Abstract

For the design of computer-generated holograms reconstructing certain intensity patterns with phase freedom, we use an object-oriented approach. The given intensity pattern is decomposed into elementary objects for which appropriate phase-only hologram functions can be constructed. The total hologram function is found by the subsequent superposition of its constituents, with a relative amplitude and phase weighting for each of them. Thus, the degrees of freedom are dramatically reduced compared with those of sampling approaches. The design algorithm allows us to compensate on the one hand for the intensity and phase distribution of the impinging laser beam and on the other hand for the shape of the hologram aperture. We report on the computer-aided design of such holograms, as well as their fabrication through the use of laser lithography and reactive ion etching. Optical reconstructions are shown.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. -H. Lee, “Computer-generated holograms: techniques and applications,” in Progress In Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 119–232.
    [CrossRef]
  2. M. R. Schroeder, IEEE Trans. Inf. Theory IT-16, 85–89 (1970).
    [CrossRef]
  3. D. C. Chu, J. W. Goodman, “Spectrum shaping with parity sequences,” Appl. Opt. 11, 1716–1724 (1972).
    [CrossRef] [PubMed]
  4. L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Method of making an object-dependent diffusor,” U.S. patent3,619,022 (9November1971).
  5. R. W. Gerchberg, W. O. Saxton, Optik (Stuttgart) 35, 237–246 (1972).
  6. W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic, New York, 1978).
  7. J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. 19, 297–305 (1980).
  8. F. Wyrowski, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
    [CrossRef]
  9. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  10. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1990).
  11. U. Krackhardt, J. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fanout elements,” Appl. Opt. 31, 27–37 (1992).
    [CrossRef] [PubMed]
  12. J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
  13. H. P. Herzig, D. Prongue, R. Dändliker, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Opt. Phys. 29, L1307–L1309 (1990).
    [CrossRef]
  14. M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
    [CrossRef] [PubMed]
  15. R. Bräuer, F. Wyrowski, O. Bryngdahl, “Diffusors in digital holography,” J. Opt. Soc. Am. A 8, 572–578 (1991).
    [CrossRef]
  16. P. W. Rhodes, D. L. Shealy, “Refractive optical system for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980).
    [CrossRef] [PubMed]
  17. B. R. Frieden, “Lossless conversion of a plane laser wave to a plane wave of uniform irradiance,” Appl. Opt. 4, 1400–1403 (1965).
    [CrossRef]
  18. N. C. Roberts, “Beam shaping by holographic filters,” Appl. Opt. 28, 31–32 (1989).
    [CrossRef] [PubMed]
  19. C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian laser beam to a near field uniform beam,” Opt. Eng. 30, 537–543 (1991).
    [CrossRef]
  20. M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 207–309 (1991).
    [CrossRef]
  21. C. Frère, D. Leseberg, O. Bryngdahl, “Computer-generated holograms of three-dimensional objects composed of line segments,” J. Opt. Soc. Am. A 3, 726–730 (1986).
    [CrossRef]
  22. S. Weissbach, F. Wyrowski, O. Bryngdahl, “Digital phase holograms: coding and quantization with an error diffusion concept,” Opt. Commun. 72, 37–41 (1989).
    [CrossRef]
  23. T. Sandström, J. K. Tison, “Highly accurate pattern generation using acousto-optical deflection,” in Optical/Laser Microlithography IV, V. Pol, ed., Proc. SPIE 1463, 629–637 (1991).
  24. U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
    [CrossRef]
  25. Z. Novotny, “Reactive ion etching of dielectric and semiconductor layers in CHF3 and C2F6,” Czech. J. Phys. 38, 689–695 (1988).
    [CrossRef]
  26. U. Krackhardt, N. Streibl, J. Schwider, “Fabrication errors of computer generated multilevel phase holograms,” Optik (Stuttgart) 95, 137–146 (1994).

1994 (1)

U. Krackhardt, N. Streibl, J. Schwider, “Fabrication errors of computer generated multilevel phase holograms,” Optik (Stuttgart) 95, 137–146 (1994).

1993 (1)

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

1992 (1)

1991 (3)

R. Bräuer, F. Wyrowski, O. Bryngdahl, “Diffusors in digital holography,” J. Opt. Soc. Am. A 8, 572–578 (1991).
[CrossRef]

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian laser beam to a near field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 207–309 (1991).
[CrossRef]

1990 (1)

H. P. Herzig, D. Prongue, R. Dändliker, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Opt. Phys. 29, L1307–L1309 (1990).
[CrossRef]

1989 (3)

N. C. Roberts, “Beam shaping by holographic filters,” Appl. Opt. 28, 31–32 (1989).
[CrossRef] [PubMed]

S. Weissbach, F. Wyrowski, O. Bryngdahl, “Digital phase holograms: coding and quantization with an error diffusion concept,” Opt. Commun. 72, 37–41 (1989).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

1988 (2)

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

Z. Novotny, “Reactive ion etching of dielectric and semiconductor layers in CHF3 and C2F6,” Czech. J. Phys. 38, 689–695 (1988).
[CrossRef]

1987 (1)

1986 (1)

1982 (1)

1980 (2)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. 19, 297–305 (1980).

P. W. Rhodes, D. L. Shealy, “Refractive optical system for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980).
[CrossRef] [PubMed]

1972 (2)

1970 (1)

M. R. Schroeder, IEEE Trans. Inf. Theory IT-16, 85–89 (1970).
[CrossRef]

1965 (1)

Aleksoff, C. C.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian laser beam to a near field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Allebach, J. P.

Bräuer, R.

Bryngdahl, O.

Chu, D. C.

Dändliker, R.

H. P. Herzig, D. Prongue, R. Dändliker, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Opt. Phys. 29, L1307–L1309 (1990).
[CrossRef]

Ellis, K. K.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian laser beam to a near field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Fienup, J. R.

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

J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. 19, 297–305 (1980).

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1990).

Frère, C.

Frieden, B. R.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, Optik (Stuttgart) 35, 237–246 (1972).

Golub, M. A.

M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 207–309 (1991).
[CrossRef]

Goodman, J. W.

Herzig, H. P.

H. P. Herzig, D. Prongue, R. Dändliker, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Opt. Phys. 29, L1307–L1309 (1990).
[CrossRef]

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Method of making an object-dependent diffusor,” U.S. patent3,619,022 (9November1971).

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Method of making an object-dependent diffusor,” U.S. patent3,619,022 (9November1971).

Krackhardt, U.

U. Krackhardt, N. Streibl, J. Schwider, “Fabrication errors of computer generated multilevel phase holograms,” Optik (Stuttgart) 95, 137–146 (1994).

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

U. Krackhardt, J. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fanout elements,” Appl. Opt. 31, 27–37 (1992).
[CrossRef] [PubMed]

Lee, W. -H.

W. -H. Lee, “Computer-generated holograms: techniques and applications,” in Progress In Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 119–232.
[CrossRef]

Leseberg, D.

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Method of making an object-dependent diffusor,” U.S. patent3,619,022 (9November1971).

Mait, J.

Neagle, B. D.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian laser beam to a near field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Novotny, Z.

Z. Novotny, “Reactive ion etching of dielectric and semiconductor layers in CHF3 and C2F6,” Czech. J. Phys. 38, 689–695 (1988).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1990).

Prongue, D.

H. P. Herzig, D. Prongue, R. Dändliker, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Opt. Phys. 29, L1307–L1309 (1990).
[CrossRef]

Rhodes, P. W.

Roberts, N. C.

Sandström, T.

T. Sandström, J. K. Tison, “Highly accurate pattern generation using acousto-optical deflection,” in Optical/Laser Microlithography IV, V. Pol, ed., Proc. SPIE 1463, 629–637 (1991).

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, Optik (Stuttgart) 35, 237–246 (1972).

W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic, New York, 1978).

Schrader, M.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Schroeder, M. R.

M. R. Schroeder, IEEE Trans. Inf. Theory IT-16, 85–89 (1970).
[CrossRef]

Schwider, J.

U. Krackhardt, N. Streibl, J. Schwider, “Fabrication errors of computer generated multilevel phase holograms,” Optik (Stuttgart) 95, 137–146 (1994).

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Seldowitz, M. A.

Shealy, D. L.

Sisakyan, I. N.

M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 207–309 (1991).
[CrossRef]

Soifer, V. A.

M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 207–309 (1991).
[CrossRef]

Streibl, N.

U. Krackhardt, N. Streibl, J. Schwider, “Fabrication errors of computer generated multilevel phase holograms,” Optik (Stuttgart) 95, 137–146 (1994).

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

U. Krackhardt, J. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fanout elements,” Appl. Opt. 31, 27–37 (1992).
[CrossRef] [PubMed]

Sweeney, D. W.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1990).

Tison, J. K.

T. Sandström, J. K. Tison, “Highly accurate pattern generation using acousto-optical deflection,” in Optical/Laser Microlithography IV, V. Pol, ed., Proc. SPIE 1463, 629–637 (1991).

Turunen, J.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

Vasara, A.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1990).

Weissbach, S.

S. Weissbach, F. Wyrowski, O. Bryngdahl, “Digital phase holograms: coding and quantization with an error diffusion concept,” Opt. Commun. 72, 37–41 (1989).
[CrossRef]

Westerholm, J.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

Wyrowski, F.

Appl. Opt. (7)

Czech. J. Phys. (1)

Z. Novotny, “Reactive ion etching of dielectric and semiconductor layers in CHF3 and C2F6,” Czech. J. Phys. 38, 689–695 (1988).
[CrossRef]

IEEE Trans. Inf. Theory (1)

M. R. Schroeder, IEEE Trans. Inf. Theory IT-16, 85–89 (1970).
[CrossRef]

J. Opt. Soc. Am. A (3)

Jpn. J. Appl. Opt. Phys. (1)

H. P. Herzig, D. Prongue, R. Dändliker, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Opt. Phys. 29, L1307–L1309 (1990).
[CrossRef]

Opt. Commun. (1)

S. Weissbach, F. Wyrowski, O. Bryngdahl, “Digital phase holograms: coding and quantization with an error diffusion concept,” Opt. Commun. 72, 37–41 (1989).
[CrossRef]

Opt. Eng. (4)

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. 19, 297–305 (1980).

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian laser beam to a near field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

Opt. Lasers Eng. (1)

M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 207–309 (1991).
[CrossRef]

Optik (Stuttgart) (2)

R. W. Gerchberg, W. O. Saxton, Optik (Stuttgart) 35, 237–246 (1972).

U. Krackhardt, N. Streibl, J. Schwider, “Fabrication errors of computer generated multilevel phase holograms,” Optik (Stuttgart) 95, 137–146 (1994).

Other (5)

T. Sandström, J. K. Tison, “Highly accurate pattern generation using acousto-optical deflection,” in Optical/Laser Microlithography IV, V. Pol, ed., Proc. SPIE 1463, 629–637 (1991).

W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic, New York, 1978).

W. -H. Lee, “Computer-generated holograms: techniques and applications,” in Progress In Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 119–232.
[CrossRef]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Method of making an object-dependent diffusor,” U.S. patent3,619,022 (9November1971).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1990).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

Diagram of the reconstruction geometry: An incident wave on aperture D is to be focused into a pregiven focal pattern A.

Fig. 2
Fig. 2

Phase function of a hologram with a circular aperture focusing a homogenous beam into a straight line.

Fig. 3
Fig. 3

Phase function of a hologram with a circular aperture focusing a Gaussian beam into a straight line.

Fig. 4
Fig. 4

Phase function of a hologram with a square aperture focusing a homogenous beam into an inclined straight line.

Fig. 5
Fig. 5

Symetrical segmentation of the square aperture of Fig. 4.

Fig. 6
Fig. 6

Phase function of a hologram focusing into a modulated circle.

Fig. 7
Fig. 7

Central part of the binary phase mask focusing into a wheel (Fig. 8).

Fig. 8
Fig. 8

Reconstruction of the wheel focus (Fig. 7) from a binary phase hologram.

Fig. 9
Fig. 9

Central part of the first binary mask layer of a four-level phase mask focusing into an arrow (Fig. 11).

Fig. 10
Fig. 10

Central part of the second binary mask layer of a four-level phase mask focusing into an arrow (Fig. 11).

Fig. 11
Fig. 11

Reconstruction of the arrow focus from a four-level phase mask hologram.

Fig. 12
Fig. 12

Simulated reconstruction of a laser warning sign from a four-level phase mask hologram.

Fig. 13
Fig. 13

Optical reconstruction of a laser warning sign from a four-level phase mask hologram.

Tables (1)

Tables Icon

Table 1 Object Phase-Only Hologram Functions Implemented to Date

Equations (8)

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

I [ x ( u ) ] det x u = I 0 ( u )
E = D I 0 ( u ) d 2 u = A I ( x ) d 2 x .
k ψ ( u ) = k ψ 0 ( u ) + ϕ ( u ) ,
ψ ( u ) = x ( u ) - u z ,
I 0 ( u ) = I ¯ 0 exp ( - u 2 2 σ 2 ) ,
H ( u ) = k b k A k exp { i [ ϕ k ( u ) + α k ] } .
Φ ( u ) = arg ( k b k A k exp { i [ ϕ k ( u ) + α k ] } ) .
η = sinc 2 ( 1 Z ) ,

Metrics