Abstract

An optical system constructed around a dynamic diffractive optic element, a ferroelectric liquid-crystal spatial light modulator in binary phase-only modulation mode, is investigated. The spatial light modulator is successively adjusted according to the direct binary search technique to diffract an incoming laser light beam into a predecided intensity distribution by use of feed back from the diffracted light. It was found that the feedback signal was noisy and that vibrations and limited bistability in the spatial light modulator’s pixels were the main noise sources. The final diffraction efficiency depends on the degree of noise in the feedback signal, but even under fairly noisy conditions the iterations were found to converge properly.

© 1997 Optical Society of America

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References

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  2. J. A. Neff, R. A. Athale, S. H. Lee, “Two-Dimensional Spatial Light Modulators: A Tutorial,” Proc. IEEE 78, 826–855 (1990).
    [CrossRef]
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  12. T. Matuszczyk, “Multiplexing methods for surface-stabilized ferroelectric liquid crystal devices,” Ph.D. Dissertation (Chalmers University of Technology, Göteborg, Sweden, 1995).
  13. B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Efficient design of direct-binary-search computer-generated holograms,” J. Opt. Soc. Am. A 8, 652–660 (1991).
    [CrossRef]

1996

1994

1992

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing. Observation of metastable states,” J. Mod. Opt. 39, 2531–2539 (1992).
[CrossRef]

1991

1990

J. A. Neff, R. A. Athale, S. H. Lee, “Two-Dimensional Spatial Light Modulators: A Tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

1987

1972

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Allebach, J. P.

Athale, R. A.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-Dimensional Spatial Light Modulators: A Tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Bengtsson, J.

Crossland, W. A.

Dames, M. P.

Dowling, S. J.

Farn, M. W.

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” in Computer and Optically Generated Holographic Optics, Vol. IV, I. Cindrich, S. H. Lee, eds., Proc. SPIE34–42 (1991).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 172–216.

Hall, T. J.

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing. Observation of metastable states,” J. Mod. Opt. 39, 2531–2539 (1992).
[CrossRef]

Jennison, B. K.

Kirk, A. G.

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing. Observation of metastable states,” J. Mod. Opt. 39, 2531–2539 (1992).
[CrossRef]

Lee, S. H.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-Dimensional Spatial Light Modulators: A Tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Löfving, B.

Matuszczyk, T.

T. Matuszczyk, “Multiplexing methods for surface-stabilized ferroelectric liquid crystal devices,” Ph.D. Dissertation (Chalmers University of Technology, Göteborg, Sweden, 1995).

McKee, P.

Mears, R. J.

Neff, J. A.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-Dimensional Spatial Light Modulators: A Tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

O’Brien, D. C.

Paige, E. G. S.

E. G. S. Paige, R. H. Scarbrough, G. G. Yang, “Feedback generated holograms,” Electron. Lett. 30, 1174–1175 (1994).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Scarbrough, R. H.

E. G. S. Paige, R. H. Scarbrough, G. G. Yang, “Feedback generated holograms,” Electron. Lett. 30, 1174–1175 (1994).
[CrossRef]

Seldowitz, M. A.

Sweeney, D. W.

Wilkinson, T. D.

Wood, D.

Yang, G. G.

E. G. S. Paige, R. H. Scarbrough, G. G. Yang, “Feedback generated holograms,” Electron. Lett. 30, 1174–1175 (1994).
[CrossRef]

Appl. Opt.

Electron. Lett.

E. G. S. Paige, R. H. Scarbrough, G. G. Yang, “Feedback generated holograms,” Electron. Lett. 30, 1174–1175 (1994).
[CrossRef]

J. Mod. Opt.

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing. Observation of metastable states,” J. Mod. Opt. 39, 2531–2539 (1992).
[CrossRef]

J. Opt. Soc. Am. A

Optik (Stuttgart)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Proc. IEEE

J. A. Neff, R. A. Athale, S. H. Lee, “Two-Dimensional Spatial Light Modulators: A Tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 172–216.

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” in Computer and Optically Generated Holographic Optics, Vol. IV, I. Cindrich, S. H. Lee, eds., Proc. SPIE34–42 (1991).
[CrossRef]

T. Matuszczyk, “Multiplexing methods for surface-stabilized ferroelectric liquid crystal devices,” Ph.D. Dissertation (Chalmers University of Technology, Göteborg, Sweden, 1995).

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Figures (7)

Fig. 1
Fig. 1

Optical system with its feedback loop.

Fig. 2
Fig. 2

Recorded speckle intensity pattern on the CCD camera in the diffraction plane.

Fig. 3
Fig. 3

Calculated standard deviation per pixel from the 100 captured CCD camera pictures shown in Fig. 2.

Fig. 4
Fig. 4

Diffraction plane image after 200,000 iterations in the feedback loop.

Fig. 5
Fig. 5

Cross-correlation improvement during optical and simulated iterations of the diffraction pattern shown in Fig. 4.

Fig. 6
Fig. 6

Optically iterated binary phase on the SLM.

Fig. 7
Fig. 7

Computer calculated ideal binary phase.

Tables (1)

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Table 1 Noise Estimates from Different Optical Systems

Equations (6)

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e=U-Uref4,
σnoise=σmin+σmaxĨk,lαD˜k,lβ,
Ĩk,l=Ik,lImax, D˜k,l=Ĩk+1,l-Ĩk,l2+Ĩk,l+1-Ĩk,l2, α=0.1, β=1.0, σmin=1.0, σmax25.
σ=kxk-x˜2N-11/2,
x˜=k xkN,
RN= U2Uref2 U41/2 Uref41/2,

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