Abstract

We describe a simple method of refocusing optical systems that is based on the use of two identical phase filters. These filters are divided in annuli and each annulus is divided into sectors with a particular phase value. A controlled focus displacement is achieved by rotating one filter with respect to the other. This displacement is related with the filter parameters. Transverse responses are studied as a function of filters relative position. Furthermore, the experimental set up shows that theoretical prediction fit well with experimental results. The main advantage of this system is the ease of fabrication so that it could be useful in different applications requiring small size, light weight or thin systems, like mobile phone cameras, microscopy tomography, and others.

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References

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    [CrossRef]
  13. ITME Institute of Electronic Materials Technology, Warsaw, Poland.

2008

N. A. Riza, “Axial scanning confocal microscopy with no moving parts,” Opt. Photon. News 19(12), 33 (2008).
[CrossRef]

E. J. Botcherby, R. Juskaitis, M. J. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281(4), 880–887 (2008).
[CrossRef]

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

H. Ren, S. Xu, Y. J. Lin, and S. T. Wu, “Adaptive-focus lenses,” Opt. Photon. News 19(10), 42–47 (2008).
[CrossRef]

S. Bernet and M. Ritsch-Marte, “Adjustable refractive power from diffractive moiré elements,” Appl. Opt. 47(21), 3722–3730 (2008).
[CrossRef] [PubMed]

2006

D. Graham-Rowe, “Liquid lenses make a splash,” Nat. Photonics sample, 2–4 (2006).
[CrossRef]

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]

2004

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

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun. 241(4-6), 249–253 (2004).
[CrossRef]

1991

1967

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]

Bara, S.

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]

Bernet, S.

Booth, M. J.

E. J. Botcherby, R. Juskaitis, M. J. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281(4), 880–887 (2008).
[CrossRef]

Botcherby, E. J.

E. J. Botcherby, R. Juskaitis, M. J. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281(4), 880–887 (2008).
[CrossRef]

Cagigal, M. P.

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun. 241(4-6), 249–253 (2004).
[CrossRef]

Canales, V. F.

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun. 241(4-6), 249–253 (2004).
[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]

Graham-Rowe, D.

D. Graham-Rowe, “Liquid lenses make a splash,” Nat. Photonics sample, 2–4 (2006).
[CrossRef]

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]

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]

Jaroszewicz, Z.

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]

Juskaitis, R.

E. J. Botcherby, R. Juskaitis, M. J. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281(4), 880–887 (2008).
[CrossRef]

Kolodziejczyk, A.

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]

Lin, Y. J.

H. Ren, S. Xu, Y. J. Lin, and S. T. Wu, “Adaptive-focus lenses,” Opt. Photon. News 19(10), 42–47 (2008).
[CrossRef]

Lohmann, A. W.

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]

Moreno, V.

Oti, J. E.

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun. 241(4-6), 249–253 (2004).
[CrossRef]

Paris, D. P.

Ren, H.

H. Ren, S. Xu, Y. J. Lin, and S. T. Wu, “Adaptive-focus lenses,” Opt. Photon. News 19(10), 42–47 (2008).
[CrossRef]

Ritsch-Marte, M.

Riza, N. A.

N. A. Riza, “Axial scanning confocal microscopy with no moving parts,” Opt. Photon. News 19(12), 33 (2008).
[CrossRef]

Valle, P. J.

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun. 241(4-6), 249–253 (2004).
[CrossRef]

Wilson, T.

E. J. Botcherby, R. Juskaitis, M. J. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281(4), 880–887 (2008).
[CrossRef]

Wu, S. T.

H. Ren, S. Xu, Y. J. Lin, and S. T. Wu, “Adaptive-focus lenses,” Opt. Photon. News 19(10), 42–47 (2008).
[CrossRef]

Xu, S.

H. Ren, S. Xu, Y. J. Lin, and S. T. Wu, “Adaptive-focus lenses,” Opt. Photon. News 19(10), 42–47 (2008).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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

Nat. Photonics

D. Graham-Rowe, “Liquid lenses make a splash,” Nat. Photonics sample, 2–4 (2006).
[CrossRef]

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

Nature

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]

Opt. Commun.

E. J. Botcherby, R. Juskaitis, M. J. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281(4), 880–887 (2008).
[CrossRef]

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun. 241(4-6), 249–253 (2004).
[CrossRef]

Opt. Photon. News

N. A. Riza, “Axial scanning confocal microscopy with no moving parts,” Opt. Photon. News 19(12), 33 (2008).
[CrossRef]

H. Ren, S. Xu, Y. J. Lin, and S. T. Wu, “Adaptive-focus lenses,” Opt. Photon. News 19(10), 42–47 (2008).
[CrossRef]

Other

L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent 3,305,294 (1967).

ITME Institute of Electronic Materials Technology, Warsaw, Poland.

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Figures (9)

Fig. 1
Fig. 1

Phase distribution for a single phase filter (a), for two filters superimposed (b) and for two filters superimposed but one rotated π/2 with respect to the other (c).

Fig. 2
Fig. 2

Phase distribution single phase filter (a), two filters superimposed (b), two filters superimposed, the first one rotated π/2 with respect to the second one, (c) and two filters superimposed, the first one rotated π with respect to the other (d). In all cases, the values are modulus 2π. Note that in such case 3π/2 = -π /2 and π = -π.

Fig. 3
Fig. 3

Optical system consisting on a lens (L) and two identical phase filters (F1 and F2). Analysis will be performed axially or transversally around the lens focal point P.

Fig. 4
Fig. 4

Phase annulus value as a function of the pupil radius for a four annuli filter (a) and a eight annuli filter (b).

Fig. 5
Fig. 5

Strehl ratio as a function of the displacement produced by rotating the filters in Fig. 2.

Fig. 6
Fig. 6

Picture of the transversal PSF (a) for the clear pupil, (b) for the pupil covered with two three annuli filters without rotation, (c) once one filter has been rotated π/2 with respect to the other and (d) once one filter has been rotated π with respect to the other.

Fig. 7
Fig. 7

Experimental setup: Laser beam (532 nm), pin hole (PH), collimating lens (CL), pupil (P), two filters F1 and F2, imaging lens IL (focal length: 20 cm), CCD camera and scanning device (SD).

Fig. 8
Fig. 8

Phase distribution of the couple of filters with no rotation (a), composed of four sectors (in red) of phase π over a zero phase background. Phase distribution for a rotation angle θ 0 = π/2, where the phase grows from zero to 2π with steps of π/2 (b).

Fig. 9
Fig. 9

Transversal light distribution at the focus for the configuration shown in Fig. 8, with no rotation (a) and for a rotation angle θ 0 = π/2 (b).

Equations (1)

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U ( v , ψ , u ) = 2 0 2 π d θ 0 1 d ρ P ( ρ , θ ) ρ exp ( j v ρ cos ( θ ψ ) )  exp ( j u ρ 2 / 2 ) ,

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