Abstract

The design of a kinoform by the use of simulated annealing is discussed. The simulated annealing process is applied to decrease the reconstruction noise and to adjust the phase distribution of the kinoform to the configuration of the recording device. A liquid-crystal spatial light modulator is used to display the kinoform. The reconstructed image of the optimized kinoform is found to be in good agreement with the computed image. Some experimental results obtained with a liquid-crystal spatial light modulator are presented. The phase quantization effect of the kinoform is discussed.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. P. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wave front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
    [CrossRef]
  2. M. C. Gallagher, B. Lui, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. 12, 2328–2335 (1973).
    [CrossRef] [PubMed]
  3. T. Yatagai, M. Takeda, “Effect of phase nonlinearity in kinoform,” Optick 43, 337–352 (1975).
  4. H. Dammann, “Blazed synthetic phase-only holograms,” Optik 31, 95–104 (1970).
  5. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
  6. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 32, 2758–2769 (1982).
    [CrossRef]
  7. F. Wyrowski, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
    [CrossRef]
  8. 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]
  9. B. K. Jennison, J. P. Allebach, “Analysis of the leakage from computer-generated holograms synthesized by direct binary search,” J. Opt. Soc. Am. A. 6, 234–243 (1989).
    [CrossRef]
  10. S. Kirkpatrick, C. D. Gellatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [CrossRef] [PubMed]
  11. J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
  12. M. S. Kim, C. C. Guest, “Simulated annealing algorithm for binary phase only filters in pattern classification,” Appl. Opt. 29, 1203–1208 (1990).
    [CrossRef] [PubMed]
  13. M. S. Kim, M. R. Feldman, C. C. Guest, “Optimum encoding of binary phase only filters with a simulated annealing algorithm,” Opt. Lett. 14, 545–547 (1989).
    [CrossRef] [PubMed]
  14. J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
    [CrossRef] [PubMed]
  15. H. Szu, R. Hartley, “Fast simulated annealing,” Phys. Lett. 122, 157–162 (1987).
    [CrossRef]

1991 (1)

1990 (1)

1989 (3)

M. S. Kim, M. R. Feldman, C. C. Guest, “Optimum encoding of binary phase only filters with a simulated annealing algorithm,” Opt. Lett. 14, 545–547 (1989).
[CrossRef] [PubMed]

B. K. Jennison, J. P. Allebach, “Analysis of the leakage from computer-generated holograms synthesized by direct binary search,” J. Opt. Soc. Am. A. 6, 234–243 (1989).
[CrossRef]

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

1988 (1)

1987 (2)

1983 (1)

S. Kirkpatrick, C. D. Gellatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

1982 (1)

1980 (1)

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

1975 (1)

T. Yatagai, M. Takeda, “Effect of phase nonlinearity in kinoform,” Optick 43, 337–352 (1975).

1973 (1)

1970 (1)

H. Dammann, “Blazed synthetic phase-only holograms,” Optik 31, 95–104 (1970).

1969 (1)

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

Allebach, J. P.

B. K. Jennison, J. P. Allebach, “Analysis of the leakage from computer-generated holograms synthesized by direct binary search,” J. Opt. Soc. Am. A. 6, 234–243 (1989).
[CrossRef]

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]

Amako, J.

Bryngdahl, O.

Dammann, H.

H. Dammann, “Blazed synthetic phase-only holograms,” Optik 31, 95–104 (1970).

Feldman, M. R.

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 32, 2758–2769 (1982).
[CrossRef]

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

Gallagher, M. C.

Gellatt, C. D.

S. Kirkpatrick, C. D. Gellatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Guest, C. C.

Hartley, R.

H. Szu, R. Hartley, “Fast simulated annealing,” Phys. Lett. 122, 157–162 (1987).
[CrossRef]

Hirsch, P. M.

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

Jennison, B. K.

B. K. Jennison, J. P. Allebach, “Analysis of the leakage from computer-generated holograms synthesized by direct binary search,” J. Opt. Soc. Am. A. 6, 234–243 (1989).
[CrossRef]

Jordan, J. A.

L. P. 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. Gellatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Lesem, L. P.

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

Lui, B.

Seldowitz, M. A.

Sonehara, T.

Sweeney, D. W.

Szu, H.

H. Szu, R. Hartley, “Fast simulated annealing,” Phys. Lett. 122, 157–162 (1987).
[CrossRef]

Takeda, M.

T. Yatagai, M. Takeda, “Effect of phase nonlinearity in kinoform,” Optick 43, 337–352 (1975).

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).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gellatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Westerholm, J.

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

Wyrowski, F.

Yatagai, T.

T. Yatagai, M. Takeda, “Effect of phase nonlinearity in kinoform,” Optick 43, 337–352 (1975).

Appl. Opt. (5)

IBM J. Res. Dev. (1)

L. P. 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. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. A. (1)

B. K. Jennison, J. P. Allebach, “Analysis of the leakage from computer-generated holograms synthesized by direct binary search,” J. Opt. Soc. Am. A. 6, 234–243 (1989).
[CrossRef]

Opt. Eng. (2)

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

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

Opt. Lett. (1)

Optick (1)

T. Yatagai, M. Takeda, “Effect of phase nonlinearity in kinoform,” Optick 43, 337–352 (1975).

Optik (1)

H. Dammann, “Blazed synthetic phase-only holograms,” Optik 31, 95–104 (1970).

Phys. Lett. (1)

H. Szu, R. Hartley, “Fast simulated annealing,” Phys. Lett. 122, 157–162 (1987).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gellatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

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 (9)

Fig. 1
Fig. 1

Schematic illustration of the optical reconstruction setup used for the synthetic Fourier-transform kinoform. The kinoform is illustrated by a plane wave. The reconstructed image is derived in the focal plane of the Fourier lens.

Fig. 2
Fig. 2

Flow diagram demonstrating the process of phase optimization of the kinoform by simulated annealing.

Fig. 3
Fig. 3

Reconstructed image of the optimized kinoform for 16 quantization levels for the iteration of (a) t = 10, (b) t = 100, (c) t = 300, (d) t = 500.

Fig. 4
Fig. 4

Value of the cost function E as a function of the iteration number t during simulated annealing. The desired image is the letter E consisting of 64 × 64 pixels. The phase quantization level is L = 16; the initial temperature is T0 = 1.0.

Fig. 5
Fig. 5

Reconstructed images of the optimized kinoform for different quantization levels L: (a) L = 2, (b) L = 4, (c) L = 8, (d) L = 16.

Fig. 6
Fig. 6

Value of the cost function E as a function of the iteration number t for the kinoform with different quantization levels. The same initial phase distribution is used for quantized levels. Because the phase of the kinoform is quantized before optimization, the initial value of the cost function differs for each quantized level.

Fig. 7
Fig. 7

Phase (open circles) and amplitude modulation (filled circles) characteristics of the LCSLM for a He–Ne laser (632.8 nm).

Fig. 8
Fig. 8

Schematic illustration of the experimental configuration using the LCSLM.

Fig. 9
Fig. 9

Optimized kinoform (a) reconstructed and (b) reconstructed intensity with the use of the LCSLM (see Fig. 5). The phase quantization level is L = 16.

Equations (7)

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

U ( u , v ) = exp [ i θ ( u , v ) ] ,
θ ( u , v ) = 2 n π L ,             n = 0 , 1 , , L - 1 ,
I ( x , y ) = | U ( u , v ) exp [ - 2 π i λ f ( u x + v y ) d u d v ] | 2 ,
E = I 0 ( x , y ) - α I ( x , y ) 2 d x d y ,
α = I 0 ( x , y ) d x d y I ( x , y ) d x d y .
P ( Δ E ) = exp ( - Δ E T ) ,
T = T 0 1 + t ,

Metrics