Abstract

We present a method to design the pure-phase distribution based on phase optimization for realizing the three-dimensional (3D) intensity modulation on curved surfaces (CS) and apply it to fabricate desired 3D patterns on CS. 3D intensity patterns are reconstructed numerically as well as fabricated experimentally on CS with high quality, which demonstrates the validity of the method. Since the arbitrary phase profile of diffractive optical elements (DOEs) on CS can be mapped into the 3D optical intensity distribution on CS, the method can be directly applied to fabricate any desired DOEs on CS. As far as we know, it is the first time to design the pure-phase distribution for realizing the 3D intensity modulation on CS and apply it to fabricate arbitrary patterns on CS.

© 2014 Optical Society of America

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2013 (1)

2011 (2)

R. Shi, J. Liu, J. Xu, D. Liu, Y. Pan, J. Xie, and Y. Wang, “Designing and fabricating diffractive optical elements with a complex profile by interference,” Opt. Lett. 36(20), 4053–4055 (2011).
[Crossref] [PubMed]

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]

2010 (3)

2009 (1)

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 (1)

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

2007 (2)

2004 (1)

2002 (1)

2000 (2)

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,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

1999 (2)

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]

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. B 17(6), 2965–2969 (1999).
[Crossref]

1998 (1)

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science 280(5372), 2089–2091 (1998).
[Crossref] [PubMed]

1995 (1)

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. B 13(6), 2732–2735 (1995).
[Crossref]

1992 (1)

1968 (1)

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,” Science 280(5372), 2089–2091 (1998).
[Crossref] [PubMed]

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. B 17(6), 2965–2969 (1999).
[Crossref]

Baker, K. M.

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,” Science 280(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,” Nature 404(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. B 13(6), 2732–2735 (1995).
[Crossref]

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. B 17(6), 2965–2969 (1999).
[Crossref]

Christmas, J.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

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. B 17(6), 2965–2969 (1999).
[Crossref]

Collings, N.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

Crossland, W. A.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[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. B 17(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,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

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. B 17(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]

Georgiou, A.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

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,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

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,” Science 280(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. B 17(6), 2965–2969 (1999).
[Crossref]

Kanicki, J.

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

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.

Lee, H.

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

Li, C.

Li, F.

Li, X.

Liu, D.

Liu, H.

Liu, J.

Liu, P.

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.

Mizutani, A.

Moore, J.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

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. B 17(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,” Science 280(5372), 2089–2091 (1998).
[Crossref] [PubMed]

Radtke, D.

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. B 17(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. B 13(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. B 13(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. B 13(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,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Shewell, J. R.

Shi, R.

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. B 13(6), 2732–2735 (1995).
[Crossref]

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. B 17(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. B 17(6), 2965–2969 (1999).
[Crossref]

Stumpf, M.

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

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,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Wang, T.

Wang, Y.

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,” Science 280(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. B 17(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. B 17(6), 2965–2969 (1999).
[Crossref]

Xiao, R.

Xie, J.

Xie, Y.

Xu, J.

Xu, W.

Xu, Z.

Yoo, G.

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

Yu, W.

Zeitner, U.

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

Zeitner, U. D.

Zhang, D.

Zhang, H.

Zhao, H.

Zhao, J.

Zhong, H.

Zou, B.

Appl. Opt. (4)

J. Micromech. Microeng. (1)

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. A, Pure Appl. Opt. (1)

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

J. Opt. Soc. Am. (1)

J. Vac. Sci. Technol. B (2)

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. B 17(6), 2965–2969 (1999).
[Crossref]

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. B 13(6), 2732–2735 (1995).
[Crossref]

Microelectron. Eng. (2)

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]

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

Nature (1)

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,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (1)

Science (1)

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science 280(5372), 2089–2091 (1998).
[Crossref] [PubMed]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

J. Nishii, “Glass-imprinting for optical device fabrication,” in Advances in Optical Materials, OSA Technical Digest (CD) (Optical Society of America, 2009), paper AThC1.

S. Yan, Design of Diffractive Micro-optics (National Defense Industry, 2011), pp. 25, 70, 284 (in Chinese).

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Figures (10)

Fig. 1
Fig. 1 Schematic view of the light wave propagation from the plane P 1 to the curved surface.
Fig. 2
Fig. 2 Flowchart of the phase retrieval method.
Fig. 3
Fig. 3 (a) Top view and (b) Sampling pixel of cylindrical surface.
Fig. 4
Fig. 4 Numerical simulation for 3D binary pattern: intensity distributions of (a) an ideal pattern and (b) the reconstructed pattern, (c) relative error as a function of iteration.
Fig. 5
Fig. 5 Numerical simulation for 3D gray level badge pattern: intensity distributions of (a) an ideal pattern, (b) the reconstructed pattern, (c) relative error as a function of iteration.
Fig. 6
Fig. 6 Numerical simulation for 3D gray level pattern “cameraman” (a = 1/10, b = 1, c = 1): intensity distributions of (a) an ideal pattern, (b) the reconstructed pattern, and (c) relative error as a function of iteration.
Fig. 7
Fig. 7 Numerical simulation for 3D gray level pattern “cameraman” (a = 1, b = 1, c = 1): intensity distributions of (a) an ideal pattern, (b) the reconstructed pattern, and (c) relative error as a function of iteration.
Fig. 8
Fig. 8 Schematic view of experimental setup.
Fig. 9
Fig. 9 (a) Photograph of the 3D binary pattern fabricated on the cylindrical lens. (b) Enlarged picture of the fabricated pattern.
Fig. 10
Fig. 10 (a) Photograph of the 3D gray level badge pattern fabricated on the cylindrical lens. (b) Enlarged picture of the fabricated pattern.

Equations (2)

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U ˜ ( Χ 2 )= 1 jλ U( Χ 1 ) exp(jkr) r cosθ dσ
U( Χ 1 )= j λ ' U ˜ ( Χ 2 ) exp(jkr') r' cos θ ' dσ'

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