Abstract

Tunable lenses are becoming ubiquitous, in applications including microscopy, optical coherence tomography, computer vision, quality control, and presbyopic corrections. Many applications require an accurate control of the optical power of the lens in response to a time-dependent input waveform. We present a fast focimeter (3.8 KHz) to characterize the dynamic response of tunable lenses, which was demonstrated on different lens models. We found that the temporal response is repetitive and linear, which allowed the development of a robust compensation strategy based on the optimization of the input wave, using a linear time-invariant model. To our knowledge, this work presents the first procedure for a direct characterization of the transient response of tunable lenses and for compensation of their temporal distortions, and broadens the potential of tunable lenses also in high-speed applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

2017 (7)

M. Vinas, C. Dorronsoro, A. Radhakrishnan, C. Benedi-Garcia, E. A. LaVilla, J. Schwiegerling, and S. Marcos, “Comparison of vision through surface modulated and spatial light modulated multifocal optics,” Biomed. Opt. Express 8(4), 2055–2068 (2017).
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J. Jarosz, P. Mecê, J. M. Conan, C. Petit, M. Paques, and S. Meimon, “High temporal resolution aberrometry in a 50-eye population and implications for adaptive optics error budget,” Biomed. Opt. Express 8(4), 2088–2105 (2017).
[Crossref] [PubMed]

C. Jie, Y. Cheng, Q. Hao, F. Zhang, K. Zhang, X. Li, K. Li, and Y. Peng, “Improving the performance of time-domain pulsed echo laser profile using tunable lens,” Opt. Express 25(7), 7970–7983 (2017).
[Crossref] [PubMed]

D. Volpi, I. D. C. Tullis, P. R. Barber, E. M. Augustyniak, S. C. Smart, K. A. Vallis, and B. Vojnovic, “Electrically tunable fluidic lens imaging system for laparoscopic fluorescence-guided surgery,” Biomed. Opt. Express 8(7), 3232–3247 (2017).
[Crossref] [PubMed]

V. Akondi, C. Dorronsoro, E. Gambra, and S. Marcos, “Temporal multiplexing to simulate multifocal intraocular lenses: theoretical considerations,” Biomed. Opt. Express 8(7), 3410–3425 (2017).
[Crossref] [PubMed]

N. Padmanaban, R. Konrad, T. Stramer, E. A. Cooper, and G. Wetzstein, “Optimizing virtual reality for all users through gaze-contingent and adaptive focus displays,” Proc. Natl. Acad. Sci. U.S.A. 114(9), 2183–2188 (2017).
[Crossref] [PubMed]

Z. Wang, W. Qu, F. Yang, A. Tian, and A. Asundi, “Absolute measurement of aspheric lens with electrically tunable lens in digital holography,” Opt. Lasers Eng. 88, 313–318 (2017).
[Crossref]

2016 (3)

2015 (3)

2014 (1)

2013 (2)

F. O. Fahrbach, F. F. Voigt, B. Schmid, F. Helmchen, and J. Huisken, “Rapid 3D light-sheet microscopy with a tunable lens,” Opt. Express 21(18), 21010–21026 (2013).
[Crossref] [PubMed]

F. Sanàbria, F. Díaz Doutón, M. Aldaba, and J. Pujol, “Spherical refractive correction with an electro-optical liquid lens in a double-pass system,” J. Eur. Opt. Soc. Rapid Publ. 8, 13062 (2013).
[Crossref]

2011 (1)

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses.” Optical Design and Engineering IV,” International Society for Optics and Photonics 8167, 81670W (2011).

2009 (3)

2008 (3)

X. Huang, C. M. Cheng, L. Wang, B. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, “Thermally tunable polymer microlenses,” Appl. Phys. Lett. 92(25), 251904 (2008).
[Crossref]

H. Ren and S. T. Wu, “Tunable-focus liquid microlens array using dielectrophoretic effect,” Opt. Express 16(4), 2646–2652 (2008).
[Crossref] [PubMed]

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

2006 (2)

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

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(4), 041120 (2006).
[Crossref]

2005 (1)

C. A. López, C. C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87(13), 134102 (2005).
[Crossref]

2004 (1)

2003 (2)

2000 (1)

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

1999 (1)

1998 (1)

A. Glasser and M. C. Campbell, “Presbyopia and the optical changes in the human crystalline lens with age,” Vision Res. 38(2), 209–229 (1998).
[Crossref] [PubMed]

Agarwal, A. K.

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

Akondi, V.

Aldaba, M.

F. Sanàbria, F. Díaz Doutón, M. Aldaba, and J. Pujol, “Spherical refractive correction with an electro-optical liquid lens in a double-pass system,” J. Eur. Opt. Soc. Rapid Publ. 8, 13062 (2013).
[Crossref]

Alonso-Sanz, J. R.

Annibale, P.

Artal, P.

Aschwanden, M.

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses.” Optical Design and Engineering IV,” International Society for Optics and Photonics 8167, 81670W (2011).

Asundi, A.

Z. Wang, W. Qu, F. Yang, A. Tian, and A. Asundi, “Absolute measurement of aspheric lens with electrically tunable lens in digital holography,” Opt. Lasers Eng. 88, 313–318 (2017).
[Crossref]

Augustyniak, E. M.

Barber, P. R.

Beebe, D. J.

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

Benedi-Garcia, C.

Berge, B.

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

Blum, M.

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses.” Optical Design and Engineering IV,” International Society for Optics and Photonics 8167, 81670W (2011).

Büeler, M.

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses.” Optical Design and Engineering IV,” International Society for Optics and Photonics 8167, 81670W (2011).

Campbell, M. C.

A. Glasser and M. C. Campbell, “Presbyopia and the optical changes in the human crystalline lens with age,” Vision Res. 38(2), 209–229 (1998).
[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(4), 041120 (2006).
[Crossref]

Chau, F. S.

Chen, S. C.

Cheng, C. M.

X. Huang, C. M. Cheng, L. Wang, B. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, “Thermally tunable polymer microlenses,” Appl. Phys. Lett. 92(25), 251904 (2008).
[Crossref]

Cheng, S.

Cheng, Y.

Cheng, Y.-S. L.

Chronis, N.

Conan, J. M.

Cooper, E. A.

N. Padmanaban, R. Konrad, T. Stramer, E. A. Cooper, and G. Wetzstein, “Optimizing virtual reality for all users through gaze-contingent and adaptive focus displays,” Proc. Natl. Acad. Sci. U.S.A. 114(9), 2183–2188 (2017).
[Crossref] [PubMed]

Cormack, R. H.

Cuenca, R.

Cwiklinski, L.

De Nicola, S.

Del Águila-Carrasco, A. J.

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(4), 041120 (2006).
[Crossref]

Díaz Doutón, F.

F. Sanàbria, F. Díaz Doutón, M. Aldaba, and J. Pujol, “Spherical refractive correction with an electro-optical liquid lens in a double-pass system,” J. Eur. Opt. Soc. Rapid Publ. 8, 13062 (2013).
[Crossref]

Dong, L.

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

Dorronsoro, C.

Dvornikov, A.

Fahrbach, F. O.

Ferraro, P.

Finizio, A.

Gambra, E.

Glasser, A.

A. Glasser and M. C. Campbell, “Presbyopia and the optical changes in the human crystalline lens with age,” Vision Res. 38(2), 209–229 (1998).
[Crossref] [PubMed]

Gopinath, J. T.

Gratton, E.

Grätzel, C.

M. Blum, M. Büeler, C. Grätzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses.” Optical Design and Engineering IV,” International Society for Optics and Photonics 8167, 81670W (2011).

Grilli, S.

Grulkowski, I.

Gu, C.

Hao, Q.

Hashimoto, K.

Helmchen, F.

Hirsa, A. H.

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

C. A. López, C. C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87(13), 134102 (2005).
[Crossref]

Ho, M. S.

X. Huang, C. M. Cheng, L. Wang, B. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, “Thermally tunable polymer microlenses,” Appl. Phys. Lett. 92(25), 251904 (2008).
[Crossref]

Hua, H.

Huang, X.

X. Huang, C. M. Cheng, L. Wang, B. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, “Thermally tunable polymer microlenses,” Appl. Phys. Lett. 92(25), 251904 (2008).
[Crossref]

Huisken, J.

Ishikawa, M.

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

H. Oku, K. Hashimoto, and M. Ishikawa, “Variable-focus lens with 1-kHz bandwidth,” Opt. Express 12(10), 2138–2149 (2004).
[Crossref] [PubMed]

Jabbour, J. M.

Jarosz, J.

Jeong, K. H.

Jiang, H.

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

Jiang, J.

Jie, C.

Jo, J. A.

Karnowski, K.

Ke, Y.

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(4), 041120 (2006).
[Crossref]

Konrad, R.

N. Padmanaban, R. Konrad, T. Stramer, E. A. Cooper, and G. Wetzstein, “Optimizing virtual reality for all users through gaze-contingent and adaptive focus displays,” Proc. Natl. Acad. Sci. U.S.A. 114(9), 2183–2188 (2017).
[Crossref] [PubMed]

Krupenkin, T.

T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett. 82(3), 316–318 (2003).
[Crossref]

LaVilla, E. A.

LeDuc, P. R.

X. Huang, C. M. Cheng, L. Wang, B. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, “Thermally tunable polymer microlenses,” Appl. Phys. Lett. 92(25), 251904 (2008).
[Crossref]

Lee, C. C.

C. A. López, C. C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87(13), 134102 (2005).
[Crossref]

Lee, L.

Li, K.

Li, X.

Lin, Q.

X. Huang, C. M. Cheng, L. Wang, B. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, “Thermally tunable polymer microlenses,” Appl. Phys. Lett. 92(25), 251904 (2008).
[Crossref]

Liu, G.

Liu, S.

López, C. A.

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

C. A. López, C. C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87(13), 134102 (2005).
[Crossref]

López-Gil, N.

Mach, P.

T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett. 82(3), 316–318 (2003).
[Crossref]

Maitland, K. C.

Malik, B. H.

Manzanera, S.

Marcos, S.

Marín-Franch, I.

Marrakchi, Y.

Mecê, P.

Meimon, S.

Miccio, L.

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(4), 041120 (2006).
[Crossref]

Moreno-Barriuso, E.

Navarro, R.

Oku, H.

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

H. Oku, K. Hashimoto, and M. Ishikawa, “Variable-focus lens with 1-kHz bandwidth,” Opt. Express 12(10), 2138–2149 (2004).
[Crossref] [PubMed]

Olsovsky, C.

Padmanaban, N.

N. Padmanaban, R. Konrad, T. Stramer, E. A. Cooper, and G. Wetzstein, “Optimizing virtual reality for all users through gaze-contingent and adaptive focus displays,” Proc. Natl. Acad. Sci. U.S.A. 114(9), 2183–2188 (2017).
[Crossref] [PubMed]

Papadatou, E.

Paques, M.

Pascual, D.

Paturzo, M.

Peng, Y.

Perez-Merino, P.

Peseux, J.

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

Petit, C.

Pujol, J.

F. Sanàbria, F. Díaz Doutón, M. Aldaba, and J. Pujol, “Spherical refractive correction with an electro-optical liquid lens in a double-pass system,” J. Eur. Opt. Soc. Rapid Publ. 8, 13062 (2013).
[Crossref]

Qu, W.

Z. Wang, W. Qu, F. Yang, A. Tian, and A. Asundi, “Absolute measurement of aspheric lens with electrically tunable lens in digital holography,” Opt. Lasers Eng. 88, 313–318 (2017).
[Crossref]

Radhakrishnan, A.

Ren, H.

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(4), 041120 (2006).
[Crossref]

Sanàbria, F.

F. Sanàbria, F. Díaz Doutón, M. Aldaba, and J. Pujol, “Spherical refractive correction with an electro-optical liquid lens in a double-pass system,” J. Eur. Opt. Soc. Rapid Publ. 8, 13062 (2013).
[Crossref]

Sawides, L.

Schmid, B.

Schwiegerling, J.

Smart, S. C.

Sobczuk, F.

Stramer, T.

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Tian, A.

Z. Wang, W. Qu, F. Yang, A. Tian, and A. Asundi, “Absolute measurement of aspheric lens with electrically tunable lens in digital holography,” Opt. Lasers Eng. 88, 313–318 (2017).
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Wang, Z.

Z. Wang, W. Qu, F. Yang, A. Tian, and A. Asundi, “Absolute measurement of aspheric lens with electrically tunable lens in digital holography,” Opt. Lasers Eng. 88, 313–318 (2017).
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Wetzstein, G.

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Z. Wang, W. Qu, F. Yang, A. Tian, and A. Asundi, “Absolute measurement of aspheric lens with electrically tunable lens in digital holography,” Opt. Lasers Eng. 88, 313–318 (2017).
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Supplementary Material (1)

NameDescription
» Visualization 1       Raw tilted slit images when a tunable lens is measured with the high-speed focimeter. Left side: reference (no prism). Right side: displaced images through the prism. Besides relative displacement, the defocus causes some widening in the image of the

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Figures (9)

Fig. 1
Fig. 1 Principle of the high-speed focimeter. (a) The image of the intermediate image of the slit (S’) through the prism (P) is laterally displaced (right side of the image plane) with respect to the reference without prism (left side of the image plane). The displacement increases (green arrow) when the distance between the prism and the image plane increases (blue arrow). (b) The tunable lens (TL) creates an intermediate image of the slit. (c) The prism (P) deviates the optical axis.
Fig. 2
Fig. 2 Optical set-up. S: Slit (an incoherent polychromatic light source and a diffuser are not shown); L1 and L2: 4F projection system; L3 and L4: 4F additional projection system for calibration; TL: Tunable lens; TrL: Trial lenses; S’: Intermediate slit image; P: (prism); MO: Macro objective; HSC: High Speed camera. (a) Configuration without the prism providing a reference image RI. (b) Configuration with a prism in the region of the intermediate image S’, providing a displaced image DI, with a displacement (with respect to the reference) that changes with the axial position of the intermediate slit image S’ and therefore changes with the optical power of the tunable lens TL. Both configurations co-exist in the same set-up, as the prism P only affects one-half of the intermediate image S’.
Fig. 3
Fig. 3 Raw tilted slit images when trial lenses are measured. Left side of each image: reference (no displacement). Right side: displaced images through the prism: a) 0 diopters (D) -without trial lens-; b) −0.75 D; c) −1.75 D. Besides relative displacement, the defocus causes some widening in the image of the slit. The images taken through the prism (right-half of the slit images) are weaker due to reflection and transmission losses, and due to the prismatic deviation of the light.
Fig. 4
Fig. 4 High speed focimetry measurements. The graphs represent the measured response of the tunable lens (optical power as a function of time), when a square electric input wave is used. The wave period is 100 ms for all the plots, except for (d), which has a period of 20 ms. The step height is 3 D in (a)-(f) and 2 D in (g)–(i). (a) Measured temporal response for tunable lens 30C#2. (b) Measured temporal step response function when the slit is not tilted. (c) Measured temporal step response function when the slit is tilted and the superresolution algorithm is applied. (d) Measured temporal response of a different unit (30C#3) obtained from a superposition of 9 cycles (20 ms). Results with: (e) two other units of a different tunable lens model (30TC#1 in black, representing a tunable lens with strong and asymmetric dynamic artifacts; 30TC#2 in blue, with a moderate dynamic behavior) and (f) large aperture lens (40TC#1; slow average speed).
Fig. 5
Fig. 5 Transient response of tunable lens 30C#4 for a cycle of 40 ms and different steps heights (1 to 3 D in 0.5 D steps). (a) Absolute response: measured optical power as a function of time. (b) Normalized transient response to justify the linearity of the response with varying optical power. (c) Impulse response.
Fig. 6
Fig. 6 a) Transient response of tunable lens 30C#3 at different excitation frequencies for a square wave of 3 D of amplitude. b) The corresponding histograms showing the distribution of focal positions of the temporal response.
Fig. 7
Fig. 7 a) Modified square input wave with a transient correction step (2 ms, 0.2 D), to generate an improved square step response. b) The corresponding measured temporal response (tunable lens 30C#4) showed a reduced overshoot (orange curve) in comparison with the measured step response to a square input wave (black curve).
Fig. 8
Fig. 8 Compensation of transient response. (a) Nominal response of the tunable lens (blue); predicted (gray) and measured (black) transient response of tunable lens 30C#4. (b) Compensated input wave (orange) that minimizes the effect of the transient response, providing a predicted temporal response with compensation (yellow) close to the nominal (intended) response (blue). (c) Measured temporal response with compensation of transient response, 3 superimposed repetitions. (d) Histograms of focus positions measured with (red) and without (gray) compensation of transient response.
Fig. 9
Fig. 9 High speed focimetry measurements of other active optical elements. (a) Deformable mirror with monochromatic light (555 nm), and (b) spatial light modulator (555 nm).

Tables (1)

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Table 1 Tunable lenses used.

Equations (4)

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s( t )=u( t )*h( t ).
θ=arcsin [nsin(α)]α,
θ=α[ n1 ].
d=r·α[ n1 ].

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