Abstract

A systematic design idea for liquid-filled cylindrical zoom lenses with ideal imaging quality over a wide focal length range is introduced in detail. The PWC method is used to calculate the initial structure parameters of the zoom lenses, and the optical design software ZEMAX is used to eliminate the spherical aberration at different focal lengths. Lenses named SLCL-Doublet are finally designed, which are formed by a symmetric liquid-core cylindrical lens (SLCL) filled with variable refractive index (RI) liquid and a doublet cylindrical lens capable of significantly weakening the spherical aberration. The focal length of the SLCL-Doublet continuously decreases from 101.406 mm to 54.162 mm as the liquid RI changes from 1.3300 to 1.5000. Calculated over 75% of the full aperture, the root mean square (RMS) spot radius of the SLCL-Doublet is always less than 7 µm over the whole focal length range, and the peak-to-valley wavefront error remains below the λ/4 limit when the focal length ranges from 62.373 mm to 65.814 mm, within which the lenses approach the diffraction limit, demonstrating improvement in the optical performance over that of previously designed liquid-core cylindrical lenses. The sources of potential fabrication and installation errors in the practical implementation of the SLCL-Doublet are also analyzed in detail. The SLCL-Doublet is demonstrated to be characterized by high imaging quality and easy installation, which enriches the types of core optical element for measuring the liquid RI and liquid diffusion coefficient and provides guarantee for improving the measurement accuracy.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

S. I. Bae, Y. Lee, Y. H. Seo, and K. H. Jeong, “Antireflective structures on highly flexible and large area elastomer membrane for tunable liquid-filled endoscopic lens,” Nanoscale 11(3), 856–861 (2019).
[Crossref]

2018 (2)

K. Dobek, “Motionless microscopy with tunable thermal lens,” Opt. Express 26(4), 3892–3902 (2018).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “Mems-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[Crossref]

2017 (3)

2016 (3)

L. C. Sun, C. Du, Q. Li, and X. Y. Pu, “Asymmetric liquid-core cylindrical lens used to measure liquid diffusion coefficient,” Appl. Opt. 55(8), 2011–2017 (2016).
[Crossref]

L. C. Sun and X. Y. Pu, “A novel visualization technique for measuring liquid diffusion coefficient based on asymmetric liquid-core cylindrical lens,” Sci. Rep. 6(1), 28264 (2016).
[Crossref]

D. Liang and X. Y. Wang, “Zoom optical system using tunable polymer lens,” Opt. Commun. 371, 189–195 (2016).
[Crossref]

2015 (3)

2014 (2)

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,” Opt. Lasers Eng. 50(12), 1677–1682 (2012).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

2007 (2)

D. Shaw and T. E. Sun, “Optical properties of variable-focus liquid-filled optical lenses with different membrane shapes,” Opt. Eng. 46(2), 024002 (2007).
[Crossref]

M. Ye, B. Wang, T. Takahashi, and S. Sato, “Properties of variable-focus liquid crystal lens and its application in focusing system,” Opt. Rev. 14(4), 173–175 (2007).
[Crossref]

2006 (1)

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

2004 (1)

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004).
[Crossref]

2003 (2)

N. Chronis, G. L. Liu, K. H. Jeong, and L. P. Lee, “Tunable liquid-filled microlens array integrated with microfluidic network,” Opt. Express 11(19), 2370–2378 (2003).
[Crossref]

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82(19), 3171–3172 (2003).
[Crossref]

2000 (1)

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

Agarwal, A. K.

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

Arbabi, A.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “Mems-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[Crossref]

Arbabi, E.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “Mems-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[Crossref]

Asatryan, K.

Bae, S. I.

S. I. Bae, Y. Lee, Y. H. Seo, and K. H. Jeong, “Antireflective structures on highly flexible and large area elastomer membrane for tunable liquid-filled endoscopic lens,” Nanoscale 11(3), 856–861 (2019).
[Crossref]

Barrera-Rivera, K. A.

Beebe, D. J.

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

Berdichevsky, Y.

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82(19), 3171–3172 (2003).
[Crossref]

Berge, B.

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

Brender, T.

Calixto, S.

Chau, F. S.

Chen, J. B.

Chen, M.

Chen, M. S.

Chen, P. J.

Cheri, M. S.

Choi, J.

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82(19), 3171–3172 (2003).
[Crossref]

Chronis, N.

Dobek, K.

Dong, L.

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

Du, C.

Evensen, M.

Faraji-Dana, M.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “Mems-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[Crossref]

Faraon, A.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “Mems-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[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,” Opt. Lasers Eng. 50(12), 1677–1682 (2012).
[Crossref]

Galstian, T.

Gwag, J. S.

Hendriks, B. H. W.

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004).
[Crossref]

Heo, K. C.

Horie, Y.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “Mems-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[Crossref]

Jeong, K. H.

S. I. Bae, Y. Lee, Y. H. Seo, and K. H. Jeong, “Antireflective structures on highly flexible and large area elastomer membrane for tunable liquid-filled endoscopic lens,” Nanoscale 11(3), 856–861 (2019).
[Crossref]

N. Chronis, G. L. Liu, K. H. Jeong, and L. P. Lee, “Tunable liquid-filled microlens array integrated with microfluidic network,” Opt. Express 11(19), 2370–2378 (2003).
[Crossref]

Jiang, H. R.

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

Kamali, S. M.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “Mems-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[Crossref]

Kopp, D.

Kuiper, S.

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004).
[Crossref]

Kwon, J. H.

Latifi, H.

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,” Opt. Lasers Eng. 50(12), 1677–1682 (2012).
[Crossref]

Lee, Y.

S. I. Bae, Y. Lee, Y. H. Seo, and K. H. Jeong, “Antireflective structures on highly flexible and large area elastomer membrane for tunable liquid-filled endoscopic lens,” Nanoscale 11(3), 856–861 (2019).
[Crossref]

Leung, H. M.

Li, Q.

Liang, D.

D. Liang and X. Y. Wang, “Zoom optical system using tunable polymer lens,” Opt. Commun. 371, 189–195 (2016).
[Crossref]

Lien, V.

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82(19), 3171–3172 (2003).
[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(12), 1677–1682 (2012).
[Crossref]

Lin, Y. H.

Liu, C. M.

Liu, G. L.

Lo, Y. H.

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82(19), 3171–3172 (2003).
[Crossref]

Meng, W. D.

Moghaddam, M. S.

Peng, R. L.

Peseux, J.

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

Presniakov, V.

Pu, X. Y.

Richa, A. M.

Rosete-Aguilar, M.

Sánchez-Marin, F. J.

Sánchez-Morales, M. E.

Sato, S.

M. Ye, B. Wang, T. Takahashi, and S. Sato, “Properties of variable-focus liquid crystal lens and its application in focusing system,” Opt. Rev. 14(4), 173–175 (2007).
[Crossref]

Seo, Y. H.

S. I. Bae, Y. Lee, Y. H. Seo, and K. H. Jeong, “Antireflective structures on highly flexible and large area elastomer membrane for tunable liquid-filled endoscopic lens,” Nanoscale 11(3), 856–861 (2019).
[Crossref]

Shahraki, H.

Shaw, D.

D. Shaw and T. E. Sun, “Optical properties of variable-focus liquid-filled optical lenses with different membrane shapes,” Opt. Eng. 46(2), 024002 (2007).
[Crossref]

Shen, C.

Song, F. X.

Sova, O.

Sun, L. C.

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(2), 024002 (2007).
[Crossref]

Takahashi, T.

M. Ye, B. Wang, T. Takahashi, and S. Sato, “Properties of variable-focus liquid crystal lens and its application in focusing system,” Opt. Rev. 14(4), 173–175 (2007).
[Crossref]

Wang, B.

M. Ye, B. Wang, T. Takahashi, and S. Sato, “Properties of variable-focus liquid crystal lens and its application in focusing system,” Opt. Rev. 14(4), 173–175 (2007).
[Crossref]

Wang, D.

Wang, Q. H.

Wang, X. Y.

D. Liang and X. Y. Wang, “Zoom optical system using tunable polymer lens,” Opt. Commun. 371, 189–195 (2016).
[Crossref]

Xia, Y.

Ye, M.

M. Ye, B. Wang, T. Takahashi, and S. Sato, “Properties of variable-focus liquid crystal lens and its application in focusing system,” Opt. Rev. 14(4), 173–175 (2007).
[Crossref]

Yu, H. B.

Zappe, H.

Zhang, D. Y.

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82(19), 3171–3172 (2003).
[Crossref]

Zhou, G. Y.

Zhou, X.

Zhuang, S. L.

Zohrabyan, A.

Appl. Opt. (5)

Appl. Phys. Lett. (2)

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004).
[Crossref]

D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phys. Lett. 82(19), 3171–3172 (2003).
[Crossref]

Eur. Phys. J. E: Soft Matter Biol. Phys. (1)

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

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Korea (1)

Nanoscale (1)

S. I. Bae, Y. Lee, Y. H. Seo, and K. H. Jeong, “Antireflective structures on highly flexible and large area elastomer membrane for tunable liquid-filled endoscopic lens,” Nanoscale 11(3), 856–861 (2019).
[Crossref]

Nat. Commun. (1)

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “Mems-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[Crossref]

Nature (1)

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

Opt. Commun. (1)

D. Liang and X. Y. Wang, “Zoom optical system using tunable polymer lens,” Opt. Commun. 371, 189–195 (2016).
[Crossref]

Opt. Eng. (1)

D. Shaw and T. E. Sun, “Optical properties of variable-focus liquid-filled optical lenses with different membrane shapes,” Opt. Eng. 46(2), 024002 (2007).
[Crossref]

Opt. Express (7)

Opt. Lasers Eng. (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,” Opt. Lasers Eng. 50(12), 1677–1682 (2012).
[Crossref]

Opt. Rev. (1)

M. Ye, B. Wang, T. Takahashi, and S. Sato, “Properties of variable-focus liquid crystal lens and its application in focusing system,” Opt. Rev. 14(4), 173–175 (2007).
[Crossref]

Sci. Rep. (1)

L. C. Sun and X. Y. Pu, “A novel visualization technique for measuring liquid diffusion coefficient based on asymmetric liquid-core cylindrical lens,” Sci. Rep. 6(1), 28264 (2016).
[Crossref]

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Figures (12)

Fig. 1.
Fig. 1. Flow chart of the design procedure.
Fig. 2.
Fig. 2. Top view of the SLCL.
Fig. 3.
Fig. 3. Top view of the SLCL-Doublet.
Fig. 4.
Fig. 4. Focal length curves of the SLCL-Doublet lenses with variable RI of the liquid filled in the lenses. The black curve indicates the focal length f of the SLCL-Doublet lenses, and the red curve indicates the back focal length fB.
Fig. 5.
Fig. 5. Simulation results of the designed SLCL-Doublet lenses based on ZEMAX when the width of the incident light (entrance pupil) is 19 mm. (a-d) are the ray tracing drawings, (a'-d’) are the focal spot diagrams, and (a''-d'’) are the ray aberration fan diagrams. (a, a’, a'’) n = 1.3300, f = 101.406 mm; (b, b’, b'’) n = 1.3800, f = 80.598 mm; (c, c’, c'’) n = 1.4300, f = 66.938 mm; (d, d’, d'’) n = 1.5000, f = 54.162 mm.
Fig. 6.
Fig. 6. GEO and RMS radii of the focal spot, and the peak-to-valley and RMS wavefront aberrations as a function of the SLCL-Doublet lens focal length. The λ/4 limit is denoted by the blue line.
Fig. 7.
Fig. 7. Changes in the RMS radius of the focal spot with the RI of the liquid filled in the lens for a series of liquid-core cylindrical lenses.
Fig. 8.
Fig. 8. MTF curves for a series of liquid-core cylindrical lenses filled with different kinds of liquid. (a) RI of the liquid is 1.3300. (b) RI of the liquid is 1.3800. (c) RI of the liquid is 1.4300. (d) RI the of liquid is 1.5000.
Fig. 9.
Fig. 9. Variation in RMS spot radius with focal length curves for SLCL-Doublet lenses with curvature radius errors. (a) Error of ±0.5% for each surface. (b) Different radius errors for the 5th surface and 7th surface.
Fig. 10.
Fig. 10. Variation in RMS spot radius with focal length curves for SLCL-Doublet lenses with 0.03 mm thickness errors.
Fig. 11.
Fig. 11. Variation in RMS spot radius with focal length curves for SLCL-Doublet lenses with decentering errors. (a) Error of 0.03 mm for each surface. (b) Different decentering errors for the 5th surface and 7th surface.
Fig. 12.
Fig. 12. Variation in RMS spot radius with focal length curves for SLCL-Doublet lenses with different tilt errors.

Tables (2)

Tables Icon

Table 1. Initial structure of the proposed optical design.

Tables Icon

Table 2. Calculated values of fB and f in relation to the RI of the liquid.

Equations (15)

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

S I  =  1 k h P , P = n i ( i i ) ( i u ) = ( Δ u Δ ( 1 / n ) ) 2 Δ u n = ( u u 1 / n 1 / n ) 2 ( u n u n ) .
C I = 1 k l u n i ( Δ n n Δ n n ) , Δ n = n F n C , Δ n = n F n C .
i = ( l R ) u / R , i = n i / n , u = u + i i , l = ( i R / u ) + R .
l i = l i 1 d i 1 , u i = u i 1 , n i = n i 1 .
S ID = h 4 { [ n K9 + 2 n K9 φ F + n F2 + 2 n F2 φ R ] ρ 6 2 + [ 2 n K9 + 1 n K9 1 φ F 2 4 n K9 + 4 n K9 φ F σ 6 2 n F2 + 1 n F2 1 φ R 2 4 n F2 + 4 n F2 φ R σ 6 ] ρ 6 3 n K9 + 1 n K9 1 φ F 2 σ 6 + 3 n K9 + 2 n K9 φ F σ 6 2 + n K9 2 ( n K9 1 ) 2 φ F 3 + 3 n F2 + 1 n F2 1 φ R 2 σ 6 + 3 n F2 + 2 n F2 φ R σ 6 2 + n F2 2 ( n F2 1 ) 2 φ R 3 } ,
C ID  =  1 2 h 2 φ v  =  h 2 ( φ F v K9  +  φ R v F2 ) .
f B  =  l 7 ,
n i l i n i l i = n i n i R i ( i = 1 , 2 , , 7 ) ,
l 1 = ,
l i + 1 = l i d i ( i = 1 , 2 , , 6 ) .
f = D / 2 u 7 ,
u i = l i u i l i ( i = 2 , 3 , , 7 ) ,
u i + 1 = u i ( i = 2 , 3 , , 6 ) ,
u 1 = u 1 + i 1 i 1 ,
u 1 = 0 , i 1 = D / 2 R 1 , i 1 = n 1 n 1 i 1 .

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