Abstract

The use of diffractive optical elements (DOEs) to generate complex raster images for a primarily artistic purpose is dealt with. Aspects of human vision that are relevant for the design of such elements are discussed. A design method based on an iterative Fourier transform algorithm and extended with elements from the direct-binary-search and the simulated-annealing algorithms is described. The proposed method provides a large set of parameters that can be adjusted freely to optimize it for any given design task. For demonstration a phase-only DOE was designed that generates an image of a Chinese dragon as a diffraction pattern. It was realized as a surface-relief element on a planar substrate through multilevel binary lithography and reactive-ion etching. Experimental tests confirm the usefulness of the design and the fabrication procedures to achieve excellent image quality.

© 2001 Optical Society of America

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References

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2000 (3)

1998 (1)

J. N. Mait, “Diffractive beauty,” Opt. Photon. News 9(11), 21–25 (1998).
[CrossRef]

1997 (1)

1996 (1)

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

1995 (1)

1994 (1)

J. Jahns, “Planar packaging of free-space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
[CrossRef]

1990 (1)

1989 (1)

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

1988 (1)

1987 (1)

1986 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220(5), 671–680 (1983).

1982 (1)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” App. Opt. 21, 2758–2769 (1982).
[CrossRef]

1969 (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Aagedal, H.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

H. Aagedal, F. Wyrowski, M. Schmid, “Paraxial beam splitting and shaping,” in Diffractive Optics for Industrial and Commercial Applications,” J. Turunen, F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), pp. 165–188.

Akahori, H.

Allebach, J. P.

Arrizón, V.

Beth, T.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

Brenner, K.-H.

Bryngdahl, O.

Campbell, F. W.

F. W. Campbell, L. Maffei, “Contrast and spatial frequency,” in Recent Progress in Perception, Readings from Scientific American Series (Scientific American, Washington, D.C., 1976), pp. 30–36; ISBN 0-7167-0534-6.

Collings, V. B.

D. H. McBurney, V. B. Collings, Introduction to Sensation–Perception (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Eckert, W.

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithms: a comparison,” App. Opt. 21, 2758–2769 (1982).
[CrossRef]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220(5), 671–680 (1983).

Goodman, J. W.

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

Guest, C. C.

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Jahns, J.

W. Eckert, V. Arrizón, S. Sinzinger, J. Jahns, “Compact planar-integrated optical correlator for spatially incoherent signals,” Appl. Opt. 39, 759–765 (2000).
[CrossRef]

J. Jahns, “Planar packaging of free-space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
[CrossRef]

S. Sinzinger, J. Jahns, Microoptics (Wiley VCH, Weinheim, Germany, 1999).

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Kim, M. S.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220(5), 671–680 (1983).

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Maffei, L.

F. W. Campbell, L. Maffei, “Contrast and spatial frequency,” in Recent Progress in Perception, Readings from Scientific American Series (Scientific American, Washington, D.C., 1976), pp. 30–36; ISBN 0-7167-0534-6.

Mait, J. N.

McBurney, D. H.

D. H. McBurney, V. B. Collings, Introduction to Sensation–Perception (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Morrison, R.

R. Morrison, “Diffractive optics beauty contest,” Opt. Photon. News 11(11), 40–41 (2000).
[CrossRef]

Petterson, R.

R. Petterson, Visual Information (Educational Technology, Englewood Cliffs, N.J., 1993).

Russ, J. C.

J. C. Russ, The Image Processing Handbook (CRC Press, Boca Raton, Fla., 1995).

Schmid, M.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

H. Aagedal, F. Wyrowski, M. Schmid, “Paraxial beam splitting and shaping,” in Diffractive Optics for Industrial and Commercial Applications,” J. Turunen, F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), pp. 165–188.

Seldowitz, M. A.

Sinzinger, S.

W. Eckert, V. Arrizón, S. Sinzinger, J. Jahns, “Compact planar-integrated optical correlator for spatially incoherent signals,” Appl. Opt. 39, 759–765 (2000).
[CrossRef]

S. Sinzinger, “Microoptical correlators for security applications,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 41 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000).

S. Sinzinger, J. Jahns, Microoptics (Wiley VCH, Weinheim, Germany, 1999).

Stern, M. B.

M. B. Stern, “Binary optics fabrication,” in Micro-Optics, H.-P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 53–85.

Streibl, N.

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

Sweeney, D. W.

Teiwes, S.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

Testorf, M.

van Renesse, R. L.

R. L. van Renesse, Optical Document Security (Artech House, Norwood, Mass., 1994).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220(5), 671–680 (1983).

Wyrowski, F.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

F. Wyrowski, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
[CrossRef]

H. Aagedal, F. Wyrowski, M. Schmid, “Paraxial beam splitting and shaping,” in Diffractive Optics for Industrial and Commercial Applications,” J. Turunen, F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), pp. 165–188.

App. Opt. (1)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” App. Opt. 21, 2758–2769 (1982).
[CrossRef]

Appl. Opt. (4)

IBM J. Res. Dev. (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

J. Mod. Opt. (2)

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (2)

Opt. Photon. News (2)

J. N. Mait, “Diffractive beauty,” Opt. Photon. News 9(11), 21–25 (1998).
[CrossRef]

R. Morrison, “Diffractive optics beauty contest,” Opt. Photon. News 11(11), 40–41 (2000).
[CrossRef]

Proc. IEEE (1)

J. Jahns, “Planar packaging of free-space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220(5), 671–680 (1983).

Other (14)

R. Petterson, Visual Information (Educational Technology, Englewood Cliffs, N.J., 1993).

F. W. Campbell, L. Maffei, “Contrast and spatial frequency,” in Recent Progress in Perception, Readings from Scientific American Series (Scientific American, Washington, D.C., 1976), pp. 30–36; ISBN 0-7167-0534-6.

J. C. Russ, The Image Processing Handbook (CRC Press, Boca Raton, Fla., 1995).

H. Aagedal, F. Wyrowski, M. Schmid, “Paraxial beam splitting and shaping,” in Diffractive Optics for Industrial and Commercial Applications,” J. Turunen, F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), pp. 165–188.

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

M. B. Stern, “Binary optics fabrication,” in Micro-Optics, H.-P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 53–85.

D. H. McBurney, V. B. Collings, Introduction to Sensation–Perception (Prentice-Hall, Englewood Cliffs, N.J., 1977).

H.-P. Herzig, ed., Micro-Optics (Taylor & Francis, London, 1997).

S. Sinzinger, J. Jahns, Microoptics (Wiley VCH, Weinheim, Germany, 1999).

J. Turunen, F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, Berlin, 1997).

See the URL http://www.osa.org/mtg_conf/archive.htm .

See the URL http://www.mathworks.com .

R. L. van Renesse, Optical Document Security (Artech House, Norwood, Mass., 1994).

S. Sinzinger, “Microoptical correlators for security applications,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 41 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000).

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Figures (10)

Fig. 1
Fig. 1

Basic setup for generating raster images with DOEs. O(m), of the order of meters; O(cm), of the order of centimeters; O(dm), of the order of decimeters.

Fig. 2
Fig. 2

Assumed basic structure of the DOEs.

Fig. 3
Fig. 3

Processing loop of an IFTA. FFT, fast Fourier transform.

Fig. 4
Fig. 4

Flow chart of the proposed DOE design algorithm.

Fig. 5
Fig. 5

Several stages in the design process of the dragon DOE: η is the numerically obtained diffraction efficiency; the SNR is defined as the ratio of the average intensity of all diffraction orders that are part of the body of the dragon and the highest intensity anywhere in the background.

Fig. 6
Fig. 6

Projection geometry for the dragon DOE.

Fig. 7
Fig. 7

Finished dragon DOE on a fused-silica substrate.

Fig. 8
Fig. 8

Central part of the experimentally observed diffraction pattern depicting a rastered dragon. The picture was recorded with a high-resolution 16-bit CCD camera.

Fig. 9
Fig. 9

Close-up of the image of Fig. 8 showing the discrete nature of the diffraction pattern and the zeroth-order blur.

Fig. 10
Fig. 10

Several repetitions of the dragon image in the experimentally observed diffraction pattern, confirming the theoretically predicted sinc modulation. Note that gray levels in this image result from a logarithmic intensity mapping of the raw data from the CCD camera.

Equations (15)

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

gx, y=tx, ysx, y=combx, ypx, ysx, y,
gx, y=combx, ywx, yex, ysx, y,
wx, y=n=1Nm=1M expiϕn,mδx-n/N, y-m/M,
ex, y=rectNxrectMy.
sx, y=rectx/Precty/Q,
Gu, v=gx, y=combu, vWu, vEu, vSu, v,
Wu, v=wx, y=1NMn=1Nm=1M expiϕnm×expi2πnuN+mvM,
Eu, v=ex, y=sincu/Nsincv/M,
Su, v=sx, y=PQ sincPusincQv.
aij=|wij|=C,  i, j,
Akl=Idk, l1/2|Ek, l|,
ϕij=argwij=p1i+p2i2+p3 j+p4 j2
wij=C expi argw˜ij.
W˜kl=αklAkl expi argWkl+1-αklWkl.
DL tan βL λNe.

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