Abstract

We present an iterative design method for liquid-tunable aspherical lenses capable of diffraction-limited performance over a wide focal length range. The lenses are formed by a thin elastomer meniscus with a variable thickness profile engineered to deform into an ideal asphere under uniform pressure load. Compared to their more conventional counterparts, the proposed lenses significantly reduce spherical aberration over a larger portion of the aperture. The design procedure begins with the semi-analytical calculation of the meniscus thickness profile using large-deflection thin plate theory. This initial profile is then further optimized using coupled finite element analysis and ray-tracing simulations iteratively. We apply the developed method to design a tunable aspherical lens with 3 mm clear aperture and 8 mm optimum focal length, and numerically demonstrate the improvement in optical performance over conventional tunable-lenses over a focal length range from 6 mm to 12 mm. Using 80% of the clear aperture, the lens has better than λ/4 RMS surface error over the focal length range from 7.7 mm to 8.5 mm, corresponding to 10% tuning of focal length with diffraction-limited performance. The sources of potential fabrication errors in a practical implementation of such a lens are also analyzed in detail in terms of their influence on optical performance.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2014 (3)

2013 (3)

A. Santiago-Alvarado, J. González-García, F. Itubide-Jiménez, M. Campos-Garcíab, V.M. Cruz-Martineza, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik - International Journal for Light and Electron Optics 124, 1003–1010 (2013).
[Crossref]

G. R. Lemaitre, “Optical design and active optics methods in astronomy,” Opt. Rev. 20, 103–117 (2013).
[Crossref]

P.-H. Cu-Nguyen, A. Grewe, M. Hillenbrand, S. Sinzinger, A. Seifert, and H. Zappe, “Tunable hyperchromatic lens system for confocal hyperspectral sensing,” Opt. Express 21, 27611–27621 (2013).
[Crossref]

2012 (1)

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

2011 (1)

2010 (1)

2009 (1)

2008 (4)

S. Manzanera, C. Canovas, P. M. Prieto, and P. Artal, “A wavelength tunable wavefront sensor for the human eye,” Opt. Express 16, 7748–7755 (2008).
[Crossref] [PubMed]

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

H. B. Yu, G. Y. Zhou, F. S. Chau, F. W. Lee, and S. H. Wang, “A tunable Shack–Hartmann wavefront sensor based on a liquid-filled microlens array,” J. Micromech. Microeng 18, 105017 (2008).
[Crossref]

K. Aljasem, A. Werber, A. Seifert, and H. Zappe, “Fiber optic tunable probe for endoscopic optical coherence tomography,” J. Opt. A: Pure Appl. Opt. 10, 044012 (2008).
[Crossref]

2006 (2)

W. Greger, T. Hsel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke, “Low-cost deformable mirror for laser focussing,” Proc. SPIE 6374, 63740F (2006).
[Crossref]

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, “Fluidic lenses with variable focal length,” Appl. Phys. Lett. 88, 041120 (2006).
[Crossref]

2005 (1)

2004 (1)

2003 (1)

Aljasem, K.

K. Aljasem, A. Werber, A. Seifert, and H. Zappe, “Fiber optic tunable probe for endoscopic optical coherence tomography,” J. Opt. A: Pure Appl. Opt. 10, 044012 (2008).
[Crossref]

Artal, P.

Ataman, Ç.

P. P. Zhao, Ç. Ataman, and H. Zappe, “An endoscopic microscope with liquid-tunable aspheric lenses for continuous zoom capability,” Proc. SPIE9130, 913004–11 (2014).
[Crossref]

Berdichevsky, Y.

Campos-Garcíab, M.

A. Santiago-Alvarado, J. González-García, F. Itubide-Jiménez, M. Campos-Garcíab, V.M. Cruz-Martineza, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik - International Journal for Light and Electron Optics 124, 1003–1010 (2013).
[Crossref]

Canovas, C.

Carré, J. F.

M. Ferrari, G. R. Lemaitre, S. P. Mazzanti, O. von der Luehe, B. di Biagio, P. Montiel, D. Revest, P. Joulie, and J. F. Carré, “Highly variable curvature mirrors for the Very Large Telescope Interferometer,” Proc. SPIE2201, 811–820 (1994).
[Crossref]

Carreel, B.

k. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Chan, M. L.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, “Fluidic lenses with variable focal length,” Appl. Phys. Lett. 88, 041120 (2006).
[Crossref]

Chau, F. S.

Choi, S. T.

Christian, W.

Chronis, N.

Cruz-Martineza, V.M.

A. Santiago-Alvarado, J. González-García, F. Itubide-Jiménez, M. Campos-Garcíab, V.M. Cruz-Martineza, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik - International Journal for Light and Electron Optics 124, 1003–1010 (2013).
[Crossref]

Cu-Nguyen, P.-H.

Dharmatilleke, S.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, “Fluidic lenses with variable focal length,” Appl. Phys. Lett. 88, 041120 (2006).
[Crossref]

di Biagio, B.

M. Ferrari, G. R. Lemaitre, S. P. Mazzanti, O. von der Luehe, B. di Biagio, P. Montiel, D. Revest, P. Joulie, and J. F. Carré, “Highly variable curvature mirrors for the Very Large Telescope Interferometer,” Proc. SPIE2201, 811–820 (1994).
[Crossref]

Fellner, T.

W. Greger, T. Hsel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke, “Low-cost deformable mirror for laser focussing,” Proc. SPIE 6374, 63740F (2006).
[Crossref]

Ferrari, M.

M. Ferrari, G. R. Lemaitre, S. P. Mazzanti, O. von der Luehe, B. di Biagio, P. Montiel, D. Revest, P. Joulie, and J. F. Carré, “Highly variable curvature mirrors for the Very Large Telescope Interferometer,” Proc. SPIE2201, 811–820 (1994).
[Crossref]

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,” Optics and Lasers in Engineering 50, 1677–1682 (2012).
[Crossref]

González-García, J.

A. Santiago-Alvarado, J. González-García, F. Itubide-Jiménez, M. Campos-Garcíab, V.M. Cruz-Martineza, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik - International Journal for Light and Electron Optics 124, 1003–1010 (2013).
[Crossref]

Greger, W.

W. Greger, T. Hsel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke, “Low-cost deformable mirror for laser focussing,” Proc. SPIE 6374, 63740F (2006).
[Crossref]

Grewe, A.

Herkommer, A. M.

Hillenbrand, M.

Hsel, T.

W. Greger, T. Hsel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke, “Low-cost deformable mirror for laser focussing,” Proc. SPIE 6374, 63740F (2006).
[Crossref]

Itubide-Jiménez, F.

A. Santiago-Alvarado, J. González-García, F. Itubide-Jiménez, M. Campos-Garcíab, V.M. Cruz-Martineza, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik - International Journal for Light and Electron Optics 124, 1003–1010 (2013).
[Crossref]

Jeong, K. H.

Joulie, P.

M. Ferrari, G. R. Lemaitre, S. P. Mazzanti, O. von der Luehe, B. di Biagio, P. Montiel, D. Revest, P. Joulie, and J. F. Carré, “Highly variable curvature mirrors for the Very Large Telescope Interferometer,” Proc. SPIE2201, 811–820 (1994).
[Crossref]

Justis, N.

Khaw, A. H.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, “Fluidic lenses with variable focal length,” Appl. Phys. Lett. 88, 041120 (2006).
[Crossref]

Kobrin, P.

Lee, F. W.

H. B. Yu, G. Y. Zhou, F. S. Chau, F. W. Lee, S. H. Wang, and H. M. Leung, “A liquid-filled tunable double-focus microlens,” Opt. Express 17, 4782–4790 (2009).
[Crossref] [PubMed]

H. B. Yu, G. Y. Zhou, F. S. Chau, F. W. Lee, and S. H. Wang, “A tunable Shack–Hartmann wavefront sensor based on a liquid-filled microlens array,” J. Micromech. Microeng 18, 105017 (2008).
[Crossref]

Lee, K.-S.

Lee, L. P.

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,” Optics and Lasers in Engineering 50, 1677–1682 (2012).
[Crossref]

Lemaitre, G. R.

G. R. Lemaitre, “Optical design and active optics methods in astronomy,” Opt. Rev. 20, 103–117 (2013).
[Crossref]

M. Ferrari, G. R. Lemaitre, S. P. Mazzanti, O. von der Luehe, B. di Biagio, P. Montiel, D. Revest, P. Joulie, and J. F. Carré, “Highly variable curvature mirrors for the Very Large Telescope Interferometer,” Proc. SPIE2201, 811–820 (1994).
[Crossref]

G. R. Lemaitre, Astronomical Optics and Elasticity Theory: Active Optics Methods (Springer Science & Business Media, 2008).

Leung, H. M.

Liebetraut, P.

Lien, V.

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,” Optics and Lasers in Engineering 50, 1677–1682 (2012).
[Crossref]

Liu, G. L.

Lo, Y. H.

Mader, D.

Manukyan, G.

k. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Manzanera, S.

Mazzanti, S. P.

M. Ferrari, G. R. Lemaitre, S. P. Mazzanti, O. von der Luehe, B. di Biagio, P. Montiel, D. Revest, P. Joulie, and J. F. Carré, “Highly variable curvature mirrors for the Very Large Telescope Interferometer,” Proc. SPIE2201, 811–820 (1994).
[Crossref]

Mishra, k.

k. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Montiel, P.

M. Ferrari, G. R. Lemaitre, S. P. Mazzanti, O. von der Luehe, B. di Biagio, P. Montiel, D. Revest, P. Joulie, and J. F. Carré, “Highly variable curvature mirrors for the Very Large Telescope Interferometer,” Proc. SPIE2201, 811–820 (1994).
[Crossref]

Moran, P. M.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, “Fluidic lenses with variable focal length,” Appl. Phys. Lett. 88, 041120 (2006).
[Crossref]

Mueller, C.

W. Greger, T. Hsel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke, “Low-cost deformable mirror for laser focussing,” Proc. SPIE 6374, 63740F (2006).
[Crossref]

Mugele, F.

k. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Murade, C.

k. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Narayanaswamy, S.

Oh, J. M.

k. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Park, S.-Y.

Prieto, P. M.

Rafferty, P.

A. Santiago-Alvarado, J. González-García, F. Itubide-Jiménez, M. Campos-Garcíab, V.M. Cruz-Martineza, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik - International Journal for Light and Electron Optics 124, 1003–1010 (2013).
[Crossref]

Reinecke, H.

W. Greger, T. Hsel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke, “Low-cost deformable mirror for laser focussing,” Proc. SPIE 6374, 63740F (2006).
[Crossref]

Revest, D.

M. Ferrari, G. R. Lemaitre, S. P. Mazzanti, O. von der Luehe, B. di Biagio, P. Montiel, D. Revest, P. Joulie, and J. F. Carré, “Highly variable curvature mirrors for the Very Large Telescope Interferometer,” Proc. SPIE2201, 811–820 (1994).
[Crossref]

Rodriguez, I.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, “Fluidic lenses with variable focal length,” Appl. Phys. Lett. 88, 041120 (2006).
[Crossref]

Roghair, I.

k. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

Santiago-Alvarado, A.

A. Santiago-Alvarado, J. González-García, F. Itubide-Jiménez, M. Campos-Garcíab, V.M. Cruz-Martineza, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik - International Journal for Light and Electron Optics 124, 1003–1010 (2013).
[Crossref]

Schoth, A.

W. Greger, T. Hsel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke, “Low-cost deformable mirror for laser focussing,” Proc. SPIE 6374, 63740F (2006).
[Crossref]

Seabury, C.

Seifert, A.

S. Thiele, A. Seifert, and A. M. Herkommer, “Wave-optical design of a combined refractive-diffractive varifocal lens,” Opt. Express 22, 13343–13350 (2014).
[Crossref] [PubMed]

P.-H. Cu-Nguyen, A. Grewe, M. Hillenbrand, S. Sinzinger, A. Seifert, and H. Zappe, “Tunable hyperchromatic lens system for confocal hyperspectral sensing,” Opt. Express 21, 27611–27621 (2013).
[Crossref]

K. Aljasem, A. Werber, A. Seifert, and H. Zappe, “Fiber optic tunable probe for endoscopic optical coherence tomography,” J. Opt. A: Pure Appl. Opt. 10, 044012 (2008).
[Crossref]

N. Weber, H. Zappe, and A. Seifert, “High-precision optical & fluidic micro-bench for endoscopic imaging,” in “International Conference on Optical MEMS and Nanophotonics,” (2010), pp. 85–86.

N. Weber, H. Zappe, and A. Seifert, “Optical micro-system with highly flexible tunability for endoscopic micro-probes,” in “International Conference on Optical MEMS and Nanophotonics,” (2011), pp. 51–52.

Seifert, Andreas

Seo, G. W.

Sinzinger, S.

Son, B. S.

Tan, K. W.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, “Fluidic lenses with variable focal length,” Appl. Phys. Lett. 88, 041120 (2006).
[Crossref]

Thiele, S.

Timosenko, S. P.

S. P. Timosenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, 1996).

van den Ende, D.

k. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

von der Luehe, O.

M. Ferrari, G. R. Lemaitre, S. P. Mazzanti, O. von der Luehe, B. di Biagio, P. Montiel, D. Revest, P. Joulie, and J. F. Carré, “Highly variable curvature mirrors for the Very Large Telescope Interferometer,” Proc. SPIE2201, 811–820 (1994).
[Crossref]

Waibel, P.

Wang, S. H.

H. B. Yu, G. Y. Zhou, F. S. Chau, F. W. Lee, S. H. Wang, and H. M. Leung, “A liquid-filled tunable double-focus microlens,” Opt. Express 17, 4782–4790 (2009).
[Crossref] [PubMed]

H. B. Yu, G. Y. Zhou, F. S. Chau, F. W. Lee, and S. H. Wang, “A tunable Shack–Hartmann wavefront sensor based on a liquid-filled microlens array,” J. Micromech. Microeng 18, 105017 (2008).
[Crossref]

Weber, N.

N. Weber, H. Zappe, and A. Seifert, “High-precision optical & fluidic micro-bench for endoscopic imaging,” in “International Conference on Optical MEMS and Nanophotonics,” (2010), pp. 85–86.

N. Weber, “Highly flexible micro-bench system for endoscopic micro-probes,” Ph.D. thesis, University of Freiburg (2013).

N. Weber, H. Zappe, and A. Seifert, “Optical micro-system with highly flexible tunability for endoscopic micro-probes,” in “International Conference on Optical MEMS and Nanophotonics,” (2011), pp. 51–52.

Werber, A.

K. Aljasem, A. Werber, A. Seifert, and H. Zappe, “Fiber optic tunable probe for endoscopic optical coherence tomography,” J. Opt. A: Pure Appl. Opt. 10, 044012 (2008).
[Crossref]

A. Werber and H. Zappe, “Tunable microfluidic microlenses,” Appl. Opt. 44, 3238–3245 (2005).
[Crossref] [PubMed]

Wilde, J.

W. Greger, T. Hsel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke, “Low-cost deformable mirror for laser focussing,” Proc. SPIE 6374, 63740F (2006).
[Crossref]

Woinowsky-Krieger, S.

S. P. Timosenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, 1996).

Yang, Q. D.

Yu, H. B.

Zappe, H.

P.-H. Cu-Nguyen, A. Grewe, M. Hillenbrand, S. Sinzinger, A. Seifert, and H. Zappe, “Tunable hyperchromatic lens system for confocal hyperspectral sensing,” Opt. Express 21, 27611–27621 (2013).
[Crossref]

P. Waibel, D. Mader, P. Liebetraut, H. Zappe, and Andreas Seifert, “Chromatic aberration control for tunable all-silicone membrane microlenses,” Opt. Express 19, 18584–18592 (2011).
[Crossref] [PubMed]

K. Aljasem, A. Werber, A. Seifert, and H. Zappe, “Fiber optic tunable probe for endoscopic optical coherence tomography,” J. Opt. A: Pure Appl. Opt. 10, 044012 (2008).
[Crossref]

A. Werber and H. Zappe, “Tunable microfluidic microlenses,” Appl. Opt. 44, 3238–3245 (2005).
[Crossref] [PubMed]

N. Weber, H. Zappe, and A. Seifert, “Optical micro-system with highly flexible tunability for endoscopic micro-probes,” in “International Conference on Optical MEMS and Nanophotonics,” (2011), pp. 51–52.

N. Weber, H. Zappe, and A. Seifert, “High-precision optical & fluidic micro-bench for endoscopic imaging,” in “International Conference on Optical MEMS and Nanophotonics,” (2010), pp. 85–86.

P. P. Zhao, Ç. Ataman, and H. Zappe, “An endoscopic microscope with liquid-tunable aspheric lenses for continuous zoom capability,” Proc. SPIE9130, 913004–11 (2014).
[Crossref]

Zhang, D. Y.

Zhao, P. P.

P. P. Zhao, Ç. Ataman, and H. Zappe, “An endoscopic microscope with liquid-tunable aspheric lenses for continuous zoom capability,” Proc. SPIE9130, 913004–11 (2014).
[Crossref]

Zhou, G. Y.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, “Fluidic lenses with variable focal length,” Appl. Phys. Lett. 88, 041120 (2006).
[Crossref]

J. Micromech. Microeng (1)

H. B. Yu, G. Y. Zhou, F. S. Chau, F. W. Lee, and S. H. Wang, “A tunable Shack–Hartmann wavefront sensor based on a liquid-filled microlens array,” J. Micromech. Microeng 18, 105017 (2008).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

K. Aljasem, A. Werber, A. Seifert, and H. Zappe, “Fiber optic tunable probe for endoscopic optical coherence tomography,” J. Opt. A: Pure Appl. Opt. 10, 044012 (2008).
[Crossref]

Opt. Express (8)

H. B. Yu, G. Y. Zhou, F. S. Chau, F. W. Lee, S. H. Wang, and H. M. Leung, “A liquid-filled tunable double-focus microlens,” Opt. Express 17, 4782–4790 (2009).
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H. B. Yu, G. Y. 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] [PubMed]

P. Waibel, D. Mader, P. Liebetraut, H. Zappe, and Andreas Seifert, “Chromatic aberration control for tunable all-silicone membrane microlenses,” Opt. Express 19, 18584–18592 (2011).
[Crossref] [PubMed]

P.-H. Cu-Nguyen, A. Grewe, M. Hillenbrand, S. Sinzinger, A. Seifert, and H. Zappe, “Tunable hyperchromatic lens system for confocal hyperspectral sensing,” Opt. Express 21, 27611–27621 (2013).
[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] [PubMed]

S. Thiele, A. Seifert, and A. M. Herkommer, “Wave-optical design of a combined refractive-diffractive varifocal lens,” Opt. Express 22, 13343–13350 (2014).
[Crossref] [PubMed]

S. Manzanera, C. Canovas, P. M. Prieto, and P. Artal, “A wavelength tunable wavefront sensor for the human eye,” Opt. Express 16, 7748–7755 (2008).
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N. Chronis, G. L. Liu, K. H. Jeong, and L. P. Lee, “Tunable liquid-filled microlens array integrated with mi-crofluidic network,” Opt. Express 11, 2370–2378 (2003).
[Crossref] [PubMed]

Opt. Rev. (1)

G. R. Lemaitre, “Optical design and active optics methods in astronomy,” Opt. Rev. 20, 103–117 (2013).
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Optics and Lasers in Engineering (1)

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

Optik - International Journal for Light and Electron Optics (1)

A. Santiago-Alvarado, J. González-García, F. Itubide-Jiménez, M. Campos-Garcíab, V.M. Cruz-Martineza, and P. Rafferty, “Simulating the functioning of variable focus length liquid-filled lenses using the finite element method (FEM),” Optik - International Journal for Light and Electron Optics 124, 1003–1010 (2013).
[Crossref]

Proc. SPIE (1)

W. Greger, T. Hsel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke, “Low-cost deformable mirror for laser focussing,” Proc. SPIE 6374, 63740F (2006).
[Crossref]

Sci. Rep. (1)

k. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4, 6378 (2014).
[Crossref] [PubMed]

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G. R. Lemaitre, Astronomical Optics and Elasticity Theory: Active Optics Methods (Springer Science & Business Media, 2008).

S. P. Timosenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, 1996).

N. Weber, H. Zappe, and A. Seifert, “High-precision optical & fluidic micro-bench for endoscopic imaging,” in “International Conference on Optical MEMS and Nanophotonics,” (2010), pp. 85–86.

N. Weber, H. Zappe, and A. Seifert, “Optical micro-system with highly flexible tunability for endoscopic micro-probes,” in “International Conference on Optical MEMS and Nanophotonics,” (2011), pp. 51–52.

N. Weber, “Highly flexible micro-bench system for endoscopic micro-probes,” Ph.D. thesis, University of Freiburg (2013).

P. P. Zhao, Ç. Ataman, and H. Zappe, “An endoscopic microscope with liquid-tunable aspheric lenses for continuous zoom capability,” Proc. SPIE9130, 913004–11 (2014).
[Crossref]

M. Ferrari, G. R. Lemaitre, S. P. Mazzanti, O. von der Luehe, B. di Biagio, P. Montiel, D. Revest, P. Joulie, and J. F. Carré, “Highly variable curvature mirrors for the Very Large Telescope Interferometer,” Proc. SPIE2201, 811–820 (1994).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 (a) Schematic depiction of a liquid-filled tunable lens consisting of a rigid frame as the lens chamber sealed by an elastomer membrane from the top and rigid substrate from the bottom. The chamber is filled with a liquid. By applying external pressure through pressure inlet, the membrane can be inflated (deflated) to have a convex (concave) profile. (b) Schematic diagram of the tunable lens developed in this work, where a meniscus of variable thickness replaces the uniform membrane. The meniscus has a plano-convex shape with a base thickness tb and sag thickness of ts.
Fig. 2
Fig. 2 Flow chart of the design procedure to obtain the meniscus thickness distribution for a given profile.
Fig. 3
Fig. 3 (a) Normalized meniscus thickness profiles calculated at different pressures and identical t0 of 38 µm. All three configurations produce the same lens profile z(r). As the pressure decreases, the meniscus decreases more gradually towards the edge, lowering the effective rigidity. (b) Normalized meniscus thickness profiles calculated for different t0 and an identical pressure of 1 KPa. In this case, the meniscus thickness at the center exhibits a more gradual decrease towards the edge. In all cases, the meniscus material is PDMS (E = 1.37 MPa, ν = 0.499).
Fig. 4
Fig. 4 Analytically calculated and optimized initial meniscus thickness distribution for the tunable aspherical lens. With the diameter of 3 mm, the normalized initial meniscus profile has a base thickness of 20 µm, and a maximum sag height of 38 µm.
Fig. 5
Fig. 5 (a) FEA results depicting the meniscus deflection as a function of pressure ranging from 0.2 KPa to 3 KPa within steps of 0.2 KPa. The inset plots the axial deflection at the center as a function of pressure, which is highly nonlinear due to the large deformation effects. (b) The deviation from the desired aspherical profile at different focal lengths. The deviation is minimum at the design focal length of 8 mm and grows significantly as the lens is tuned. Due to the base thickness, the pressure necessary for the optimum focal length is 1.2 KPa instead of 1 KPa (the value used to obtain the analytical profile).
Fig. 6
Fig. 6 MTF curves of the tunable lens with variable thickness meniscus as our designed for different focal lengths, by comparison, the blue curves are the MTF of the tunable lens with 30 µm uniform thickness meniscus. (a) Focal length of 6 mm. (b) Focal length of 8 mm. (c) Focal length of 10 mm. (d) Focal length of 12 mm.
Fig. 7
Fig. 7 The RMS error in the MTF as a function of effective lens focal length. The λ/4 limit is denoted by the red line. Diffraction limited performance can be obtained between 7.7 mm and 8.5 mm focal lengths, which corresponds to an effective tuning range 10%.
Fig. 8
Fig. 8 MTF curves for tunable lenses with base thickness errors of ±0.5 µm, ±1 µm, ±2 µm. (a) Focal length of 6 mm. (b) Focal length of 8 mm. (c) Focal length of 10 mm (d) Focal length of 12 mm.
Fig. 9
Fig. 9 MTF curves for tunable lenses with meniscus tilt errors of 0.01°, 0.02° and 0.04°. (a) Focal length of 6 mm. (b) Focal length of 8 mm. (c) Focal length of 10 mm. (d) Focal length of 12 mm.
Fig. 10
Fig. 10 The RMS error in the MTF as a function of effective lens focal length. The λ/4 limit is denoted by the black line. (a) shows the RMS due to the meniscus base thickness error. (b) shows the RMS due to the meniscus tilt.

Equations (9)

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Z ( r ) = C r 2 1 + 1 ( 1 + K ) C 2 r 2 + k = 2 α k r 2 k ,
D ( r ) = E t 3 ( r ) 12 ( 1 ν 2 ) ,
d 2 u d r 2 + ( 1 t d t d r + 1 r ) d u d r + ( ν t d t d r 1 r ) u r + 1 2 ( 1 t d t d r + 1 ν r ) ( d u d r ) 2 + d 2 u d r 2 d u d r = 0 ,
d ( 2 z ) d r + ( d 2 z d r 2 + ν r d z d r ) 1 D d D d r 1 t 2 ( d u d r + ν u r + 1 2 ( d z d r ) 2 ) d z d r Pr 2 D = 0.
t ( ρ ) ρ = 0 = 1 , t ( ρ ) ρ = 1 = 0 , u ( ρ ) ρ = 0 = 0 , ( d u d r ) r = 0 = ε .
t o ( r ) = m 1 exp ( r n 1 ) + m 2 exp ( r n 2 ) + t b ,
Z P ( r ) = A n r 8 + B n r 7 + C n r 6 + D n r 5 + E n r 4 + F n r 3 + G n r 2 + H n r + I n ,
A n ( P ) = i = 0 8 a i P i ,
Z P ( r ) = i = 0 8 a i P i r 8 + i = 0 8 b i P i r 7 + i = 0 8 c i P i r 6 + i = 0 8 d i P i r 5 + i = 0 8 e i P i r 4 + i = 0 8 f i P i r 3 + i = 0 8 g i P i r 2 + i = 0 8 h i P i r + i = 0 8 i i P i .

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