Abstract

We demonstrate a novel method for the modulation of the optical intensity on curved surfaces (CS) by interference and apply it to fabricate diffractive optical elements (DOEs) with arbitrary profile and large area on CS. The intensity on CS is modulated accurately by two phase distributions. Both a binary pattern and a gray pattern are reconstructed numerically on the lens surfaces with big curvatures in large areas, while a binary and non-periodic pattern is produced experimentally on a lens surface with a radius of curvature in 25.8 mm. The simulations together with the experiment demonstrate the validity of the method. To our knowledge, it is the first time to present an approach for fabricating DOEs with arbitrary profile and large area on CS by interference.

© 2013 OSA

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2012

2011

2010

2009

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng.19(5), 055017 (2009).
[CrossRef]

2008

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt.47(10), 1567–1574 (2008).
[CrossRef] [PubMed]

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett.33(21), 2443–2445 (2008).
[CrossRef] [PubMed]

2007

2004

2002

2000

K. Kintaka, J. Nishii, and N. Tohge, “Diffraction gratings of photosensitive ZrO2 gel films fabricated with the two-ultraviolet-beam interference method,” Appl. Opt.39(4), 489–493 (2000).
[CrossRef] [PubMed]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404(6773), 53–56 (2000).
[CrossRef] [PubMed]

1999

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

K. M. Baker, “Highly corrected close-packed microlens arrays and moth-eye structuring on curved surfaces,” Appl. Opt.38(2), 352–356 (1999).
[CrossRef] [PubMed]

1998

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science280(5372), 2089–2091 (1998).
[CrossRef] [PubMed]

1995

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B13(6), 2732–2735 (1995).
[CrossRef]

1992

1968

Adams, A.

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science280(5372), 2089–2091 (1998).
[CrossRef] [PubMed]

Ahrenberg, L.

Bailey, T.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Baker, K. M.

Benzie, P.

Brittain, S. T.

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science280(5372), 2089–2091 (1998).
[CrossRef] [PubMed]

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404(6773), 53–56 (2000).
[CrossRef] [PubMed]

Carter, J. M.

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B13(6), 2732–2735 (1995).
[CrossRef]

Chen, B. C.

Choi, B.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Choi, W. M.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Colburn, M.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Damle, S.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404(6773), 53–56 (2000).
[CrossRef] [PubMed]

Dong, J. W.

Duparré, J.

Ekerdt, J.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Esquivel, J. P.

T. Senn, J. P. Esquivel, N. Sabate, and B. Lochel, “Fabrication of high aspect ratio nanostructures on 3D surfaces,” Microelectron. Eng.88(9), 3043–3048 (2011).
[CrossRef]

Fujita, H.

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng.19(5), 055017 (2009).
[CrossRef]

Geddes, J. B.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Harada, T.

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404(6773), 53–56 (2000).
[CrossRef] [PubMed]

He, H. X.

Huang, Y.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Ito, T.

Jackman, R. J.

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science280(5372), 2089–2091 (1998).
[CrossRef] [PubMed]

Johnson, S.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Joseph, J.

Kikuta, H.

Kim, B. J.

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng.19(5), 055017 (2009).
[CrossRef]

Kim, J. G.

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng.19(5), 055017 (2009).
[CrossRef]

Kintaka, K.

Kita, T.

Ko, H. C.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Kumar, P.

Li, C.

Li, F.

Liu, D.

Liu, H.

Liu, J.

Liu, Y. Z.

Lochel, B.

T. Senn, J. P. Esquivel, N. Sabate, and B. Lochel, “Fabrication of high aspect ratio nanostructures on 3D surfaces,” Microelectron. Eng.88(9), 3043–3048 (2011).
[CrossRef]

Lu, Z.

Magnor, M.

Malyarchuk, V.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Masuda, N.

Mizutani, A.

Nishii, J.

Nounu, H.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Pan, Y.

Prentiss, M. G.

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science280(5372), 2089–2091 (1998).
[CrossRef] [PubMed]

Pu, Y. Y.

Radtke, D.

Rogers, J. A.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Ruchhoeft, P.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Sabate, N.

T. Senn, J. P. Esquivel, N. Sabate, and B. Lochel, “Fabrication of high aspect ratio nanostructures on 3D surfaces,” Microelectron. Eng.88(9), 3043–3048 (2011).
[CrossRef]

Savas, T. A.

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B13(6), 2732–2735 (1995).
[CrossRef]

Schattenburg, M. L.

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B13(6), 2732–2735 (1995).
[CrossRef]

Senn, T.

T. Senn, J. P. Esquivel, N. Sabate, and B. Lochel, “Fabrication of high aspect ratio nanostructures on 3D surfaces,” Microelectron. Eng.88(9), 3043–3048 (2011).
[CrossRef]

Shah, S. N.

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B13(6), 2732–2735 (1995).
[CrossRef]

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404(6773), 53–56 (2000).
[CrossRef] [PubMed]

Shewell, J. R.

Shi, R.

Shimobaba, T.

Singh, K.

Smith, H. I.

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B13(6), 2732–2735 (1995).
[CrossRef]

Song, J.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Sreenivasan, S. V.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Stewart, M.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Stoykovich, M. P.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Sun, Q.

Takahira, S.

Takama, N.

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng.19(5), 055017 (2009).
[CrossRef]

Tohge, N.

Tünnermann, A.

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404(6773), 53–56 (2000).
[CrossRef] [PubMed]

Wang, B.

Wang, H. Z.

Wang, S.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Wang, T.

Wang, X.

Wang, Y.

Watson, J.

Weng, Z.

Whitesides, G. M.

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science280(5372), 2089–2091 (1998).
[CrossRef] [PubMed]

Willson, C. G.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Wolf, E.

Wolfe, J. C.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17(6), 2965–2969 (1999).
[CrossRef]

Xiao, J.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Xie, J.

Xie, Y.

Xu, J.

Xu, W.

Xu, Z.

Yu, C. J.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature454(7205), 748–753 (2008).
[CrossRef] [PubMed]

Yu, W.

Zeitner, U. D.

Zhang, D.

Zhang, H.

Zhang, Y.

Zhao, D.

Zhao, J.

Appl. Opt.

J. Micromech. Microeng.

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng.19(5), 055017 (2009).
[CrossRef]

J. Opt. Soc. Am.

J. Vac. Sci. Technol. B

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Figures (8)

Fig. 1
Fig. 1

Schematic view of the light wave propagation from a source surface to a destination surface. SS-source surface, DS-destination surface.

Fig. 2
Fig. 2

(a) Calculation process of the desired light wave from CS to the input plane, (b) Michelson interferometer system for realizing the modulation of light intensity distribution.

Fig. 3
Fig. 3

(a) Side view of a convex lens surface, (b) Schematic view of the modeling of a convex lens surface.

Fig. 4
Fig. 4

Intensity distributions of (a) an ideal pattern, and the reconstructed patterns of (b) case 1, (c) case 2.

Fig. 5
Fig. 5

Intensity distributions of (a) the ideal NPCR pattern, and (b) the reconstructed NPCR pattern.

Fig. 6
Fig. 6

Dependence of SNR on the diffraction distance between the input plane and the curved surface.

Fig. 7
Fig. 7

Schematic view of experimental setup.

Fig. 8
Fig. 8

(a) Photograph of the pattern fabricated on the convex lens. (b) Enlarged picture of the fabricated pattern.

Equations (4)

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U( P 2 )= 1 jλ U( P 1 ) exp(jkr) r cosθ dσ,
U( P 1 )= j λ U( P 2 ) exp(jkr) r cosθ dσ,
φ 1 =arg(D)± cos 1 ( abs(D) /2 ), φ 2 =arg(D e i φ 1 ),
U(A)=HuF{ e iφ1 }+HuF{ e iφ2 },

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