Abstract

Rotationally tunable diffractive optical elements (DOEs) consist of two stacked diffractive optical elements which are rotated with respect to each other around their central optical axis. The combined diffractive element acts as a highly efficient diffractive lens, which changes its optical power as a function of the mutual rotation angle. Here we show that the principle can be extended to produce polychromatic tunable lenses, i.e. lenses which have the same optical power, and the same diffraction efficiency within the full tuning range at three or more selectable wavelengths. The basic principle is to use higher order DOEs, which will be polychromatic at harmonics of a fundamental wavelength. The method can be applied to other types of optical elements which are tunable by rotation, like axicons, or generalized lenses with arbitrary radial phase profiles, or to elements tunable by a mutual translation, like diffractive Alvarez lenses.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Demonstration of focus-tunable diffractive Moiré-lenses

Stefan Bernet, Walter Harm, and Monika Ritsch-Marte
Opt. Express 21(6) 6955-6966 (2013)

Adjustable refractive power from diffractive moiré elements

Stefan Bernet and Monika Ritsch-Marte
Appl. Opt. 47(21) 3722-3730 (2008)

Diffractive array optics tuned by rotation

Adrian Grewe, Patrick Fesser, and Stefan Sinzinger
Appl. Opt. 56(1) A89-A96 (2017)

References

  • View by:
  • |
  • |
  • |

  1. L. Guoqiang, “Adaptive Lens,” Prog. in Opt. 55, 199–283 (2010).
    [Crossref]
  2. H. Ren, D. Fox, P. A. Anderson, B. Wu, and S.-T. Wu, “Tunable-focus liquid lens controlled using a servo motor,” Opt. Express 14, 8031 (2006).
    [Crossref] [PubMed]
  3. G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett 34, 2793–2795 (2009).
    [Crossref] [PubMed]
  4. B. Berge, “Liquid lens technology: Principle of electrowetting based lenses and applications to imaging,” Proc. IEEE MEMS, 227–230 (2004).
  5. S. Xu, Y.-J. Lin, and S.-T. Wu, “Dielectric liquid microlens with well-shaped electrode,” Opt. Express 17, 10499 (2009).
    [Crossref] [PubMed]
  6. 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]
  7. M. Duocastella, G. Vicidomini, and A. Diaspro, “Simultaneous multiplane confocal microscopy using acoustic tunable lenses,” Opt. Express 22, 19293–19301 (2014).
    [Crossref] [PubMed]
  8. T. Nose and S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5, 1425–1433 (1989).
    [Crossref]
  9. H. Ren, D. Fox, B. Wu, and S. T. Wu, “Liquid crystal lens with large focal length tunability and low operating voltage,” Opt. Express 15, 11328–11335 (2007).
    [Crossref] [PubMed]
  10. P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Tunable-focus flat liquid-crystal diffractive lens,” Opt. Lett. 35, 336–338 (2010).
    [Crossref] [PubMed]
  11. A. W. Lohmann, “A new class of varifocal lenses,” Appl. Opt. 9, 1669–1671 (1970).
    [Crossref] [PubMed]
  12. L. W. Alvarez, “Two-element variable-power spherical lens” U.S. patent 3,305,294 (3December1964).
  13. S. Barbero, “The Alvarez and Lohmann refractive lenses revisited,” Opt. Express 17, 9376–9390 (2009).
    [Crossref] [PubMed]
  14. S. Barbero and J. Rubinstein, “Adjustable-focus lenses based on the Alvarez principle,” J. Opt. 13, 125705 (2011).
    [Crossref]
  15. A. Kolodziejczyk and Z. Jaroszewicz, “Diffractive elements of variable optical power and high diffraction efficiency,” Appl. Opt. 32, 4317–4322 (1993).
    [Crossref] [PubMed]
  16. I. M. Barton, S. N. Dixit, L. J. Summers, C. A. Thompson, K. Avicola, and J. Wilhelmsen, “Diffractive Alvarez lens,” Opt. Lett. 25, 1–3 (2000).
    [Crossref]
  17. A. W. Lohmann and D. P. Paris, “Variable Fresnel Zone Pattern,” Appl. Opt. 6, 1567–1570 (1967).
    [Crossref] [PubMed]
  18. S. Bernet and M. Ritsch-Marte, “Adjustable refractive power from diffractive Moiré elements,” Appl. Opt. 47, 3722–3730 (2008).
    [Crossref] [PubMed]
  19. J. Ojeda-Castaneda, S. Ledesma, and C. M. Gómez-Sarabia, “Tunable apodizers and tunable focalizers using helical pairs,” Photon. Lett. Pol. 5, 20–22 (2013).
  20. S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive Moiré-lenses,” Opt. Express 21, 6955–6966 (2013).
    [Crossref] [PubMed]
  21. A. Grewe, P. Fesser, and S. Sinzinger, “Diffractive array optics tuned by rotation,” Appl. Opt. 56, A89–A96 (2016).
    [Crossref]
  22. F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6, 33543 (2016).
    [Crossref] [PubMed]
  23. D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. 34, 2462–2468 (1995).
    [Crossref] [PubMed]
  24. D. W. Sweeney and G. E. Sommargren, “Harmonic diffractive lenses,” Appl. Opt. 34, 2469–2475 (1995).
    [Crossref] [PubMed]
  25. B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).
  26. S. Sinzinger and M. Testorf, “Transition between diffractive and refractive micro-optical components,” Appl. Opt. 34, 5970–5976 (1995).
    [Crossref] [PubMed]
  27. W. Harm, S. Bernet, M. Ritsch-Marte, I. Harder, and N. Lindlein, “Adjustable diffractive spiral phase plates,” Opt. Express 23, 413–421 (2015).
    [Crossref] [PubMed]
  28. A. Grewe and S. Sinzinger, “Efficient quantization of tunable helix phase plates,” Opt. Lett. 41, 4755–4758 (2016).
    [Crossref] [PubMed]

2016 (3)

2015 (1)

2014 (1)

2013 (2)

J. Ojeda-Castaneda, S. Ledesma, and C. M. Gómez-Sarabia, “Tunable apodizers and tunable focalizers using helical pairs,” Photon. Lett. Pol. 5, 20–22 (2013).

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

2011 (1)

S. Barbero and J. Rubinstein, “Adjustable-focus lenses based on the Alvarez principle,” J. Opt. 13, 125705 (2011).
[Crossref]

2010 (2)

2009 (3)

2008 (2)

2007 (1)

2006 (1)

2000 (1)

1995 (3)

1993 (1)

1989 (1)

T. Nose and S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5, 1425–1433 (1989).
[Crossref]

1970 (1)

1967 (1)

Alvarez, L. W.

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

Anderson, P. A.

Arnold, C. B.

Avicola, K.

Barbero, S.

S. Barbero and J. Rubinstein, “Adjustable-focus lenses based on the Alvarez principle,” J. Opt. 13, 125705 (2011).
[Crossref]

S. Barbero, “The Alvarez and Lohmann refractive lenses revisited,” Opt. Express 17, 9376–9390 (2009).
[Crossref] [PubMed]

Barton, I. M.

Berge, B.

B. Berge, “Liquid lens technology: Principle of electrowetting based lenses and applications to imaging,” Proc. IEEE MEMS, 227–230 (2004).

Bernet, S.

Chau, F. S.

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett 34, 2793–2795 (2009).
[Crossref] [PubMed]

Diaspro, A.

Dixit, S. N.

Dodge, M. R.

Duocastella, M.

Faklis, D.

Fesser, P.

Fox, D.

Fu, Q.

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6, 33543 (2016).
[Crossref] [PubMed]

Gómez-Sarabia, C. M.

J. Ojeda-Castaneda, S. Ledesma, and C. M. Gómez-Sarabia, “Tunable apodizers and tunable focalizers using helical pairs,” Photon. Lett. Pol. 5, 20–22 (2013).

Grewe, A.

Guoqiang, L.

L. Guoqiang, “Adaptive Lens,” Prog. in Opt. 55, 199–283 (2010).
[Crossref]

Harder, I.

Harm, W.

Heide, F.

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6, 33543 (2016).
[Crossref] [PubMed]

Heidrich, W.

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6, 33543 (2016).
[Crossref] [PubMed]

Jaroszewicz, Z.

Kolodziejczyk, A.

Kress, B.

B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).

Kumar, A. S.

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett 34, 2793–2795 (2009).
[Crossref] [PubMed]

Ledesma, S.

J. Ojeda-Castaneda, S. Ledesma, and C. M. Gómez-Sarabia, “Tunable apodizers and tunable focalizers using helical pairs,” Photon. Lett. Pol. 5, 20–22 (2013).

Leung, H. M.

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett 34, 2793–2795 (2009).
[Crossref] [PubMed]

Lin, Y.-J.

Lindlein, N.

Lohmann, A. W.

Mathine, D. L.

McLeod, E.

Mermillod-Blondin, A.

Meyrueis, P.

B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).

Morris, G. M.

Nose, T.

T. Nose and S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5, 1425–1433 (1989).
[Crossref]

Ojeda-Castaneda, J.

J. Ojeda-Castaneda, S. Ledesma, and C. M. Gómez-Sarabia, “Tunable apodizers and tunable focalizers using helical pairs,” Photon. Lett. Pol. 5, 20–22 (2013).

Paris, D. P.

Peng, Y.

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6, 33543 (2016).
[Crossref] [PubMed]

Peyghambarian, N.

Peyman, G.

Ren, H.

Ritsch-Marte, M.

Rubinstein, J.

S. Barbero and J. Rubinstein, “Adjustable-focus lenses based on the Alvarez principle,” J. Opt. 13, 125705 (2011).
[Crossref]

Sato, S.

T. Nose and S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5, 1425–1433 (1989).
[Crossref]

Schwiegerling, J.

Sinzinger, S.

Sommargren, G. E.

Summers, L. J.

Sweeney, D. W.

Testorf, M.

Thompson, C. A.

Valley, P.

Vicidomini, G.

Wilhelmsen, J.

Wu, B.

Wu, S. T.

Wu, S.-T.

Xu, S.

Yu, H.

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett 34, 2793–2795 (2009).
[Crossref] [PubMed]

Zhou, G.

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett 34, 2793–2795 (2009).
[Crossref] [PubMed]

Appl. Opt. (8)

J. Opt. (1)

S. Barbero and J. Rubinstein, “Adjustable-focus lenses based on the Alvarez principle,” J. Opt. 13, 125705 (2011).
[Crossref]

Liq. Cryst. (1)

T. Nose and S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5, 1425–1433 (1989).
[Crossref]

Opt. Express (7)

Opt. Lett (1)

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett 34, 2793–2795 (2009).
[Crossref] [PubMed]

Opt. Lett. (4)

Photon. Lett. Pol. (1)

J. Ojeda-Castaneda, S. Ledesma, and C. M. Gómez-Sarabia, “Tunable apodizers and tunable focalizers using helical pairs,” Photon. Lett. Pol. 5, 20–22 (2013).

Prog. in Opt. (1)

L. Guoqiang, “Adaptive Lens,” Prog. in Opt. 55, 199–283 (2010).
[Crossref]

Sci. Rep. (1)

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6, 33543 (2016).
[Crossref] [PubMed]

Other (3)

B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).

B. Berge, “Liquid lens technology: Principle of electrowetting based lenses and applications to imaging,” Proc. IEEE MEMS, 227–230 (2004).

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Principle of MDOE lenses: (a): Two structured DOEs are placed on top of each other to form a MDOE lens. Rotation of one of the elements with respect to the other changes the optical power of the combined lens. (b) One of the two identical MDOE elements which are placed on top of each other (with one of them flipped upside down), with a phase function according to Eq. (1). Gray levels correspond to phase values between 0 and 2π. (c) One of the two quantized MDOE elements according to Eq. (7), which will form, after combination with a second, flipped element, a lens without sectors of different optical powers.

Fig. 2
Fig. 2

Diffraction efficiency of a first order sectorless (quantized) MDOE according to Eq. (7) as a function of wavelength, rotation angle, and optical power. The color code in the upper graphs refers to the diffraction efficiency. The simulation assumed a design wavelength of 532 nm, a pixel size of 1μm×1μm, a lens diameter of 1.28 mm, and a factor a = 2.6 × 108m−2. The left row shows the situation for a rotation angle of 15°. The upper graph shows the efficiency (corresponding color table at the right) as a function of readout wavelength, and optical power. Below, the efficiency is plotted again as a function of the wavelength, at the optical power level of 11.5 m−1, which is indicated above, and which corresponds to the nominal optical power expected according to Eq. (20) for the design wavelength. Middle: Corresponding graphs for a mutual rotation angle of 30° between the two elements. Right: Results for a mutual rotation angle of 60°.

Fig. 3
Fig. 3

Diffraction efficiency of a 5th order (at 532 nm) non-quantized MDOE lens as a function of wavelength, rotation angle, and optical power. Upper row: Efficiencies at three different rotation angles (left: 15°, middle: 30°, right: 60°) as a function of wavelength and optical powers. Bottom row: Efficiencies at the optical power levels indicated above as a function of the wavelength. Within the visible range there exist 3 wavelengths, namely 665 nm, 532 nm, and 443 nm, which are 4th order, 5th order and 6th order (indicated in the figure) harmonics of the fundamental wavelength 2660 nm, and which have the same optical power for all rotation angles.

Fig. 4
Fig. 4

Efficiency of a 10th order MDOE lens with a phase profile according to Eq. (15) as a function of wavelength, rotation angle, and optical power. The parameters are the same as those used for Fig. 3.

Fig. 5
Fig. 5

Diffraction efficiency of a 5th order quantized MDOE (without sector formation) according to Eq. (24) as a function of wavelength, rotation angle, and optical power. The parameters are the same as those used for Fig. 3. The lens is optimized for maximal efficiency (without sector formation) in the 5th diffraction order at a wavelength of 532 nm.

Equations (27)

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

T 1 = exp [ i a r 2 φ ] T 2 = exp [ i a r 2 φ ] ,
a < ( 2 p R ) 1 ,
T 2 ; rot = { exp [ i a r 2 ( φ θ ) ] for θ < φ < 2 π exp [ i a r 2 ( φ θ + 2 π ) ] for 0 φ θ .
T joint = { exp [ i a r 2 θ ] for θ φ < 2 π exp [ i a r 2 ( θ 2 π ) ] for 0 φ < θ .
T parab = exp [ i π r 2 λ f ] ,
f 1 1 = θ a λ / π for θ φ < 2 π and f 2 1 = ( θ 2 π ) a λ / π for 0 φ < θ ,
T quant , 1 , 2 = exp [ ± i round { a r 2 } φ ] ,
T quant , joint = { exp [ i round { a r 2 } θ ] for θ φ < 2 π exp [ i round { a r 2 } ( θ 2 π ) ] for 0 φ < θ .
N eff = 2 π θ .
η = { sin [ π ( m Φ max / 2 π ) ] sin [ π ( m Φ max / 2 π ) N eff ] sin [ π m N eff ] π m } 2 .
η m = ( sin ( m π / N eff ) m π / N eff ) 2 = ( sin ( m θ / 2 ) m θ / 2 ) 2 .
η m = { sin [ π ( m Φ max / 2 π ) ] π ( m Φ max / 2 π ) } 2 .
m = Φ max 2 π ,
m = round { Φ max 2 π } .
Φ 1 , 2 = k mod 2 π { ± a r 2 φ } ,
Φ joint = { k mod 2 π { a r 2 θ } for θ φ < 2 π k mod 2 π { a r 2 ( θ 2 π ) } for 0 φ < θ .
Φ joint = { k λ 0 ( n ( λ ) 1 ) λ ( n 0 1 ) mod 2 π { a r 2 θ } for θ φ < 2 π k λ 0 ( n ( λ 1 ) ) λ ( n 0 1 ) mod 2 π { a r 2 ( θ 2 π ) } for 0 φ < θ .
Φ max = 2 π k λ 0 ( n ( λ ) 1 ) λ ( n 0 1 ) .
m = round { Φ max 2 π } = round { k n ( λ ) 1 n 0 1 λ 0 λ } .
f 1 1 = m θ a λ m = round { k n ( λ ) 1 n 0 1 λ 0 λ } θ a λ π for θ φ < 2 π f 2 1 = m ( θ 2 π ) a λ π = round { k n ( λ ) 1 n 0 1 λ 0 λ } ( θ 2 π ) a λ π for 0 φ < θ .
f 1 1 = m θ a λ π = m θ a λ 0 k m π = k θ a λ 0 π for θ φ < 2 π f 2 1 = m ( θ 2 π ) a λ π = m ( θ 2 π ) a λ 0 k m π = k ( θ 2 π ) a λ 0 π for 0 φ < θ ,
round { k ( n ( λ ) 1 ) λ 0 ( n 0 1 ) λ } = round { k λ 0 λ } ,
| 2 Δ n n 0 1 | < 1 m ,
Φ 1 , 2 = k mod 2 π { round [ ± k a r 2 ] φ k } .
Φ joint = { k λ 0 λ mod 2 π { round [ k a r 2 ] θ k } for θ φ < 2 π k λ 0 λ mod 2 π { round [ k a r 2 ] ( θ 2 π ) k } for 0 φ < θ .
N eff = k 2 π θ .
η m = ( sin ( m θ / 2 k ) m θ / 2 k ) 2 .

Metrics