Abstract

We describe a Talbot array illuminator made of cascaded binary phase plates located at fractional Talbot distances. We compare the performance of such an illuminator with a conventional single-layer Talbot array illuminator in terms of compression ratio and technical feasibility.

© 1996 Optical Society of America

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References

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  1. M. J. Murdocca, A. Huang, J. Jahns, N. Streibl, “Optical design of programmable logic arrays,” Appl. Opt. 27, 1651–1660 (1988).
  2. F. A. P. Tooley, S. Wakelin, “Design of a symmetric self-electro-optic-effect cellular-logic image processor,” Appl. Opt. 32, 1850–1862 (1993).
  3. A. Kalestynski, B. Smolinska, “Spatial frequency sampling by phase modulation as a method of generating multiple images,” Appl. Opt. 16, 2261–2263 (1977).
  4. N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
  5. H. Dammann, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
  6. A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).
  7. A. Lohmann, J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337–4340 (1990).
  8. J. R. Leger, G. J. Swanson, “Efficient array illuminator using binary-optics phase plates at fractional-Talbot planes,” Opt. Lett. 15, 288–290 (1990).
  9. K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–110 (1989).
  10. H. Hamam, J. L. de Bougrenet de la Tocnaye, “Efficient Fresnel transform algorithm based on fractional Fresnel diffraction,” J. Opt. Soc. Am. A 12, 1920–1931 (1995).
  11. V. Arrizon, J. Ojeda-Castaneda, “Binary phase grating for array generation at 1/16 of Talbot length,” J. Opt. Soc. Am. A 12, 801–804 (1995).
  12. P. Berthelé, H. Hamam, J. L. de Bougrenet de la Tocnaye, “Programmable computer generated holograms using ferroelectric liquid cristal materials as phase modulators,” Ferroelectrics (to be published).

1995 (2)

1993 (1)

1990 (2)

1989 (2)

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–110 (1989).

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

1988 (2)

M. J. Murdocca, A. Huang, J. Jahns, N. Streibl, “Optical design of programmable logic arrays,” Appl. Opt. 27, 1651–1660 (1988).

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

1977 (1)

1971 (1)

H. Dammann, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).

Arrizon, V.

Berthelé, P.

P. Berthelé, H. Hamam, J. L. de Bougrenet de la Tocnaye, “Programmable computer generated holograms using ferroelectric liquid cristal materials as phase modulators,” Ferroelectrics (to be published).

Campbell, R. J.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Dammann, H.

H. Dammann, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).

de Bougrenet de la Tocnaye, J. L.

H. Hamam, J. L. de Bougrenet de la Tocnaye, “Efficient Fresnel transform algorithm based on fractional Fresnel diffraction,” J. Opt. Soc. Am. A 12, 1920–1931 (1995).

P. Berthelé, H. Hamam, J. L. de Bougrenet de la Tocnaye, “Programmable computer generated holograms using ferroelectric liquid cristal materials as phase modulators,” Ferroelectrics (to be published).

Dempsey, J.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Hamam, H.

H. Hamam, J. L. de Bougrenet de la Tocnaye, “Efficient Fresnel transform algorithm based on fractional Fresnel diffraction,” J. Opt. Soc. Am. A 12, 1920–1931 (1995).

P. Berthelé, H. Hamam, J. L. de Bougrenet de la Tocnaye, “Programmable computer generated holograms using ferroelectric liquid cristal materials as phase modulators,” Ferroelectrics (to be published).

Huang, A.

Jahns, J.

Kalestynski, A.

Lebreton, G.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Leger, J. R.

Lohmann, A.

Mathew, J. G. H.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Murdocca, M. J.

Ojeda-Castaneda, J.

Patorski, K.

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–110 (1989).

Redmond, I.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Smith, S. D.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Smolinska, B.

Streibl, N.

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

M. J. Murdocca, A. Huang, J. Jahns, N. Streibl, “Optical design of programmable logic arrays,” Appl. Opt. 27, 1651–1660 (1988).

Swanson, G. J.

Taghizadeh, M. R.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Thomas, J. A.

Tooley, F. A. P.

Wakelin, S.

Walker, A. C.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Appl. Opt. (4)

J. Mod. Opt. (1)

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

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

Opt. Commun. (1)

H. Dammann, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).

Opt. Eng. (1)

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Opt. Lett. (1)

Prog. Opt. (1)

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–110 (1989).

Other (1)

P. Berthelé, H. Hamam, J. L. de Bougrenet de la Tocnaye, “Programmable computer generated holograms using ferroelectric liquid cristal materials as phase modulators,” Ferroelectrics (to be published).

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Figures (6)

Fig. 1
Fig. 1

Binary Talbot AIL operating at the fractional Talbot distance (1/6)Z T .

Fig. 2
Fig. 2

Two-layer AIL with the fractional Talbot distance (1/6)Z T (T c = 9).

Fig. 3
Fig. 3

Two-layer AIL with the fractional Talbot distances (1/6)Z T and (1/4)Z T (T c = 6).

Fig. 4
Fig. 4

Response of a two-layer array illuminator based on the quarter Talbot effect: (a) the intensity in the quarter Talbot plane and (b) the corresponding profile.

Fig. 5
Fig. 5

Optical setup for image replication based on the MAIL principle.

Fig. 6
Fig. 6

Experimental results of image replication based on the MAIL principle: (a) the reconstruction of the original hologram and (b) the replication of the original pattern by the MAIL.

Tables (1)

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Table 1 Talbot Coefficients of Lower Fractional Orders

Equations (17)

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h ( x , z ) = h ( x ) t f ( p , q , x ) ,
t f ( p , q , x ) = a = 0 q / 2 - 1 T ( a , p , q ) δ ( x - d 2 + 2 a d q ) , T ( a , p , q ) = 2 q b = 0 q / 2 - 1 exp [ - i π ( 2 b 2 q p + b ) ] exp ( i π 4 b a q ) .
t f ( p , q , x ) = a = 0 q - 1 T ( a , p , q ) δ ( x - a d q ) , T ( a , p , q ) = 1 q b = 0 q - 1 exp [ - i 2 π ( b 2 q p ) ] exp ( i 2 π b a q ) ,
T ( a p , p , q ) = exp [ i π a ( 2 a q p - 1 ) ] T ( 0 , p , q ) .
T ( 2 a p , p , q ) = exp ( i 2 π a 2 q p ) T ( 0 , p , q ) .
T ( a , 1 , q ) = 2 q exp [ i π a ( 2 a q - 1 ) ] exp ( - i π 4 ) .
a = 0 q / 2 - 1 | h ( x + a 2 d q , 0 ) | 2 = a = 0 q / 2 - 1 | h ( x + a 2 d q , p q Z T ) | 2 = E .
h ( x - d 2 + a 2 d q ) = 2 / q T ( a , p , q ) .
h ( x - d 2 + a 2 d q ) = 2 / q exp [ i π a ( 2 a q p - 1 ) ] T ( 0 , p , q ) .
h ( x - d 2 + a 2 d q ) = exp [ - i π a ( 2 a q p - 1 ) ] .
h ( x + 2 a d q ) = exp ( - i 2 π a 2 q p )
K q 2 .
K q + 1 2 .
T ( a , p , q ) = 1 q b = 0 q - 1 t ( a , b , p , q ) , t ( a , b , p , q ) = exp [ - i 2 π ( b 2 q p ) ] exp ( i 2 π b a q ) .
T ( a p , p , q ) = 2 q b = 0 q / 2 - 1 t ( a p , b , p , q ) = 2 q b = 0 q / 2 - 1 t ( a p , a - b , p , q ) ,
t ( a p , a - b , p , q ) = exp - i π [ 2 ( a - b ) 2 q p + a - b ] × exp [ i 2 π 2 ( a - b ) a q p ] = exp [ i π a ( 2 a q p - 1 ) ] t ( 0 , b , p , q ) ,
T ( a p , p , q ) = exp [ i π a ( 2 a q p - 1 ) ] T ( 0 , p , q ) .

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