Abstract

We present a modified configuration of a tunable Alvarez lens with a refocusing frequency of 1 kHz or more. In contrast to the classic Alvarez lens, the approach does not utilize a translational motion of two sub-lenses with respect to each other, but uses a 4f-setup to image two diffractive sub-lenses onto each other. Hereby focus tuning is achieved by rotating a galvo-mirror which affects the overlap of the two sub-lenses which together form an effective lens of refractive power which depends on the rotation angle of the galvo-mirror. We have demonstrated tuning of the optical power in a system where the diffractive Alvarez lens is realized by an LCOS-SLM. We consider our Alvarez setup especially suitable for applications where high refocusing rates are important, as for example in 3D life cell monitoring or tracking.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive Moiré-lenses,” Opt. Express 21, 6955–6966 (2013).
    [Crossref] [PubMed]
  5. S. Bernet and M. Ritsch-Marte, “Multi-color operation of tunable diffractive lenses,” Opt. Express 25, 2469–2480 (2017).
    [Crossref]
  6. B. Qi, P.A. Himmer, M.L. Gordon, V.X.D. Yang, D.L. Dickensheets, and I.A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a microelectromechanical mirror,” Opt. Commun. 232, 123–128 (2004).
    [Crossref]
  7. W.J. Shain, N.A. Vickers, B.B. Goldberg, T. Bifano, and J. Mertz, “Extended depth-of-field microscopy with a high-speed deformable mirror,” Opt. Lett. 42, 995–998 (2017).
    [Crossref] [PubMed]
  8. A. Kaplan, N. Friedman, and N. Davidson, “Acousto-optic lens with very fast focus scanning,” Opt. Lett. 26, 1078–1080 (2001).
    [Crossref]
  9. A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. 33, 2146–2148 (2008).
    [Crossref] [PubMed]
  10. L.W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent 3,305,294 (3. December1964)
  11. W. E. Humphrey, “Remote subjective refractor employing continuously variable sphere-cylinder corrections,” Opt. Eng. 25, 286–291 (1976).
  12. W. E. Humphrey, “Apparatus for opthalmological prescription readout,” US Patent 3,927,933 (1974).
  13. S. S. Rege, T. S. Tkaczyk, and M. R. Descour, “Application of the Alvarez-Humphrey concept to the design of a miniaturized scanning microscope,” Opt. Express 12, 2574–2588 (2004).
    [Crossref] [PubMed]
  14. G. L. Van Der Heijde, “Artificial intraocular lens e.g. Alvarez-type lens for implantation in eye, comprises two lens elements with optical thickness such that power of the lens changes by transversal displacement of one lens element relative to the other element,” Int Patent 2006/025726 (2006).
  15. A. N. Simonov, G. Vdovin, and M. C. Rombach, “Cubic optical elements for an accommodative intraocular lens,” Opt. Express 14, 7757–7775 (2006).
    [Crossref] [PubMed]
  16. H. Mukaiyama, K. Kato, and A. Komatsu, “Variable focus visual power correction device - has optical lenses superposed so that main meridians are coincident with one another,” Int Patent 93/15432 (1994).
  17. B. Spivey, “Lens for spectacles, has thickness designed so that by adjusting relative positions of two lenses in direction perpendicular to viewing direction, combined focus of two lenses is changed,” US Patent 151184 (2008).
  18. S. Roth, C. J.R. Sheppard, K. Wicker, and R. Heintzmann, “Optical photon reassignment microscopy (OPRA),” Opt. Nanoscopy 2, 5 (2013).
    [Crossref]

2017 (2)

2013 (2)

S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive Moiré-lenses,” Opt. Express 21, 6955–6966 (2013).
[Crossref] [PubMed]

S. Roth, C. J.R. Sheppard, K. Wicker, and R. Heintzmann, “Optical photon reassignment microscopy (OPRA),” Opt. Nanoscopy 2, 5 (2013).
[Crossref]

2008 (2)

2006 (2)

2004 (2)

S. S. Rege, T. S. Tkaczyk, and M. R. Descour, “Application of the Alvarez-Humphrey concept to the design of a miniaturized scanning microscope,” Opt. Express 12, 2574–2588 (2004).
[Crossref] [PubMed]

B. Qi, P.A. Himmer, M.L. Gordon, V.X.D. Yang, D.L. Dickensheets, and I.A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a microelectromechanical mirror,” Opt. Commun. 232, 123–128 (2004).
[Crossref]

2001 (1)

1976 (1)

W. E. Humphrey, “Remote subjective refractor employing continuously variable sphere-cylinder corrections,” Opt. Eng. 25, 286–291 (1976).

Alvarez, L.W.

L.W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent 3,305,294 (3. December1964)

Anderson, P.A.

Arnold, C. B.

Berge, B.

B. Berge, “Liquid lens technology: Principle of electrowetting based lenses and applications to imaging,” in 18th IEEE International Conference on Micro Electro Mechanical Systems 2005 (IEEE, 2005), pp. 227–230.

Bernet, S.

Bifano, T.

Davidson, N.

Descour, M. R.

Dickensheets, D.L.

B. Qi, P.A. Himmer, M.L. Gordon, V.X.D. Yang, D.L. Dickensheets, and I.A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a microelectromechanical mirror,” Opt. Commun. 232, 123–128 (2004).
[Crossref]

Fox, D.

Friedman, N.

Goldberg, B.B.

Gordon, M.L.

B. Qi, P.A. Himmer, M.L. Gordon, V.X.D. Yang, D.L. Dickensheets, and I.A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a microelectromechanical mirror,” Opt. Commun. 232, 123–128 (2004).
[Crossref]

Harm, W.

Heintzmann, R.

S. Roth, C. J.R. Sheppard, K. Wicker, and R. Heintzmann, “Optical photon reassignment microscopy (OPRA),” Opt. Nanoscopy 2, 5 (2013).
[Crossref]

Himmer, P.A.

B. Qi, P.A. Himmer, M.L. Gordon, V.X.D. Yang, D.L. Dickensheets, and I.A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a microelectromechanical mirror,” Opt. Commun. 232, 123–128 (2004).
[Crossref]

Humphrey, W. E.

W. E. Humphrey, “Remote subjective refractor employing continuously variable sphere-cylinder corrections,” Opt. Eng. 25, 286–291 (1976).

W. E. Humphrey, “Apparatus for opthalmological prescription readout,” US Patent 3,927,933 (1974).

Kaplan, A.

Kato, K.

H. Mukaiyama, K. Kato, and A. Komatsu, “Variable focus visual power correction device - has optical lenses superposed so that main meridians are coincident with one another,” Int Patent 93/15432 (1994).

Komatsu, A.

H. Mukaiyama, K. Kato, and A. Komatsu, “Variable focus visual power correction device - has optical lenses superposed so that main meridians are coincident with one another,” Int Patent 93/15432 (1994).

McLeod, E.

Mermillod-Blondin, A.

Mertz, J.

Mukaiyama, H.

H. Mukaiyama, K. Kato, and A. Komatsu, “Variable focus visual power correction device - has optical lenses superposed so that main meridians are coincident with one another,” Int Patent 93/15432 (1994).

Qi, B.

B. Qi, P.A. Himmer, M.L. Gordon, V.X.D. Yang, D.L. Dickensheets, and I.A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a microelectromechanical mirror,” Opt. Commun. 232, 123–128 (2004).
[Crossref]

Rege, S. S.

Ren, H.

Ritsch-Marte, M.

Rombach, M. C.

Roth, S.

S. Roth, C. J.R. Sheppard, K. Wicker, and R. Heintzmann, “Optical photon reassignment microscopy (OPRA),” Opt. Nanoscopy 2, 5 (2013).
[Crossref]

Shain, W.J.

Sheppard, C. J.R.

S. Roth, C. J.R. Sheppard, K. Wicker, and R. Heintzmann, “Optical photon reassignment microscopy (OPRA),” Opt. Nanoscopy 2, 5 (2013).
[Crossref]

Simonov, A. N.

Spivey, B.

B. Spivey, “Lens for spectacles, has thickness designed so that by adjusting relative positions of two lenses in direction perpendicular to viewing direction, combined focus of two lenses is changed,” US Patent 151184 (2008).

Tkaczyk, T. S.

Van Der Heijde, G. L.

G. L. Van Der Heijde, “Artificial intraocular lens e.g. Alvarez-type lens for implantation in eye, comprises two lens elements with optical thickness such that power of the lens changes by transversal displacement of one lens element relative to the other element,” Int Patent 2006/025726 (2006).

Vdovin, G.

Vickers, N.A.

Vitkin, I.A.

B. Qi, P.A. Himmer, M.L. Gordon, V.X.D. Yang, D.L. Dickensheets, and I.A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a microelectromechanical mirror,” Opt. Commun. 232, 123–128 (2004).
[Crossref]

Wicker, K.

S. Roth, C. J.R. Sheppard, K. Wicker, and R. Heintzmann, “Optical photon reassignment microscopy (OPRA),” Opt. Nanoscopy 2, 5 (2013).
[Crossref]

Wu, B.

Wu, S.-T.

Yang, V.X.D.

B. Qi, P.A. Himmer, M.L. Gordon, V.X.D. Yang, D.L. Dickensheets, and I.A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a microelectromechanical mirror,” Opt. Commun. 232, 123–128 (2004).
[Crossref]

Appl. Opt. (1)

Opt. Commun. (1)

B. Qi, P.A. Himmer, M.L. Gordon, V.X.D. Yang, D.L. Dickensheets, and I.A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a microelectromechanical mirror,” Opt. Commun. 232, 123–128 (2004).
[Crossref]

Opt. Eng. (1)

W. E. Humphrey, “Remote subjective refractor employing continuously variable sphere-cylinder corrections,” Opt. Eng. 25, 286–291 (1976).

Opt. Express (5)

Opt. Lett. (3)

Opt. Nanoscopy (1)

S. Roth, C. J.R. Sheppard, K. Wicker, and R. Heintzmann, “Optical photon reassignment microscopy (OPRA),” Opt. Nanoscopy 2, 5 (2013).
[Crossref]

Other (6)

H. Mukaiyama, K. Kato, and A. Komatsu, “Variable focus visual power correction device - has optical lenses superposed so that main meridians are coincident with one another,” Int Patent 93/15432 (1994).

B. Spivey, “Lens for spectacles, has thickness designed so that by adjusting relative positions of two lenses in direction perpendicular to viewing direction, combined focus of two lenses is changed,” US Patent 151184 (2008).

G. L. Van Der Heijde, “Artificial intraocular lens e.g. Alvarez-type lens for implantation in eye, comprises two lens elements with optical thickness such that power of the lens changes by transversal displacement of one lens element relative to the other element,” Int Patent 2006/025726 (2006).

W. E. Humphrey, “Apparatus for opthalmological prescription readout,” US Patent 3,927,933 (1974).

L.W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent 3,305,294 (3. December1964)

B. Berge, “Liquid lens technology: Principle of electrowetting based lenses and applications to imaging,” in 18th IEEE International Conference on Micro Electro Mechanical Systems 2005 (IEEE, 2005), pp. 227–230.

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Figures (5)

Fig. 1
Fig. 1 Working principle of the Alvarez lens: (a) A modulation of the optical power is attained when conjugate phase plates are shifted with respect to each other in the direction where their phase profile is anti-symmetric. Depending on the displacement of the sub-elements from their zero position, a lens with positive- or negative optical power is generated. (b) Refractive Alvarez sub-element with a profile function proportional to x 3 3 + x y 2 and the corresponding diffractive Alvarez sub-lens, the phase pattern of which is generated by taking the refractive phase structure modulo 2π, are shown.
Fig. 2
Fig. 2 Outline of modified Alvarez lens configurations requiring no translation motion: (a) Alvarez lens in which the sub-elements are imaged onto each other via a 4f-configuration: The black dashed lines illustrate how points on one sub-element are mapped to the other. Note that the axis inversion caused by the 4f system requires the second sub-element to be inverted as well. It can be seen that the center of the quadratic phase profile appears shifted from the optical axis by an amount which depends on the deflection angle. (b) Folded concept of an Alvarez lens: Here, only a single Alvarez sub-element is required, since the the element is imaged back onto itself.
Fig. 3
Fig. 3 Schematic setup for the modified Alvarez lens configuration with “walk-off correction”: The beam path of the setup is shown, with the galvo mirror precisely reflecting the incoming beam back into its incidence direction. In this situation the optical power of the Alvarez lens is zero. The situation changes when the galvo mirror is slightly rotated. (The dashed black lines illustrate that the SLM and the pupil are in conjugate planes. The dimensions and angles of the individual components in this drawing do not correspond to the real experimental situation; the beam angle of incidence onto the SLM, in particular, is only about 15 degree and thus smaller as shown in the Figure).
Fig. 4
Fig. 4 Superposition of the diffractive structures of the Alvarez elements to illustrate the choice of the appropriate pupil size.
Fig. 5
Fig. 5 Experimental results: (a, c and e) show axial projections of the laser beam intensity (arbitrary units) behind the lens Ls for various optical power states of the Alvarez lens (DAlvarez=0.49/0/−0.49 diopters). The design parameter A for this SLM-realized lens is chosen to be half of the maximum value, i.e. 7.85 · 108 m−3. The images were recorded by moving the camera along the optical axis (z) in a range of ±900 μm around the focal spot. Subfigures (b, d and f) show the corresponding lateral beam profiles in the respective focal plane. Subfigure (g) indicates the focal intensity distribution for an Alvarez lens without optical power (corresponds to Subfigure (d)).

Tables (1)

Tables Icon

Table 1 Comparison between experimental and theoretical determined focal lengths of the resulting lens superimposed on Alvarez lens and Ls.

Equations (15)

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ϕ i = ± A ( x 3 3 + x y 2 ) .
ϕ Alvarez = ϕ 1 + ϕ 2 = A ( ( x x 0 ) 3 3 + ( x x 0 ) y 2 ) A ( ( x + x 0 ) 3 3 + ( x + x 0 ) y 2 ) ,
ϕ Alvarez = 2 A x 0 r 2 ϕ 0
ϕ Alvarez = 2 A x 0 r 2 = ! π r 2 λ f = ϕ Parab
D Alvarez = 2 A λ π x 0 , for | x 0 | < L / 2 .
S = λ 0 2 π ( n 0 1 ) mod ( ϕ , 2 π ) ,
d ϕ d x < π p and d ϕ d y < π p .
A ( x 2 + y 2 ) < π p and A 2 π x y < π p .
A max = π p r max 2 ,
D Alvarez = 2 λ p r max 2 x 0 , | x 0 | < L / 2 = 2 λ p r max 2 f A tan ( 2 α ) , | α | < 1 2 tan 1 ( L 2 f A ) .
D Alvarez = 2 r max 2 x 0 , | x 0 | < L / 2 .
DOE : D max = ± 56.7 dpts SLM : D max = ± 1.4 dpts .
Δ D 0 = 1 M 2 Δ D = ( P P 0 ) 2 Δ D .
f res = 1 D Alvarez + 40 dpts .
d exp ( FWHM ) 2 μ m > d theory = 0.61 λ N A = 1.6 μ m .

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