Abstract

In a recent publication [Appl. Opt. 57, 8087 (2018).] a zoom system based on rotating toroidal lenses had been theoretically suggested. Here we demonstrate two different experimental realizations of such a system. The first consists of a set of four individually rotatable cylindrical lenses, and the second of four rotatable diffractive optical elements with phase structures corresponding to "saddle-lenses". It turns out that image aberrations produced by the refractive zoom system are considerably reduced by the diffractive system.

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

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References

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  1. A. Mikš and J. Novák, “Analysis of two-element zoom systems based on variable power lenses,” Opt. Express 18(7), 6797–6810 (2010).
    [Crossref]
  2. N. Savidis, G. Peyman, N. Peyghambarian, and J. Schwiegerling, “Nonmechanical zoom system through pressure-controlled tunable fluidic lenses,” Appl. Opt. 52(12), 2858–2865 (2013).
    [Crossref]
  3. A. Mikš and J. Novák, “Paraxial analysis of zoom lens composed of three tunable-focus elements with fixed position of image-space focal point and object-image distance,” Opt. Express 22(22), 27056–27062 (2014).
    [Crossref]
  4. D. Liang and X. Y. Wang, “Zoom optical system using tunable polymer lens,” Opt. Commun. 371, 189–195 (2016).
    [Crossref]
  5. T. R. M. Sales, “Optical elements with saddle shaped structures for diffusing or shaping light,” US Pat. 20090153974 A1 (2007) https://www.google.com/patents/US20090153974 .
  6. S. Bernet, “Zoomable telescope by rotation of toroidal lenses,” Appl. Opt. 57(27), 8087–8095 (2018).
    [Crossref]
  7. B. Braunecker, O. Bryngdahl, and B. Schnell, “Optical system for image rotation and magnification,” J. Opt. Soc. Am. 70(2), 137–141 (1980).
    [Crossref]
  8. S. Bernet and M. Ritsch-Marte, “Optical device with a pair of diffractive optical elements,” US Pat. 8335034 B2 (2007) https://patents.google.com/patent/US8335034 .
  9. S. Bernet and M. Ritsch-Marte, “Adjustable refractive power from diffractive Moiré elements,” Appl. Opt. 47(21), 3722–3730 (2008).
    [Crossref]
  10. J. Ojeda-Castaneda, S. Ledesma, and C. M. Gómez-Sarabia, “Tunable apodizers and tunable focalizers using helical pairs,” Photon. Lett. Pol. 5(1), 20–22 (2013).
    [Crossref]
  11. S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive Moiré-lenses,” Opt. Express 21(6), 6955–6966 (2013).
    [Crossref]
  12. A. Grewe, P. Fesser, and S. Sinzinger, “Diffractive array optics tuned by rotation,” Appl. Opt. 56(1), A89–A96 (2017).
    [Crossref]
  13. F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6(1), 33543 (2016).
    [Crossref]
  14. I. Sieber, P. Stiller, and U. Gengenbach, “Design studies of varifocal rotation optics,” Opt. Eng. 57(12), 125102 (2018).
    [Crossref]
  15. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10(10), 2181–2186 (1993).
    [Crossref]
  16. D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. 34(14), 2462–2468 (1995).
    [Crossref]
  17. D. W. Sweeney and G. E. Sommargren, “Harmonic diffractive lenses,” Appl. Opt. 34(14), 2469–2475 (1995).
    [Crossref]
  18. W. Peng and M. Nabil, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6(1), 21545 (2016).
    [Crossref]
  19. J Yang, P. Twardowski, P. Gérard, W. Yu, and J. Fontaine, “Chromatic analysis of harmonic Fresnel lenses by FDTD and angular spectrum methods,” Appl. Opt. 57(19), 5281–5287 (2018).
    [Crossref]
  20. S. Bernet and M. Ritsch-Marte, “Multi-color operation of tunable diffractive lenses,” Opt. Express 25(3), 2469–2480 (2017).
    [Crossref]

2018 (3)

2017 (2)

2016 (3)

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6(1), 33543 (2016).
[Crossref]

W. Peng and M. Nabil, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6(1), 21545 (2016).
[Crossref]

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

2014 (1)

2013 (3)

2010 (1)

2008 (1)

1995 (2)

1993 (1)

1980 (1)

Bernet, S.

Braunecker, B.

Bryngdahl, O.

Faklis, D.

Fesser, P.

Fontaine, J.

Fu, Q.

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6(1), 33543 (2016).
[Crossref]

Gengenbach, U.

I. Sieber, P. Stiller, and U. Gengenbach, “Design studies of varifocal rotation optics,” Opt. Eng. 57(12), 125102 (2018).
[Crossref]

Gérard, P.

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(1), 20–22 (2013).
[Crossref]

Grewe, A.

Harm, W.

Heide, F.

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6(1), 33543 (2016).
[Crossref]

Heidrich, W.

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6(1), 33543 (2016).
[Crossref]

Ledesma, S.

J. Ojeda-Castaneda, S. Ledesma, and C. M. Gómez-Sarabia, “Tunable apodizers and tunable focalizers using helical pairs,” Photon. Lett. Pol. 5(1), 20–22 (2013).
[Crossref]

Liang, D.

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

Lohmann, A. W.

Mikš, A.

Morris, G. M.

Nabil, M.

W. Peng and M. Nabil, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6(1), 21545 (2016).
[Crossref]

Novák, J.

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(1), 20–22 (2013).
[Crossref]

Peng, W.

W. Peng and M. Nabil, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6(1), 21545 (2016).
[Crossref]

Peng, Y.

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6(1), 33543 (2016).
[Crossref]

Peyghambarian, N.

Peyman, G.

Ritsch-Marte, M.

Sales, T. R. M.

T. R. M. Sales, “Optical elements with saddle shaped structures for diffusing or shaping light,” US Pat. 20090153974 A1 (2007) https://www.google.com/patents/US20090153974 .

Savidis, N.

Schnell, B.

Schwiegerling, J.

Sieber, I.

I. Sieber, P. Stiller, and U. Gengenbach, “Design studies of varifocal rotation optics,” Opt. Eng. 57(12), 125102 (2018).
[Crossref]

Sinzinger, S.

Sommargren, G. E.

Stiller, P.

I. Sieber, P. Stiller, and U. Gengenbach, “Design studies of varifocal rotation optics,” Opt. Eng. 57(12), 125102 (2018).
[Crossref]

Sweeney, D. W.

Twardowski, P.

Wang, X. Y.

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

Yang, J

Yu, W.

Appl. Opt. (7)

J. Opt. Soc. Am. (1)

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

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)

I. Sieber, P. Stiller, and U. Gengenbach, “Design studies of varifocal rotation optics,” Opt. Eng. 57(12), 125102 (2018).
[Crossref]

Opt. Express (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(1), 20–22 (2013).
[Crossref]

Sci. Rep. (2)

F. Heide, Q. Fu, Y. Peng, and W. Heidrich, “Encoded diffractive optics for full-spectrum computational imaging,” Sci. Rep. 6(1), 33543 (2016).
[Crossref]

W. Peng and M. Nabil, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6(1), 21545 (2016).
[Crossref]

Other (2)

T. R. M. Sales, “Optical elements with saddle shaped structures for diffusing or shaping light,” US Pat. 20090153974 A1 (2007) https://www.google.com/patents/US20090153974 .

S. Bernet and M. Ritsch-Marte, “Optical device with a pair of diffractive optical elements,” US Pat. 8335034 B2 (2007) https://patents.google.com/patent/US8335034 .

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Figures (5)

Fig. 1.
Fig. 1. Basic setup of a zoom system based on rotating saddle lenses: S$_1$, S$_2$, S$_3$ and S$_4$ are saddle lenses, which can be independently rotated around the optical axis (z-axis, indicated in the figure). The two sets S$_1$ and S$_2$, and S$_3$ and S$_4$ are combined into two tunable combi-saddle lenses Q$_1$ and Q$_2$, respectively. L$_1$ and L$_2$ are rotationally symmetric (spherical) lenses. Depending on the optical powers of the spherical lenses $L_1$ and $L_2$, the setup can represent an afocal zoomable telescope (object and image plane at infinity, beam paths within the two orthogonal $xz-$ and $yz-$ planes are indicated in the figure as dashed and solid lines, respectively), or a zoomable imaging system with object- and/or image planes at finite distances.
Fig. 2.
Fig. 2. Zoom setup for an imaging system with object and image planes at finite distances $o$ and $i$ from the entrance and exit lenses of the zoom system, respectively. The optical powers of all elements are indicated in the figure. The setup corresponds to the afocal setup sketched in Fig. 1, but with two additional lenses $L_3$ and $L_4$ located at the entrance and exit apertures of the zoom system. For obtaining a sharp image, the optical powers of the lenses $L_3$, $L_1$, $L_2$, and $L_4$ have to be $o^{-1}$, $d^{-1}$, $d^{-1}$, and $i^{-1}$, respectively. For obtaining a zoom factor of $m$ the quadrupole optical powers of the combined saddle lenses $Q_1$ and $Q_2$ have to be adjusted to be $F_{Q1}=d^{-1}/m$ and $F_{Q2}=d^{-1} m$, respectively. Note that in a thin lens approximation the ordering of all sub-lenses within the two main lens groups ($L_3$, $S_1$, $S_2$, $L_1$) and ($L_2$, $S_3$, $S_4$, $L_4$) may be arbitrarily exchanged, and their corresponding transmission functions may be distributed between the individual elements in various ways.
Fig. 3.
Fig. 3. Zoom system based on four identical cylindrical lenses $C_1-C_4$ (each with a focal length of 50 mm). The lenses are mounted in four electronic rotation stages and can be independently rotated under computer control. Upper part: Picture of the setup. The object consists of a transmissive USAF resolution target. Images are recorded with a Canon EOS 5D Mark II camera with removed objective. Middle part: Scheme of the setup, indicating the object distance $o=86$ mm, the image distance $i=$86 mm, and the distance between the two lens groups $d=120$ mm. Lower part: Pictures (a)-(f) show images of the resolution target recorded at constant object and image distances. The respective magnification factors of $m=$ 0.4, 0.8, 1.2, 1.6, 2.0 and 2.4 have been adjusted by computer controlled rotation of the four cylindrical lenses.
Fig. 4.
Fig. 4. Left: Image of one of four produced diffractive saddle lens lenses. The lenses are etched into quadratic fused silica plates (thickness 0.66 mm, edge length 10 mm) as first order diffractive elements with 16 phase levels resolution within a phase range of 2$\pi$. The diameter of the round structured surface is 8 mm. The quadrupole optical power of the saddle lens is $\pm 33$ Dpt at the design wavelength of 532 nm. Right: Exemplary sketch of the phase structure of the blazed diffractive saddle lens (not to scale). Gray levels correspond to the phase of the transmission function in a range between 0 and $2 \pi$.
Fig. 5.
Fig. 5. Upper part: Sketch of the experimental setup (not to scale). Object distance $o$, distance between the main lens groups $d$ and image distance $i$ are 190 mm, 36 mm and 190 mm, respectively. The optical power of the two spherical lenses $L_1$ and $L_2$ is 33 Dpt. The quadrupole optical powers of all four diffractive saddle lenses $S_1-S_4$ is $\pm 33$ Dpt. The beam paths in the two orthogonal $xz-$ and $yz-$ planes are indicated.

Equations (15)

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H t ( x , y ) = F x x 2 + F y y 2 2 ( n 1 ) ,
T t = exp [ i π λ ( F x x 2 + F y y 2 ) ] .
T t = exp [ i π λ F x + F y 2 ( x 2 + y 2 ) ] exp [ i π λ F x F y 2 ( x 2 y 2 ) ] =: T l T q .
T l = exp [ i π λ F l r 2 ] a n d T q = exp [ i π λ F q r 2 cos ( 2 φ ) ] .
T T = T t 1 T t 2 = exp [ i π λ ( F l 1 + F l 2 ) r 2 ] exp [ i π λ F q { cos ( 2 φ + θ ) + cos ( 2 φ θ ) } r 2 ] .
T T = exp [ i π λ ( F l 1 + F l 2 ) r 2 ] exp [ i π λ 2 F q cos ( θ ) r 2 cos ( 2 φ ) ] .
F Q = 2 F q cos ( θ ) .
F l 1 = F l 2 = d 1 ,
F Q 1 = 2 F q 1 cos θ 1 = d 1 / m a n d F Q 2 = 2 F q 2 cos θ 2 = m d 1
m m a x = 2 F q 2 d 1 .
m m i n = d 1 2 F q 1 .
Z = m m a x m m i n = ( 2 F q d 1 ) 2 .
T c = exp [ π λ F c x 2 ] .
T c = exp [ π λ F c 2 ( x 2 + y 2 ) ] exp [ π λ F c 2 ( x 2 y 2 ) ] .
H = λ 2 π ( n 1 ) { [ π F q λ r 2 cos ( 2 ϕ ) ] mod 2 π } ,

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