Abstract

In an earlier publication [Appl. Opt. 47, 3722 (2008)] we suggested an adaptive optical lens, which consists of two cascaded diffractive optical elements (DOEs). Due to the Moiré-effect the combined optical element acts as a Fresnel zone lens with a refractive power that can be continuously adjusted by a mutual rotation of the two stacked DOEs. Here we present an experimental realization of this concept. Four designs of these Moiré-DOEs (MDOEs) were fabricated in thin (0.7 mm) glass slides by lithography and subsequent etching. Each element was realized as a 16 phase level DOE designed for 633 nm illumination. Our experimental investigation shows that the Moiré-lenses have a broad adjustable refractive power range with a high efficiency, which allows one to use them for flexible beam steering and for imaging applications.

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References

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2012

2011

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

2010

2009

2008

H. Ren, S. Xu, Y.-J. Lin, and S.-T. Wu, “Adaptive-focus lenses,” Opt. Photon. News43–47Oct.2008.

B. Kleemann, M. Seeßelberg, and J. Ruoff, “Design concepts for broadband high-efficiency DOEs,” JEOS - Rapid Pub.3, 08015 (2008).
[CrossRef]

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

2007

2005

2003

R. Brunner, R. Steiner, H. J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, “New solution to realize complex optical systems by a combination of diffractive and refractive optical components,” Proc. SPIE5183, 47–55 (2003).
[CrossRef]

2000

1993

1991

1989

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

1988

1977

1970

Avicola, K.

Bará, S.

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. Express17, 9376–9390 (2009).
[CrossRef] [PubMed]

Barton, I. M.

Bernet, S.

Brunner, R.

R. Brunner, R. Steiner, H. J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, “New solution to realize complex optical systems by a combination of diffractive and refractive optical components,” Proc. SPIE5183, 47–55 (2003).
[CrossRef]

Burch, J.M.

Burkhardt, M.

R. Brunner, R. Steiner, H. J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, “New solution to realize complex optical systems by a combination of diffractive and refractive optical components,” Proc. SPIE5183, 47–55 (2003).
[CrossRef]

Cagigal, M. P.

Canales, V. F.

Chau, F. S.

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett34, 2793–2795 (2009).
[CrossRef] [PubMed]

Dixit, S. N.

Dobschal, H. J.

R. Brunner, R. Steiner, H. J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, “New solution to realize complex optical systems by a combination of diffractive and refractive optical components,” Proc. SPIE5183, 47–55 (2003).
[CrossRef]

Dodge, M. R.

Ezhov, E. G.

Fox, D.

George, N.

Greisukh, G. I.

Guoqiang, L.

L. Guoqiang, “Adaptive lens,” Progress in Opt.55, 199–283 (2010).
[CrossRef]

Helgert, M.

R. Brunner, R. Steiner, H. J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, “New solution to realize complex optical systems by a combination of diffractive and refractive optical components,” Proc. SPIE5183, 47–55 (2003).
[CrossRef]

Henao, R.

Jaroszewicz, Z.

Kalashnikov, A. V.

Kleemann, B.

B. Kleemann, M. Seeßelberg, and J. Ruoff, “Design concepts for broadband high-efficiency DOEs,” JEOS - Rapid Pub.3, 08015 (2008).
[CrossRef]

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. Lett34, 2793–2795 (2009).
[CrossRef] [PubMed]

Leung, H. M.

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett34, 2793–2795 (2009).
[CrossRef] [PubMed]

Lin, Y.-J.

S. Xu, Y.-J. Lin, and S.-T. Wu, “Dielectric liquid microlens with well-shaped electrode,” Opt. Express17, 10499 (2009).
[CrossRef] [PubMed]

H. Ren, S. Xu, Y.-J. Lin, and S.-T. Wu, “Adaptive-focus lenses,” Opt. Photon. News43–47Oct.2008.

Lohmann, A. W.

Martin, D.

R. Brunner, R. Steiner, H. J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, “New solution to realize complex optical systems by a combination of diffractive and refractive optical components,” Proc. SPIE5183, 47–55 (2003).
[CrossRef]

Mathine, D. L.

Meyrueis, P.

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

Mira, A.

Moreno, V.

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]

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]

Ruoff, J.

B. Kleemann, M. Seeßelberg, and J. Ruoff, “Design concepts for broadband high-efficiency DOEs,” JEOS - Rapid Pub.3, 08015 (2008).
[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.

Seeßelberg, M.

B. Kleemann, M. Seeßelberg, and J. Ruoff, “Design concepts for broadband high-efficiency DOEs,” JEOS - Rapid Pub.3, 08015 (2008).
[CrossRef]

Steiner, R.

R. Brunner, R. Steiner, H. J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, “New solution to realize complex optical systems by a combination of diffractive and refractive optical components,” Proc. SPIE5183, 47–55 (2003).
[CrossRef]

Stepanov, S. A.

Stone, T.

Summers, L. J.

Thompson, C. A.

Valle, P. J.

Valley, P.

Wilhelmsen, J.

Williams, D.C.

Wu, B.

Wu, S. T.

Wu, S.-T.

S. Xu, Y.-J. Lin, and S.-T. Wu, “Dielectric liquid microlens with well-shaped electrode,” Opt. Express17, 10499 (2009).
[CrossRef] [PubMed]

H. Ren, S. Xu, Y.-J. Lin, and S.-T. Wu, “Adaptive-focus lenses,” Opt. Photon. News43–47Oct.2008.

Xu, S.

S. Xu, Y.-J. Lin, and S.-T. Wu, “Dielectric liquid microlens with well-shaped electrode,” Opt. Express17, 10499 (2009).
[CrossRef] [PubMed]

H. Ren, S. Xu, Y.-J. Lin, and S.-T. Wu, “Adaptive-focus lenses,” Opt. Photon. News43–47Oct.2008.

Yu, H.

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett34, 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. Lett34, 2793–2795 (2009).
[CrossRef] [PubMed]

Appl. Opt.

J. Opt.

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

JEOS - Rapid Pub.

B. Kleemann, M. Seeßelberg, and J. Ruoff, “Design concepts for broadband high-efficiency DOEs,” JEOS - Rapid Pub.3, 08015 (2008).
[CrossRef]

Liq. Cryst.

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

Opt. Lett

G. Zhou, H. M. Leung, H. Yu, A. S. Kumar, and F. S. Chau, “Liquid tunable diffractive-refractive hybrid lens,” Opt. Lett34, 2793–2795 (2009).
[CrossRef] [PubMed]

Opt. Lett.

Opt. Photon. News

H. Ren, S. Xu, Y.-J. Lin, and S.-T. Wu, “Adaptive-focus lenses,” Opt. Photon. News43–47Oct.2008.

Proc. SPIE

R. Brunner, R. Steiner, H. J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, “New solution to realize complex optical systems by a combination of diffractive and refractive optical components,” Proc. SPIE5183, 47–55 (2003).
[CrossRef]

Progress in Opt.

L. Guoqiang, “Adaptive lens,” Progress in Opt.55, 199–283 (2010).
[CrossRef]

Other

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

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Figures (8)

Fig. 1
Fig. 1

Left: Operation principle of a MDOE: Two diffractive optical elements are combined into a ”Moiré-lens” (not to scale). Rotating one of the elements with respect to the other by an angle θ changes the optical power of the MDOE. Right: Photography of one of the produced DOEs, which - after combination with its counterpart - yields a Moiré-lens. The DOEs are realized as 16-level phase elements, etched into a glass plate (side length: 10 mm). The etched structure on the upper side is faintly visible by specular reflection of oblique illumination light.

Fig. 2
Fig. 2

Cross sections of the phase profiles of an integer Moiré lens (according to Eq. (9)) for two different relative rotation angles of 30° (left) and 330° (right). The green curve corresponds to the digitized phase profile according to Eq. (9), the blue curve to the first order lens with ideal blazed phase profile θar2, and the red curve to the minus first order lens with ideal blazed phase profile of (θ − 2π)ar2.

Fig. 3
Fig. 3

Efficiencies of the two lens terms in the bifocal MDOE lenses as a function of the relative rotation angle θ. Blue and red markers and curves correspond to numerical and analytical results for integer Moiré-lenses fabricated according to Eq. (8), respectively, whereas black and green marker and curves apply to a non-integer Moiré-lens according to Eq. (4).

Fig. 4
Fig. 4

Properties of the four produced MDOEs. All of them are etched in fused silica as 16 phase level DOEs. The right column shows a magnified sketch of the central region of the phase masks (not to scale, gray values correspond to phase levels). Element 4 is practically the same as element 2 (with smaller pixel size), therefore - for additional information - the sketch at the right shows as an example the resulting stacked Moiré lens at a mutual rotation angle of 45°.

Fig. 5
Fig. 5

Photograph of a non-integer Moiré lens according to design 1, mounted in a home made rotation stage and placed about 4 cm above a page of sample text. The mutual rotation of the two assembled DOES of about 75° corresponds to the opening angle of the red marked sector. As expected for the non-integer Moiré element 1, two Fresnel lenses with different refractive powers are created inside and outside of the marked sector resulting in a demagnification and magnification of the sample text observed through the respective lens areas. A further rotation of one DOE with respect to the other would increase the size of the marked sector, and simultaneously change the refractive powers within and without the sector according to Eq. (7).

Fig. 6
Fig. 6

Left: Experimentally measured dependence of the refractive powers of the 4 different Moiré lenses as a function of the rotation angle. The continuous lines are a linear fit to the data. Right: Relative diffraction efficiencies of the Moiré lenses as a function of their measured refractive powers. The black, blue and green continuous curves for the integer Moiré elements are fits to the data according to Eq.(10).

Fig. 7
Fig. 7

Point spread functions of Moiré lens 2 as a function of the lateral misalignment of the two stacked DOEs. The focal length of the lens was adjusted to 20 cm, and the intensity in the focal spot was imaged with a camera (ccd pixel counts are coded according to the colorbar below). One square camera pixel had a size of 9μm × 9μm. The data shows that for perfect alignment (left image) a diffraction limited PSF is produced, with a width on the order of 10 μm. For increasing misalignment (lateral misalignment between centers of the two DOEs indicated in the images) the PSF starts to split into two separated spots.

Fig. 8
Fig. 8

Test images recorded with Moiré lenses used as camera objectives. (a): Monochrome image (illumination at 633 nm with a HeNe laser) of a USAF resolution target placed at a distance of 11.0 cm in front of Moiré element 4 (diameter: 6 mm). Distance between lens and camera chip was 19.2 cm, and the focal length of the Moiré lens was adjusted to 7.0 cm. The line pairs in group 5, element 5 are still resolved, corresponding to a resolution of 50 line pairs per mm. (b) White light image of two toy cars placed at a distance of 22 cm, and 54 cm in front of Moiré element 2 (8 mm diameter), respectively. The distance between lens and camera chip was 20 cm. In (b) the focal length of the Moiré lens was adjusted to 10.5 cm, thus focusing on the nearer car. In (c) the focal length was changed to 14.5 cm, focusing on the other toy car.

Equations (12)

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T 1 = exp [ i F ( r ) φ ] T 2 = exp [ i F ( r ) φ ] .
T 2 ; rot = { exp [ i F ( r ) ( φ θ ) ] for θ φ < 2 π exp [ i F ( r ) ( φ θ + 2 π ) ] for 0 φ < θ .
T joint = { exp [ i F ( r ) ( θ ) ] for θ φ < 2 π exp [ i F ( r ) ( θ 2 π ) ] for 0 φ < θ .
F Fr ( r ) = a r 2 .
T joint ; Fr = { exp [ i θ a r 2 ] for θ φ < 2 π exp [ i ( θ 2 π ) a r 2 ] 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 .
F iFr ( r ) = round { a r 2 } .
T iFr ( r ) = exp [ i θ round { a r 2 } ] .
η 1 = ( sinc π N ) 2 .
T iFr 1 ( r ) = exp [ i φ round { ar 2 } + ibr 2 ] and T iFr 1 ( r ) = exp [ i φ round { ar 2 } + ibr 2 ] .
f offset 1 = 2 b λ / π .

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