Abstract

A design method for correcting chromatic as well as spherical aberrations of variable-focus, multi-chamber liquid lenses is described. By combining suitable optical liquids with appropriate radii of the liquid’s interfaces, liquid lenses with superior, diffraction-limited resolution over a wide focal tuning range are possible. For an infinite object distance, the analytic thin-lens approximation of an achromatic positive/negative varifocal liquid lens is derived and the obtained results are compared with ray-traced optimized designs which consider finite thicknesses and rigid cover glasses. As a design example, the optical performance of a 4 mm-diameter positive/negative f/3.6 achromatic liquid lens is given in detail.

© 2007 Optical Society of America

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References

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  1. E. F. Flint, "Variable Focus Lens," US Patent 2,300,251 (1942).
  2. B. Berge and J. Peseux, "Variable focal lens controlled by an external voltage: an application of electrowetting," Eur. Phys. J. E 3, 159-163 (2000).
    [CrossRef]
  3. S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
    [CrossRef]
  4. F. Krogmann, W. M¨onch, and H. Zappe, "A MEMS-based variable micro-lens system," J. Opt. A: Pure and Applied Optics 8, 330-+ (2006).
    [CrossRef]
  5. 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, 3171-3172 (2003).
    [CrossRef]
  6. K.-H. Jeong, G. L. Liu, N. Chronis, and L. P. Lee, "Tunable microdoublet lens array," Opt. Express 12, 2494-+ (2004). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2494>.
    [CrossRef] [PubMed]
  7. A. Werber and H. Zappe, "Tunable microfluidic microlenses," Appl. Opt. 44, 3238-3245 (2005).
    [CrossRef] [PubMed]
  8. P. Moran, S. Dharmatilleke, A. Khaw, K. Tan, M. Chan, and I. Rodrigez, "Fluidic lenses with variable focal length," Appl. Phys. Lett. 88, 041,120 (2006).
    [CrossRef]
  9. L. Pang, U. Levy, K. Campbell, A. Groisman, and Y. Fainman, "Set of two orthogonal adaptive cylindrical lenses in a monolith elastomer device," Opt. Express 13, 9003-+ (2005).
    [CrossRef] [PubMed]
  10. S. Kuiper, B. Hendriks, J. Suijver, S. Deladi, and I. H. and, "Zoom camera based on liquid lenses," Proc. SPIE, 6466, 64,660F-1-64,660F-7 (2007).
  11. R. Kingslake, Lens Design Fundamentals (Academic Press, 1978).
  12. A. E. Conrady, Applied Optics and Optical Design, Part 1, New edition 1992 (Oxford University Press and Dover Publications, 1929).
  13. Cargille Laboratories, Specifications of Cargille Optical Liquids, URL www.cargille.com (personal communication, 2007).
  14. M. Herzberger and N. R. McClure, "The Design of Superachromatic Lenses," Appl. Opt. 2, 553-560 (1963).
    [CrossRef]

2006 (1)

P. Moran, S. Dharmatilleke, A. Khaw, K. Tan, M. Chan, and I. Rodrigez, "Fluidic lenses with variable focal length," Appl. Phys. Lett. 88, 041,120 (2006).
[CrossRef]

2005 (1)

2004 (1)

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

2003 (1)

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, 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 3, 159-163 (2000).
[CrossRef]

1963 (1)

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, 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 3, 159-163 (2000).
[CrossRef]

Campbell, K.

L. Pang, U. Levy, K. Campbell, A. Groisman, and Y. Fainman, "Set of two orthogonal adaptive cylindrical lenses in a monolith elastomer device," Opt. Express 13, 9003-+ (2005).
[CrossRef] [PubMed]

Chan, M.

P. Moran, S. Dharmatilleke, A. Khaw, K. Tan, M. Chan, and I. Rodrigez, "Fluidic lenses with variable focal length," Appl. Phys. Lett. 88, 041,120 (2006).
[CrossRef]

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, 3171-3172 (2003).
[CrossRef]

Deladi, S.

S. Kuiper, B. Hendriks, J. Suijver, S. Deladi, and I. H. and, "Zoom camera based on liquid lenses," Proc. SPIE, 6466, 64,660F-1-64,660F-7 (2007).

Dharmatilleke, S.

P. Moran, S. Dharmatilleke, A. Khaw, K. Tan, M. Chan, and I. Rodrigez, "Fluidic lenses with variable focal length," Appl. Phys. Lett. 88, 041,120 (2006).
[CrossRef]

Fainman, Y.

L. Pang, U. Levy, K. Campbell, A. Groisman, and Y. Fainman, "Set of two orthogonal adaptive cylindrical lenses in a monolith elastomer device," Opt. Express 13, 9003-+ (2005).
[CrossRef] [PubMed]

Groisman, A.

L. Pang, U. Levy, K. Campbell, A. Groisman, and Y. Fainman, "Set of two orthogonal adaptive cylindrical lenses in a monolith elastomer device," Opt. Express 13, 9003-+ (2005).
[CrossRef] [PubMed]

Hendriks, B.

S. Kuiper, B. Hendriks, J. Suijver, S. Deladi, and I. H. and, "Zoom camera based on liquid lenses," Proc. SPIE, 6466, 64,660F-1-64,660F-7 (2007).

Hendriks, B. H. W.

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

Herzberger, M.

Khaw, A.

P. Moran, S. Dharmatilleke, A. Khaw, K. Tan, M. Chan, and I. Rodrigez, "Fluidic lenses with variable focal length," Appl. Phys. Lett. 88, 041,120 (2006).
[CrossRef]

Krogmann, F.

F. Krogmann, W. M¨onch, and H. Zappe, "A MEMS-based variable micro-lens system," J. Opt. A: Pure and Applied Optics 8, 330-+ (2006).
[CrossRef]

Kuiper, S.

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

S. Kuiper, B. Hendriks, J. Suijver, S. Deladi, and I. H. and, "Zoom camera based on liquid lenses," Proc. SPIE, 6466, 64,660F-1-64,660F-7 (2007).

Levy, U.

L. Pang, U. Levy, K. Campbell, A. Groisman, and Y. Fainman, "Set of two orthogonal adaptive cylindrical lenses in a monolith elastomer device," Opt. Express 13, 9003-+ (2005).
[CrossRef] [PubMed]

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, 3171-3172 (2003).
[CrossRef]

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, 3171-3172 (2003).
[CrossRef]

McClure, N. R.

Moran, P.

P. Moran, S. Dharmatilleke, A. Khaw, K. Tan, M. Chan, and I. Rodrigez, "Fluidic lenses with variable focal length," Appl. Phys. Lett. 88, 041,120 (2006).
[CrossRef]

Pang, L.

L. Pang, U. Levy, K. Campbell, A. Groisman, and Y. Fainman, "Set of two orthogonal adaptive cylindrical lenses in a monolith elastomer device," Opt. Express 13, 9003-+ (2005).
[CrossRef] [PubMed]

Peseux, J.

B. Berge and J. Peseux, "Variable focal lens controlled by an external voltage: an application of electrowetting," Eur. Phys. J. E 3, 159-163 (2000).
[CrossRef]

Rodrigez, I.

P. Moran, S. Dharmatilleke, A. Khaw, K. Tan, M. Chan, and I. Rodrigez, "Fluidic lenses with variable focal length," Appl. Phys. Lett. 88, 041,120 (2006).
[CrossRef]

Suijver, J.

S. Kuiper, B. Hendriks, J. Suijver, S. Deladi, and I. H. and, "Zoom camera based on liquid lenses," Proc. SPIE, 6466, 64,660F-1-64,660F-7 (2007).

Tan, K.

P. Moran, S. Dharmatilleke, A. Khaw, K. Tan, M. Chan, and I. Rodrigez, "Fluidic lenses with variable focal length," Appl. Phys. Lett. 88, 041,120 (2006).
[CrossRef]

Werber, A.

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, 3171-3172 (2003).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

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, 3171-3172 (2003).
[CrossRef]

P. Moran, S. Dharmatilleke, A. Khaw, K. Tan, M. Chan, and I. Rodrigez, "Fluidic lenses with variable focal length," Appl. Phys. Lett. 88, 041,120 (2006).
[CrossRef]

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

Eur. Phys. J. E (1)

B. Berge and J. Peseux, "Variable focal lens controlled by an external voltage: an application of electrowetting," Eur. Phys. J. E 3, 159-163 (2000).
[CrossRef]

Other (8)

E. F. Flint, "Variable Focus Lens," US Patent 2,300,251 (1942).

F. Krogmann, W. M¨onch, and H. Zappe, "A MEMS-based variable micro-lens system," J. Opt. A: Pure and Applied Optics 8, 330-+ (2006).
[CrossRef]

L. Pang, U. Levy, K. Campbell, A. Groisman, and Y. Fainman, "Set of two orthogonal adaptive cylindrical lenses in a monolith elastomer device," Opt. Express 13, 9003-+ (2005).
[CrossRef] [PubMed]

S. Kuiper, B. Hendriks, J. Suijver, S. Deladi, and I. H. and, "Zoom camera based on liquid lenses," Proc. SPIE, 6466, 64,660F-1-64,660F-7 (2007).

R. Kingslake, Lens Design Fundamentals (Academic Press, 1978).

A. E. Conrady, Applied Optics and Optical Design, Part 1, New edition 1992 (Oxford University Press and Dover Publications, 1929).

Cargille Laboratories, Specifications of Cargille Optical Liquids, URL www.cargille.com (personal communication, 2007).

K.-H. Jeong, G. L. Liu, N. Chronis, and L. P. Lee, "Tunable microdoublet lens array," Opt. Express 12, 2494-+ (2004). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2494>.
[CrossRef] [PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

Cross sectional view of a six-chamber liquid lens in its initial state, i.e. with infinite focal length. Here, subchambers (b1, b2) and (c1, c2) are filled with same liquid each.

Fig. 2.
Fig. 2.

Primary longitudinal spherical aberration LAp vs. the bending parameter and the focal length for an example liquid achromatic lens with different liquid ordering. Dashed lines indicate the contour lines of zero spherical aberration.

Fig. 3.
Fig. 3.

Membrane radii calculated for a thin-lens predesign of an achromatic liquid lens compared with a raytrace-optimized thick-lens design (square markers) which also considers separating glass plates. Optical properties n 1,V 1n 1 and n 2,V 2n 2 and aperture parameters y,h are as specified in the text. (a) best crown-in-front solution and (b) best flint-in-front solution over focal tuning range.

Fig. 4.
Fig. 4.

Strehl ratio of the exemplary varifocal lens (optimized design).

Fig. 5.
Fig. 5.

Exemplary crown-in-front optimized solution for a positive (left column) and negative (right column) achromatic liquid lens with f/3.6 (from top to bottom: layout, longitudinal aberration, polychromatic MTF, and OPD).

Equations (23)

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V = n d 1 Δ n ,
φ = k = 1 l φ k .
k = 1 l φ k V k = k = 1 l ( c k Δ n k ) = 0 .
L A p = L A p ( s s ) 2 y 2 s ′2 k = 1 l ( G sum ) k ,
( G sum ) = G 1 c 3 G 2 c 2 c 1 + G 3 c 2 v 1 + G 4 c c 1 2 G 5 c c 1 v 1 + G 6 c v 1 2
G 1 = 1 2 n 2 ( n 1 ) G 2 = 1 2 ( 2 n + 1 ) ( n 1 ) G 3 = 1 2 ( 3 n + 1 ) ( n 1 )
G 4 = 1 2 n ( n + 2 ) ( n 1 ) G 5 = 2 n ( n 2 1 ) G 6 = 1 2 n ( 3 n + 2 ) ( n 1 ) .
L A p = y 2 f ′2 ( c 1 2 k = 1 l α k + c 1 k = 1 l β k + k = 1 l γ k ) .
φ = c a ( n a 1 ) + c b ( n b 1 ) + c c ( n c 1 ) + c d ( n d 1 )
= c 3 ( n b n a ) + c 5 ( n c n b ) + c 7 ( n d n c )
0 = c a Δ n a + c b Δ n b + c c Δ n c + c d Δ n d
= c 3 ( Δ n b Δ n a ) + c 5 ( Δ n c Δ n b ) + c 7 ( Δ n d Δ n c ) .
φ = c b ( n b 1 ) + c c ( n c 1 )
0 = c b Δ n b + c c Δ n c
c b = Δ n c Δ n c ( n b 1 ) Δ n b ( Δ n c 1 ) φ
c c = Δ n b Δ n c ( n b 1 ) Δ n b ( Δ n c 1 ) φ .
α b = G 4 c b
β b = G 2 c b 2
γ b = G 1 c b 3
α c = G 4 c c
β c = c b c c [ G 2 c c c b + 2 G 4 + G 5 ( n b 1 ) ]
γ c = c b c c [ G 1 c c 2 c b + G 2 c c + G 3 c c ( n b 1 ) + G 4 c b + G 5 c b ( n b 1 ) + G 6 c b ( n b 1 ) 2 ]
c 3 | 1,2 = β t 2 α t ± ( β t 2 4 α t 2 γ t α t ) 1 2 ,

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