a pressure actuated membrane liquid lens,” Opt. Lasers Eng. 58, 60–66 (2014).
    [Crossref]
  30. P. Pokorný, F. Šmejkal, P. Kulmon, P. Novák, J. Novák, A. Mikš, M. Horák, and M. Jirásek, “Calculation of nonlinearly deformed membrane shape of liquid lens caused by uniform pressure,” Appl. Opt. 56, 5939–5947 (2017).
    [Crossref]
  31. P. Pokorný, F. Šmejkal, P. Kulmon, P. Novák, J. Novák, A. Mikš, M. Horák, and M. Jirásek, “Deformation of a prestressed liquid lens membrane,” Appl. Opt. 56, 9368–9376 (2017).
    [Crossref]
  32. A. Mikš and F. Šmejkal, “Dependence of the imaging properties of the liquid lens with variable focal length on membrane thickness,” Appl. Opt. 57, 6439–6445 (2018).
    [Crossref]
  33. 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]
  34. H. Yu, G. Zhou, H. M. Leung, and F. S. Chau, “Tunable liquid-filled lens integrated with aspherical surface for spherical aberration compensation,” Opt. Express 18, 9945–9954 (2010).
    [Crossref]
  35. J.-W. Du, X.-Y. Wang, S. Qiang Zhu, and D. Liang, “Doublet liquid variable-focus lens for spherical aberration correction,” Optik 130, 1244–1253 (2017).
    [Crossref]
  36. S. Reichelt and H. Zappe, “Design of spherically corrected, achromatic variable-focus liquid lenses,” Opt. Express 15, 14146–14154 (2007).
    [Crossref]
  37. L. Li, “Zoom lens design using liquid lenses for achromatic and spherical aberration corrected target,” Opt. Eng. 51, 043001 (2012).
    [Crossref]
  38. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
  39. W. Welford, Aberrations of the Symmetrical Optical Systems (Academic, 1974).
  40. “Sylgard 184 silicone elastomer kit,” http://www.dowcorning.com/ .
  41. “Specifications of Cargille optical liquids, Cargille laboratories,” https://www.cargille.com/refractive-index-liquids/ .
  42. https://www.zemax.com/ .
  43. https://www.lambdares.com/ .

2018 (1)

2017 (5)

2016 (1)

D. Liang and X.-Y. Wang, “A bio-inspired optical system with a polymer membrane and integrated structure,” Bioinsp. Biomim. 11, 066008 (2016).
[Crossref]

2015 (1)

2014 (4)

A. Mikš and P. Novák, “Calculation of a surface shape of a pressure actuated membrane liquid lens,” Opt. Lasers Eng. 58, 60–66 (2014).
[Crossref]

A. Mikš and J. Novák, “Paraxial imaging properties of double conjugate zoom lens system composed of three tunable-focus lenses,” Opt. Lasers Eng. 53, 86–89 (2014).
[Crossref]

L. Wang, H. Oku, and M. Ishikawa, “An improved low-optical-power variable focus lens with a large aperture,” Opt. Express 22, 19448–19456 (2014).
[Crossref]

S. T. Choi, B. S. Son, G. W. Seo, S.-Y. Park, and K.-S. Lee, “Opto-mechanical analysis of nonlinear elastomer membrane deformation under hydraulic pressure for variable-focus liquid-filled microlenses,” Opt. Express 22, 6133–6146 (2014).
[Crossref]

2013 (3)

2012 (2)

Y.-K. Fuh, M.-X. Lin, and S. Lee, “Characterizing aberration of a pressure-actuated tunable biconvex microlens with a simple spherically-corrected design,” Opt. Lasers Eng. 50, 1677–1682 (2012).
[Crossref]

L. Li, “Zoom lens design using liquid lenses for achromatic and spherical aberration corrected target,” Opt. Eng. 51, 043001 (2012).
[Crossref]

2011 (2)

H. Choi, D. S. Han, and Y. H. Won, “Adaptive double-sided fluidic lens of polydimethylsiloxane membranes of matching thickness,” Opt. Lett. 36, 4701–4703 (2011).
[Crossref]

L. Li, Q.-H. Wang, and W. Jiang, “Liquid lens with double tunable surfaces for large power tunability and improved optical performance,” J. Opt. 13, 115503 (2011).
[Crossref]

2010 (3)

2009 (2)

2008 (1)

2007 (4)

H. Ren and S.-T. Wu, “Variable-focus liquid lens,” Opt. Express 15, 5931–5936 (2007).
[Crossref]

D. Shaw and T. E. Sun, “Optical properties of variable-focus liquid-filled optical lenses with different membrane shapes,” Opt. Eng. 46, 024002 (2007).
[Crossref]

D. Shaw and C.-W. Lin, “Design and analysis of an asymmetrical liquid-filled lens,” Opt. Eng. 46, 123002 (2007).
[Crossref]

S. Reichelt and H. Zappe, “Design of spherically corrected, achromatic variable-focus liquid lenses,” Opt. Express 15, 14146–14154 (2007).
[Crossref]

2006 (1)

2004 (1)

1996 (1)

1993 (1)

Anderson, P. A.

Ataman, Ç.

Banerjee, A.

Berdichevsky, Y.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Chau, F. S.

Choi, H.

Choi, S. T.

Chou, Y.-C.

Christian, W.

Draheim, J.

Du, J.-W.

J.-W. Du, X.-Y. Wang, S. Qiang Zhu, and D. Liang, “Doublet liquid variable-focus lens for spherical aberration correction,” Optik 130, 1244–1253 (2017).
[Crossref]

Feng, G.-H.

Fox, D.

Fuh, Y.-K.

Y.-K. Fuh, M.-X. Lin, and S. Lee, “Characterizing aberration of a pressure-actuated tunable biconvex microlens with a simple spherically-corrected design,” Opt. Lasers Eng. 50, 1677–1682 (2012).
[Crossref]

Guoqiang, L.

L. Guoqiang, “Adaptive lens,” in Progress in Optics (Elsevier, 2010), Vol. 55, pp. 199–283.

Han, D. S.

Hasan, N.

Horák, M.

Ishikawa, M.

L. Wang, H. Oku, and M. Ishikawa, “An improved low-optical-power variable focus lens with a large aperture,” Opt. Express 22, 19448–19456 (2014).
[Crossref]

L. Wang, H. Oku, and M. Ishikawa, “Development of variable-focus lens with liquid-membrane-liquid structure and 30 mm optical aperture,” Proc. SPIE 8617, 861706 (2013).
[Crossref]

Jiang, W.

L. Li, Q.-H. Wang, and W. Jiang, “Liquid lens with double tunable surfaces for large power tunability and improved optical performance,” J. Opt. 13, 115503 (2011).
[Crossref]

Jirásek, M.

Justis, N.

Kamberger, R.

Kim, H.

Kobrin, P.

Kulmon, P.

Lee, K.-S.

Lee, S.

Y.-K. Fuh, M.-X. Lin, and S. Lee, “Characterizing aberration of a pressure-actuated tunable biconvex microlens with a simple spherically-corrected design,” Opt. Lasers Eng. 50, 1677–1682 (2012).
[Crossref]

Leung, H. M.

Li, L.

L. Li, “Zoom lens design using liquid lenses for achromatic and spherical aberration corrected target,” Opt. Eng. 51, 043001 (2012).
[Crossref]

L. Li, Q.-H. Wang, and W. Jiang, “Liquid lens with double tunable surfaces for large power tunability and improved optical performance,” J. Opt. 13, 115503 (2011).
[Crossref]

Liang, D.

J.-W. Du, X.-Y. Wang, S. Qiang Zhu, and D. Liang, “Doublet liquid variable-focus lens for spherical aberration correction,” Optik 130, 1244–1253 (2017).
[Crossref]

D. Liang and X.-Y. Wang, “A bio-inspired optical system with a polymer membrane and integrated structure,” Bioinsp. Biomim. 11, 066008 (2016).
[Crossref]

Lien, V.

Lin, C.-W.

D. Shaw and C.-W. Lin, “Design and analysis of an asymmetrical liquid-filled lens,” Opt. Eng. 46, 123002 (2007).
[Crossref]

Lin, M.-X.

Y.-K. Fuh, M.-X. Lin, and S. Lee, “Characterizing aberration of a pressure-actuated tunable biconvex microlens with a simple spherically-corrected design,” Opt. Lasers Eng. 50, 1677–1682 (2012).
[Crossref]

Lo, Y.-H.

Mastrangelo, C. H.

Mikhailenko, I.

Miks, A.

Mikš, A.

Morita, S.

Narayanaswamy, S.

Novak, J.

Novak, P.

Novák, J.

Novák, P.

Oku, H.

L. Wang, H. Oku, and M. Ishikawa, “An improved low-optical-power variable focus lens with a large aperture,” Opt. Express 22, 19448–19456 (2014).
[Crossref]

L. Wang, H. Oku, and M. Ishikawa, “Development of variable-focus lens with liquid-membrane-liquid structure and 30 mm optical aperture,” Proc. SPIE 8617, 861706 (2013).
[Crossref]

Park, S.-Y.

Pokorný, P.

Qiang Zhu, S.

J.-W. Du, X.-Y. Wang, S. Qiang Zhu, and D. Liang, “Doublet liquid variable-focus lens for spherical aberration correction,” Optik 130, 1244–1253 (2017).
[Crossref]

Rawicz, A. H.

Reichelt, S.

Ren, H.

Schneider, F.

Seabury, C.

Seo, G. W.

Shaw, D.

D. Shaw and T. E. Sun, “Optical properties of variable-focus liquid-filled optical lenses with different membrane shapes,” Opt. Eng. 46, 024002 (2007).
[Crossref]

D. Shaw and C.-W. Lin, “Design and analysis of an asymmetrical liquid-filled lens,” Opt. Eng. 46, 123002 (2007).
[Crossref]

Šmejkal, F.

Son, B. S.

Sugiura, N.

Sun, T. E.

D. Shaw and T. E. Sun, “Optical properties of variable-focus liquid-filled optical lenses with different membrane shapes,” Opt. Eng. 46, 024002 (2007).
[Crossref]

Waibel, P.

Wallrabe, U.

Wang, L.

L. Wang, H. Oku, and M. Ishikawa, “An improved low-optical-power variable focus lens with a large aperture,” Opt. Express 22, 19448–19456 (2014).
[Crossref]

L. Wang, H. Oku, and M. Ishikawa, “Development of variable-focus lens with liquid-membrane-liquid structure and 30 mm optical aperture,” Proc. SPIE 8617, 861706 (2013).
[Crossref]

Wang, Q.-H.

L. Li, Q.-H. Wang, and W. Jiang, “Liquid lens with double tunable surfaces for large power tunability and improved optical performance,” J. Opt. 13, 115503 (2011).
[Crossref]

Wang, X.-Y.

J.-W. Du, X.-Y. Wang, S. Qiang Zhu, and D. Liang, “Doublet liquid variable-focus lens for spherical aberration correction,” Optik 130, 1244–1253 (2017).
[Crossref]

D. Liang and X.-Y. Wang, “A bio-inspired optical system with a polymer membrane and integrated structure,” Bioinsp. Biomim. 11, 066008 (2016).
[Crossref]

Welford, W.

W. Welford, Aberrations of the Symmetrical Optical Systems (Academic, 1974).

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Won, Y. H.

Wu, B.

Wu, S.-T.

Yang, Q.

Yu, H.

Zappe, H.

Zhang, D.-Y.

Zhao, P.

Zhou, G.

Appl. Opt. (11)

A. H. Rawicz and I. Mikhailenko, “Modeling a variable-focus liquid-filled optical lens,” Appl. Opt. 35, 1587–1589 (1996).
[Crossref]

D.-Y. Zhang, N. Justis, V. Lien, Y. Berdichevsky, and Y.-H. Lo, “High-performance fluidic adaptive lenses,” Appl. Opt. 43, 783–787 (2004).
[Crossref]

N. Sugiura and S. Morita, “Variable-focus liquid-filled optical lens,” Appl. Opt. 32, 4181–4186 (1993).
[Crossref]

Q. Yang, P. Kobrin, C. Seabury, S. Narayanaswamy, and W. Christian, “Mechanical modeling of fluid-driven polymer lenses,” Appl. Opt. 47, 3658–3668 (2008).
[Crossref]

G.-H. Feng and Y.-C. Chou, “Flexible meniscus/biconvex lens system with fluidic-controlled tunable-focus applications,” Appl. Opt. 48, 3284–3290 (2009).
[Crossref]

A. Miks, J. Novak, and P. Novak, “Algebraic and numerical analysis of imaging properties of thin tunable-focus fluidic membrane lenses with parabolic surfaces,” Appl. Opt. 52, 2136–2144 (2013).
[Crossref]

A. Mikš and J. Novák, “Three-component double conjugate zoom lens system from tunable focus lenses,” Appl. Opt. 52, 862–865 (2013).
[Crossref]

A. Mikš and P. Novák, “Double-sided telecentric zoom lens consisting of four tunable lenses with fixed distance between object and image plane,” Appl. Opt. 56, 7020–7023 (2017).
[Crossref]

P. Pokorný, F. Šmejkal, P. Kulmon, P. Novák, J. Novák, A. Mikš, M. Horák, and M. Jirásek, “Calculation of nonlinearly deformed membrane shape of liquid lens caused by uniform pressure,” Appl. Opt. 56, 5939–5947 (2017).
[Crossref]

P. Pokorný, F. Šmejkal, P. Kulmon, P. Novák, J. Novák, A. Mikš, M. Horák, and M. Jirásek, “Deformation of a prestressed liquid lens membrane,” Appl. Opt. 56, 9368–9376 (2017).
[Crossref]

A. Mikš and F. Šmejkal, “Dependence of the imaging properties of the liquid lens with variable focal length on membrane thickness,” Appl. Opt. 57, 6439–6445 (2018).
[Crossref]

Bioinsp. Biomim. (1)

D. Liang and X.-Y. Wang, “A bio-inspired optical system with a polymer membrane and integrated structure,” Bioinsp. Biomim. 11, 066008 (2016).
[Crossref]

J. Opt. (1)

L. Li, Q.-H. Wang, and W. Jiang, “Liquid lens with double tunable surfaces for large power tunability and improved optical performance,” J. Opt. 13, 115503 (2011).
[Crossref]

Opt. Eng. (3)

D. Shaw and T. E. Sun, “Optical properties of variable-focus liquid-filled optical lenses with different membrane shapes,” Opt. Eng. 46, 024002 (2007).
[Crossref]

D. Shaw and C.-W. Lin, “Design and analysis of an asymmetrical liquid-filled lens,” Opt. Eng. 46, 123002 (2007).
[Crossref]

L. Li, “Zoom lens design using liquid lenses for achromatic and spherical aberration corrected target,” Opt. Eng. 51, 043001 (2012).
[Crossref]

Opt. Express (10)

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]

H. Yu, G. Zhou, H. M. Leung, and F. S. Chau, “Tunable liquid-filled lens integrated with aspherical surface for spherical aberration compensation,” Opt. Express 18, 9945–9954 (2010).
[Crossref]

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

A. Miks, J. Novak, and P. Novak, “Generalized refractive tunable-focus lens and its imaging characteristics,” Opt. Express 18, 9034–9047 (2010).
[Crossref]

L. Wang, H. Oku, and M. Ishikawa, “An improved low-optical-power variable focus lens with a large aperture,” Opt. Express 22, 19448–19456 (2014).
[Crossref]

S. T. Choi, B. S. Son, G. W. Seo, S.-Y. Park, and K.-S. Lee, “Opto-mechanical analysis of nonlinear elastomer membrane deformation under hydraulic pressure for variable-focus liquid-filled microlenses,” Opt. Express 22, 6133–6146 (2014).
[Crossref]

H. Ren and S.-T. Wu, “Variable-focus liquid lens,” Opt. Express 15, 5931–5936 (2007).
[Crossref]

F. Schneider, J. Draheim, R. Kamberger, P. Waibel, and U. Wallrabe, “Optical characterization of adaptive fluidic silicone-membrane lenses,” Opt. Express 17, 11813–11821 (2009).
[Crossref]

H. Ren, D. Fox, P. A. Anderson, B. Wu, and S.-T. Wu, “Tunable-focus liquid lens controlled using a servo motor,” Opt. Express 14, 8031–8036 (2006).
[Crossref]

S. Reichelt and H. Zappe, “Design of spherically corrected, achromatic variable-focus liquid lenses,” Opt. Express 15, 14146–14154 (2007).
[Crossref]

Opt. Lasers Eng. (3)

A. Mikš and P. Novák, “Calculation of a surface shape of a pressure actuated membrane liquid lens,” Opt. Lasers Eng. 58, 60–66 (2014).
[Crossref]

Y.-K. Fuh, M.-X. Lin, and S. Lee, “Characterizing aberration of a pressure-actuated tunable biconvex microlens with a simple spherically-corrected design,” Opt. Lasers Eng. 50, 1677–1682 (2012).
[Crossref]

A. Mikš and J. Novák, “Paraxial imaging properties of double conjugate zoom lens system composed of three tunable-focus lenses,” Opt. Lasers Eng. 53, 86–89 (2014).
[Crossref]

Opt. Lett. (2)

Optik (1)

J.-W. Du, X.-Y. Wang, S. Qiang Zhu, and D. Liang, “Doublet liquid variable-focus lens for spherical aberration correction,” Optik 130, 1244–1253 (2017).
[Crossref]

Proc. SPIE (1)

L. Wang, H. Oku, and M. Ishikawa, “Development of variable-focus lens with liquid-membrane-liquid structure and 30 mm optical aperture,” Proc. SPIE 8617, 861706 (2013).
[Crossref]

Other (10)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

W. Welford, Aberrations of the Symmetrical Optical Systems (Academic, 1974).

“Sylgard 184 silicone elastomer kit,” http://www.dowcorning.com/ .

“Specifications of Cargille optical liquids, Cargille laboratories,” https://www.cargille.com/refractive-index-liquids/ .

https://www.zemax.com/ .

https://www.lambdares.com/ .

L. Guoqiang, “Adaptive lens,” in Progress in Optics (Elsevier, 2010), Vol. 55, pp. 199–283.

H. Ren and S.-T. Wu, Introduction to Adaptive Lenses (Wiley, 2012).

http://www.optotune.com .

http://www.varioptic.com .

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. Scheme of liquid-membrane lens with two membranes.
Fig. 2.
Fig. 2. Scheme of liquid-membrane lens with one membrane.
Fig. 3.
Fig. 3. Scheme of two-component hybrid liquid-membrane lens (doublet) with one membrane.
Fig. 4.
Fig. 4. Scheme of three-component hybrid liquid-membrane lens (triplet) with two membranes.
Fig. 5.
Fig. 5. Aberrations of two-component hybrid liquid-membrane lens (doublet) for $f^\prime = 100\;{\rm mm}$.
Fig. 6.
Fig. 6. Aberrations of two-component hybrid liquid-membrane lens (doublet) for $f^\prime = 150\;{\rm mm}$.
Fig. 7.
Fig. 7. Aberrations of three-component hybrid liquid-membrane lens (triplet) for $f^\prime = 100\;{\rm mm}$.
Fig. 8.
Fig. 8. Aberrations of three-component hybrid liquid-membrane lens (triplet) for $f^\prime = 150\;{\rm mm}$.
Fig. 9.
Fig. 9. Aberrations of three-component hybrid liquid-membrane lens (triplet) for $f^\prime = 200\;{\rm mm}$.

Tables (3)

Tables Icon

Table 1. Parameters of Two-Component Hybrid Liquid-Membrane Lens (Doublet) with f = 100 m m , D = 20 m m , and S . R . = 0.924

Tables Icon

Table 2. Third Radius of Curvature r 3 , Radial Thickness d , and Strehl Ratio of Two-Component Hybrid Liquid-Membrane Lens (Doublet) for λ = 635 n m for Imaging of Axial Point for Different Values of Focal Length

Tables Icon

Table 3. Parameters of Three-Component Hybrid Liquid-Membrane Lens (Triplet)

Equations (34)

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

S I = i = 1 K h i 4 M i ,
S I I = i = 1 K h i 3 h ¯ i M i + i = 1 K h i 2 N i ,
S I I I = i = 1 K h i 2 h ¯ i 2 M i + 2 i = 1 K h i h ¯ i N i + i = 1 K φ i ,
S I V = i = 1 K φ i n i ,
S V = i = 1 K h i h ¯ i 3 M i + 3 i = 1 K h ¯ i 2 N i + i = 1 K h ¯ i h i ( 3 + 1 n i ) φ i ,
M i = φ i 3 ( A i X i 2 + B i X i Y i + C i Y i 2 + D i ) , N i = φ i 2 ( E i X i + G i Y i ) ,
A i = n i + 2 4 n i ( n i 1 ) 2 , B i = n i + 1 n i ( n i 1 ) , C i = 3 n i + 2 4 n i , D i = n i 2 4 ( n i 1 ) 2 , E i = B i / 2 , G i = 2 n i + 1 2 n i , φ i = ( n i 1 ) ( 1 r i 1 r i ) , X i = r i + r i r i r i , Y i = s i + s i s i s i = m i + 1 m i 1 = 1 2 s i φ i = 1 2 s i φ i , Y i + 1 = h i φ i h i + 1 φ i + 1 ( Y i 1 ) 1.
r i = 2 ( n i 1 ) φ i ( X i + 1 ) , r i = 2 ( n i 1 ) φ i ( X i 1 ) .
δ y = y P ( y P 2 + x P 2 ) 2 ( s 1 s ¯ 1 ) 3 u 1 3 u K S I + y 1 ( 3 y P 2 + x P 2 ) 2 ( s 1 s ¯ 1 ) 3 u 1 2 u K u ¯ 1 S I I y 1 2 y P 2 ( s 1 s ¯ 1 ) 3 u 1 u K u ¯ 1 2 ( 3 S I I I + I 2 S I V ) + y 1 3 2 ( s 1 s ¯ 1 ) 3 u K u ¯ 1 3 S V , δ x = x P ( y P 2 + x P 2 ) 2 ( s 1 s ¯ 1 ) 3 u 1 3 u K S I + 2 y 1 y P x P 2 ( s 1 s ¯ 1 ) 3 u 1 2 u K u ¯ 1 S I I y 1 2 x P 2 ( s 1 s ¯ 1 ) 3 u 1 u K u ¯ 1 2 ( S I I I + I 2 S I V ) ,
I = h 1 h ¯ 1 ( 1 s 1 1 s ¯ 1 ) = u 1 h ¯ 1 u ¯ 1 h 1 .
h ¯ 1 = s 1 s ¯ 1 s ¯ 1 s 1 .
h ¯ j = h j ( h ¯ 1 + i = 2 j d i 1 h i 1 h i ) ,
S I = i = 1 J U i , S I I = i = 1 J U i V i , S I I I = i = 1 J U i V i 2 , S I V = i = 1 J P i , S V = i = 1 J ( U i V i 2 + I 2 P i ) V i ,
U i = h i ( u i + 1 u i 1 / n i + 1 1 / n i ) 2 ( u i + 1 n i + 1 u i n i ) , V i = u ¯ i + 1 u ¯ i u i + 1 u i , P i = 1 h i ( u i + 1 n i u i n i + 1 ) ,
a 5 φ 1 5 + a 4 φ 1 4 + a 3 φ 1 3 + a 2 φ 1 2 + a 1 φ 1 + a 0 = 0 ,
a 5 = ( n 1 n 2 ) 3 4 n 1 2 n 2 2 ( n 1 1 ) 4 ( n 2 1 ) 2 , a 4 = ( n 1 n 2 ) 2 ( n 2 + 2 ) ( n 1 n 2 + n 1 n 2 ) 4 n 1 2 n 2 2 ( n 1 1 ) 4 ( n 2 1 ) 2 , a 3 = n 1 n 2 4 n 1 2 n 2 2 ( n 1 1 ) 4 ( n 2 1 ) 2 { n 1 3 [ S I I ( n 2 n 2 2 ) n 2 2 ] + n 1 2 [ 4 n 2 + 6 n 2 2 + 2 n 2 3 + 1 S I I ( n 2 n 2 3 ) ] n 1 [ 3 n 2 + 7 n 2 2 + 5 n 2 3 S I I ( n 2 2 n 2 3 ) ] + n 2 2 + 2 n 2 3 } , a 2 = ( 2 n 1 3 4 n 1 2 + 2 n 1 ) S I I + n 1 3 8 n 1 2 + 15 n 1 2 4 n 1 2 ( n 1 1 ) 3 ( n 2 1 ) ( n 1 1 ) S I + ( n 1 2 2 n 1 ) S I I + n 1 2 5 n 1 + 1 4 n 1 2 ( n 1 1 ) 3 2 ( 1 n 1 ) S I + n 1 2 S I I + n 1 4 n 1 n 2 ( n 1 1 ) 3 , a 1 = n 1 n 2 4 n 1 n 2 2 ( n 1 1 ) 2 ( n 2 1 ) 2 [ ( 2 S I I 2 + 2 S I I 2 S I + 2 ) n 2 3 + ( 4 S I I 2 3 S I I + 2 S I + 1 ) n 2 2 + ( 2 S I I 2 + S I I + 2 S I ) n 2 2 S I ] , a 0 = S I S I I 2 4 ( n 1 1 ) 2 1 n 2 2 ( n 1 1 ) 2 ( n 2 1 ) 2 [ ( S I I 2 2 S I I 4 + S I 2 1 4 ) n 2 3 + ( S I I 2 + S I I 2 3 S I 4 ) n 2 2 + ( S I I 2 2 S I I 4 ) n 2 + S I 4 ] .
φ 2 = 1 φ 1 .
X 1 = A B , X 2 = φ 1 ( X 1 1 ) ( n 2 1 ) φ 2 ( n 1 1 ) 1 ,
A = ( E 2 + G 1 G 2 E 2 H ) φ 1 2 + ( E 2 H 2 E 2 ) φ 1 + E 2 + G 2 + S I I , B = ( E 1 E 2 H ) φ 1 2 + ( E 2 H ) φ 1 , H = n 2 1 n 1 1 .
φ = φ 1 + φ 2 + φ 3 , C I = φ 1 / ν 2 + φ 2 / ν 3 + φ 3 / ν 4 .
φ 2 = ν 3 ( ν 2 φ ν 2 φ 1 + ν 4 φ 1 C I ν 2 ν 4 ) ν 2 ( ν 3 ν 4 ) , φ 3 = ν 4 ( ν 2 φ ν 2 φ 1 + ν 3 φ 1 C I ν 2 ν 3 ) ν 2 ( ν 3 ν 4 ) ,
n i + 1 u i + 1 n i + 1 u i + 1 = h i ( n i + 1 n i ) / r i , i = 1 , 2 , 3 , 4 ,
u 2 = φ 1 u 1 + 2 u 1 n 2 Q ( 1 n 2 1 ) , u 3 = φ 1 u 1 + 2 u 1 n 3 Q ( 1 n 3 1 ) , u 4 = φ 1 u 1 + 2 u 1 + φ 2 n 4 Q ( 1 n 4 1 ) φ 2 ( n 4 1 ) n 4 ( n 3 1 ) , u 5 = u 1 + 1 ,
S I = a 2 Q 2 + a 1 Q + a 0 ,
a 2 = 2 φ 2 n 3 2 φ 1 + φ 2 1 n 4 + n 2 + 2 φ 1 n 2 , a 1 = A 10 + A 11 u 1 , A 11 = 8 φ 1 + φ 2 1 n 4 2 ( 3 n 2 + 4 φ 1 n 2 ) 8 φ 2 n 3 , A 10 = 3 φ 1 2 n 2 1 α 1 2 n 4 1 2 n 3 φ 2 n 3 1 [ φ 1 n 4 + φ 2 n 4 2 ( 1 ( n 4 1 ) ( n 3 1 ) ) φ 1 n 3 ] 2 n 4 α 1 n 4 1 ( φ 1 n 4 + φ 2 n 4 2 α 2 1 ) φ 2 2 n 4 2 ( n 3 1 ) 2 [ n 4 2 ( n 3 1 ) n 3 2 ( n 4 1 ) ] , α 1 = φ 1 + φ 2 n 4 α 2 1 , α 2 = φ 2 ( n 4 1 ) n 4 ( n 3 1 ) , a 0 = A 02 u 1 2 + A 01 u 1 + A 00 , A 02 = 8 n 2 + φ 1 n 2 8 φ 1 + φ 2 1 n 4 + 8 φ 2 n 3 , A 01 = 5 n 3 + 6 φ 1 + 6 φ 2 6 n 3 φ 1 6 φ 1 φ 2 + φ 2 2 5 n 3 1 ( φ 1 + φ 2 1 ) n 4 ( n 3 1 ) ( n 4 1 ) [ 7 n 4 ( n 3 1 + φ 1 + φ 2 n 3 φ 1 ) + φ 2 n 3 ( n 4 8 ) ] 7 φ 1 2 n 2 1 , A 00 = n 2 φ 1 3 ( n 2 1 ) 2 n 4 2 ( n 4 1 ) 2 [ φ 1 n 4 + φ 2 n 4 2 φ 2 ( n 4 1 ) n 4 2 ( n 3 1 ) 1 ] [ φ 1 + φ 2 n 4 φ 2 ( n 4 1 ) n 4 ( n 3 1 ) 1 ] 2 + n 3 φ 2 2 ( n 3 n 4 ) n 4 2 ( n 3 1 ) 3 [ n 3 φ 2 + n 4 φ 1 ( n 3 1 ) ] .
S I I = b 0 + Q b 1 ,
b 1 = φ 1 + φ 2 1 n 4 n 2 + φ 1 n 2 φ 2 n 3 , b 0 = B 00 + B 01 u 1 , B 01 = 3 + 2 ( φ 1 n 2 + φ 2 n 3 ) 2 φ 1 + φ 2 1 n 4 , B 00 = n 4 n 4 1 [ φ 1 n 4 + φ 2 n 4 2 φ 2 ( n 4 1 ) n 4 2 ( n 3 1 ) 1 ] × [ φ 1 + φ 2 n 4 φ 2 ( n 4 1 ) n 4 ( n 3 1 ) 1 ] φ 1 2 n 2 1 + φ 2 ( n 3 n 4 ) n 4 2 ( n 3 1 ) 2 [ n 3 φ 2 + n 4 φ 1 ( n 3 1 ) ] .
1 r 1 = Q u 1 + n 2 φ 1 n 2 1 , 1 r 2 = Q u 1 + φ 1 , 1 r 3 = Q φ 2 + ( u 1 φ 1 ) ( n 3 1 ) n 3 1 , 1 r 4 = Q φ 3 n 4 1 φ 2 + ( u 1 φ 1 ) ( n 3 1 ) n 3 1 .
S I = e 3 φ 1 3 + e 2 φ 1 2 + e 1 φ 1 + e 0 ,
e 3 = A 1 A 3 B 1 + B 3 + C 1 C 3 + D 1 D 3 , e 2 = φ 2 ( 3 A 3 3 B 3 4 C 2 + 3 C 3 + 3 D 3 ) + ( 3 A 3 B 3 C 3 + 3 D 3 ) φ + A ( 2 A 1 A B 1 ) + B ( B 3 2 A 3 ) , e 1 = φ 2 2 [ 3 ( A 3 B 3 + C 3 + D 3 ) 4 C 2 + 2 B 2 X 2 ] + φ 2 [ 2 ( 3 A 3 B 3 C 3 + 3 D 3 ) φ + 2 B ( B 3 2 A 3 ) ] + ( C 3 B 3 3 A 3 3 D 3 ) φ 2 + ( 4 A 3 B ) φ + A 2 A 1 A 3 B 2 , e 0 = φ 2 3 ( A 2 X 2 2 + B 2 X 2 + A 3 B 3 C 2 + C 3 D 2 + D 3 ) + φ 2 2 [ ( 3 A 3 B 3 C 3 + 3 D 3 ) φ + ( B 3 2 A 3 ) B ] φ 2 [ ( 3 A 3 + B 3 C 3 + 3 D 3 ) φ 2 + ( B 4 φ ) A 3 B ] + ( A 3 + B 3 + C 3 + D 3 ) φ 3 ( 2 A 3 + B 3 ) B φ 2 + ( A 3 B 2 ) φ , A = φ 2 ( X 2 + 1 ) ( n 1 1 ) n 2 1 , B = φ 2 ( X 2 1 ) ( n 3 1 ) n 2 1 .
S I I = g 2 φ 1 2 + g 1 φ 1 + g 0 ,
g 2 = E 1 E 3 F 1 + F 3 , g 1 = 2 E 3 φ φ 2 ( 2 E 3 + 2 F 2 2 F 3 ) + A E 1 B E 3 , g 0 = φ 2 2 ( E 3 + F 2 F 3 E 2 X 2 ) + φ 2 ( 2 E 3 φ B E 3 ) ( E 3 + F 3 ) φ 2 + B E 3 φ .
φ 3 = φ φ 1 φ 2 , X 1 = A φ 1 + 1 , X 3 = B φ 3 1.
n 2 1 = 1.0093 λ 2 λ 2 0.013185 ,

Metrics