Abstract

It is proposed and experimentally demonstrated that a multilevel or even continuous-level phase-only computer-generated hologram can be realized by use of a binary (two-level) structure. The desired phase shift is invoked by introduction of a lateral dislocation of a high-frequency binary grating within each of the elements that constitute the hologram. An asymmetrically distributed spot array has been generated experimentally, and a uniformity error of 6% and an efficiency of 42% have been measured.

© 1996 Optical Society of America

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References

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  1. G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).
  2. D. Prongué, H. P. Herzig, R. Dändliker, M. T. Gale, Appl. Opt. 31, 5706 (1992).
    [CrossRef] [PubMed]
  3. M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, Opt. Com-mun. 88, 37 (1992).
    [CrossRef]
  4. M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, Appl. Opt. 26, 2788 (1987).
    [CrossRef] [PubMed]
  5. J. Bengtsson, N. Eriksson, A. Larsson, Appl. Opt. 35, 801 (1996).
    [CrossRef] [PubMed]
  6. G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).
  7. M. C. Hutley, Diffraction Gratings (Academic, London, 1982), Chap. 6, p. 176.
  8. T. K. Gaylord, M. G. Moharam, Proc. IEEE 73, 894 (1985).
    [CrossRef]
  9. P. Blair, M. R. Taghizadeh, W. Parkes, C. D. W. Wilkinson, Appl. Opt. 34, 2406 (1995).
    [CrossRef] [PubMed]

1996

1995

1992

D. Prongué, H. P. Herzig, R. Dändliker, M. T. Gale, Appl. Opt. 31, 5706 (1992).
[CrossRef] [PubMed]

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, Opt. Com-mun. 88, 37 (1992).
[CrossRef]

1989

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

1987

1985

T. K. Gaylord, M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Allebach, J. P.

Bengtsson, J.

Blair, P.

Dändliker, R.

Ekberg, M.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, Opt. Com-mun. 88, 37 (1992).
[CrossRef]

Eriksson, N.

Gale, M. T.

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Hård, S.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, Opt. Com-mun. 88, 37 (1992).
[CrossRef]

Herzig, H. P.

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, London, 1982), Chap. 6, p. 176.

Larsson, A.

Larsson, M.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, Opt. Com-mun. 88, 37 (1992).
[CrossRef]

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Parkes, W.

Prongué, D.

Seldowitz, M. A.

Swanson, G. J.

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Sweeney, D. W.

Taghizadeh, M. R.

P. Blair, M. R. Taghizadeh, W. Parkes, C. D. W. Wilkinson, Appl. Opt. 34, 2406 (1995).
[CrossRef] [PubMed]

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, Opt. Com-mun. 88, 37 (1992).
[CrossRef]

Turunen, J.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, Opt. Com-mun. 88, 37 (1992).
[CrossRef]

Vasara, A.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, Opt. Com-mun. 88, 37 (1992).
[CrossRef]

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Westerholm, J.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, Opt. Com-mun. 88, 37 (1992).
[CrossRef]

Wilkinson, C. D. W.

Appl. Opt.

Opt. Com-mun.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, Opt. Com-mun. 88, 37 (1992).
[CrossRef]

Opt. Eng.

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Proc. IEEE

T. K. Gaylord, M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Other

M. C. Hutley, Diffraction Gratings (Academic, London, 1982), Chap. 6, p. 176.

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Figures (3)

Fig. 1
Fig. 1

(a) Phase shift introduced by a surface-relief step-like structure, (b) Phase shift introduced by dislocation of grating grooves; only the – 1st-diffraction order is shown.

Fig. 2
Fig. 2

(a) Schematic diagram of the phase distribution in a phase-only CGH. Different gray levels represent different phase levels, (b) A magnified picture of the proposed CGH geometry with dislocated binary gratings for phase shifting. The dashed lines form a mesh with constant period Λ.

Fig. 3
Fig. 3

(a) Calculated phase pattern for a CGH generating the Greek letter Γ; different gray levels in the picture represent different phase levels ranging from 0 (black) to 2π (white), (b) A photograph taken by an infrared camera showing the reconstructed spot array Γ.

Equations (7)

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ϕ d = ( n 1 ) k 0 d ,
ϕ Δ = 2 π Δ / Λ ,
h ( x , y ) = R S sinc ( R x , S y ) k = M / 2 M / 2 1 l = N / 2 N / 2 1 exp ( j ϕ k l ) × exp [ j 2 π ( R x k + S y l ) ] ,
t ( u ) = 1 + [ exp ( j ϕ d ) 1 ] m = + [ ( W / Λ ) sinc ( m W / Λ ) × exp ( j 2 π m u / Λ ) ] ,
H ( u , υ ) = k = M / 2 M / 2 1 1 = N / 2 N / 2 1 { t ( u Δ k l ) × rect [ ( u k R ) / R , ( υ l S ) / S ] } ,
rect ( a , b ) = { 1 if a , b < ( 1 / 2 ) 0 otherwise .
h ( x , y ) = F { E i ( u ) H ( u , υ ) } 1 st order = R S ( W / Λ ) sinc ( W / Λ ) [ exp ( j ϕ d ) 1 ] × sinc [ R ( x + 1 / Λ sin θ / λ 0 ) , S y ] × k = M / 2 M / 2 1 l = N / 2 N / 2 1 exp ( j 2 π Δ k l / Λ ) × exp { j 2 π [ R k ( x + 1 / Λ sin θ / λ 0 ) + S l y ] } ,

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