Abstract

Binary phase elements in photoresist have been implemented which transform a uniform beam of light into an array of output light spots by means of the fractional Talbot effect. Arrays of more than 30 × 30 light spots with varying spot shapes have been achieved with compression ratios of up to 1:9.

© 1990 Optical Society of America

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References

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  1. H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  2. G. E. Lohman, A. W. Lohmann, “Optical Interconnection Network Utilizing Diffraction Gratings,” Opt. Eng. 27, 893–900 (1988).
    [CrossRef]
  3. N. Streibl, M. E. Prise, “Digital Optics: Architectures and Systems Requirements,” Phys. Status Solidi 150, 447–454 (1988).
    [CrossRef]
  4. H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
    [CrossRef]
  5. A. W. Lohmann, J. Schwider, N. Streibl, J. Thomas, “An Array Illuminator based on Phase Contrast,” Appl. Opt. 27, 2915–2921 (1988).
    [CrossRef] [PubMed]
  6. A. W. Lohmann, F. Sauer, “Holographic Telescope Arrays,” Appl. Opt. 27, 3003–3007 (1988).
    [CrossRef] [PubMed]
  7. T. Kubota, M. Takeda, “Array Illuminator Using Grating Couplers,” Opt. Lett. 14, 651–652 (1989).
    [CrossRef] [PubMed]
  8. N. Streibl, “Beam Shaping with Optical Array Generators,” J. Mod. Opt. 36, 1559–1573 (1989).
    [CrossRef]
  9. A. Lohmann, “An Array Illuminator Based on the Talbot Effect,” Optik 79, 41–45 (1988).
  10. W. H. F. Talbot, “Facts Relating to Optical Science, No. IV,” Philos. Mag. 9, 401–407 (1836).
  11. J. T. Winthrop, C. R. Worthington, “Theory of Fresnel Images: I,” J. Opt. Soc. Am. 55, 373–381 (1965).
    [CrossRef]
  12. A. W. Lohmann, Optical Information Processing (Uttenreuth, F.R. Germany, 1986).
  13. H. Dammann, G. Groh, M. Kock, “Restoration of Faulty Images of Periodic Objects by Means of Self-Imaging,” Appl. Opt. 10, 1454–1455 (1971).
    [CrossRef] [PubMed]
  14. D. E. Silva, “A Simple Interferometric Method of Beam Collimation,” Appl. Opt. 10, 1980–1982 (1971).
    [CrossRef]
  15. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).
  16. Y. Cohen-Sabban, D. Joyeux, “Aberration-Free Non-Paraxial Self-Imaging,” J. Opt. Soc. Am. 73, 707–719 (1983).
    [CrossRef]

1989 (2)

T. Kubota, M. Takeda, “Array Illuminator Using Grating Couplers,” Opt. Lett. 14, 651–652 (1989).
[CrossRef] [PubMed]

N. Streibl, “Beam Shaping with Optical Array Generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

1988 (5)

A. Lohmann, “An Array Illuminator Based on the Talbot Effect,” Optik 79, 41–45 (1988).

G. E. Lohman, A. W. Lohmann, “Optical Interconnection Network Utilizing Diffraction Gratings,” Opt. Eng. 27, 893–900 (1988).
[CrossRef]

N. Streibl, M. E. Prise, “Digital Optics: Architectures and Systems Requirements,” Phys. Status Solidi 150, 447–454 (1988).
[CrossRef]

A. W. Lohmann, J. Schwider, N. Streibl, J. Thomas, “An Array Illuminator based on Phase Contrast,” Appl. Opt. 27, 2915–2921 (1988).
[CrossRef] [PubMed]

A. W. Lohmann, F. Sauer, “Holographic Telescope Arrays,” Appl. Opt. 27, 3003–3007 (1988).
[CrossRef] [PubMed]

1983 (1)

1977 (1)

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

1971 (3)

1965 (1)

1836 (1)

W. H. F. Talbot, “Facts Relating to Optical Science, No. IV,” Philos. Mag. 9, 401–407 (1836).

Cohen-Sabban, Y.

Dammann, H.

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

H. Dammann, G. Groh, M. Kock, “Restoration of Faulty Images of Periodic Objects by Means of Self-Imaging,” Appl. Opt. 10, 1454–1455 (1971).
[CrossRef] [PubMed]

Gortler, K.

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Groh, G.

Joyeux, D.

Klotz, E.

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Kock, M.

Kubota, T.

Lohman, G. E.

G. E. Lohman, A. W. Lohmann, “Optical Interconnection Network Utilizing Diffraction Gratings,” Opt. Eng. 27, 893–900 (1988).
[CrossRef]

Lohmann, A.

A. Lohmann, “An Array Illuminator Based on the Talbot Effect,” Optik 79, 41–45 (1988).

Lohmann, A. W.

A. W. Lohmann, F. Sauer, “Holographic Telescope Arrays,” Appl. Opt. 27, 3003–3007 (1988).
[CrossRef] [PubMed]

G. E. Lohman, A. W. Lohmann, “Optical Interconnection Network Utilizing Diffraction Gratings,” Opt. Eng. 27, 893–900 (1988).
[CrossRef]

A. W. Lohmann, J. Schwider, N. Streibl, J. Thomas, “An Array Illuminator based on Phase Contrast,” Appl. Opt. 27, 2915–2921 (1988).
[CrossRef] [PubMed]

A. W. Lohmann, Optical Information Processing (Uttenreuth, F.R. Germany, 1986).

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Prise, M. E.

N. Streibl, M. E. Prise, “Digital Optics: Architectures and Systems Requirements,” Phys. Status Solidi 150, 447–454 (1988).
[CrossRef]

Sauer, F.

Schwider, J.

Silva, D. E.

Streibl, N.

N. Streibl, “Beam Shaping with Optical Array Generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

A. W. Lohmann, J. Schwider, N. Streibl, J. Thomas, “An Array Illuminator based on Phase Contrast,” Appl. Opt. 27, 2915–2921 (1988).
[CrossRef] [PubMed]

N. Streibl, M. E. Prise, “Digital Optics: Architectures and Systems Requirements,” Phys. Status Solidi 150, 447–454 (1988).
[CrossRef]

Takeda, M.

Talbot, W. H. F.

W. H. F. Talbot, “Facts Relating to Optical Science, No. IV,” Philos. Mag. 9, 401–407 (1836).

Thomas, J.

Winthrop, J. T.

Worthington, C. R.

Appl. Opt. (4)

J. Mod. Opt. (1)

N. Streibl, “Beam Shaping with Optical Array Generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Acta (1)

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Opt. Commun. (1)

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Opt. Eng. (1)

G. E. Lohman, A. W. Lohmann, “Optical Interconnection Network Utilizing Diffraction Gratings,” Opt. Eng. 27, 893–900 (1988).
[CrossRef]

Opt. Lett. (1)

Optik (1)

A. Lohmann, “An Array Illuminator Based on the Talbot Effect,” Optik 79, 41–45 (1988).

Philos. Mag. (1)

W. H. F. Talbot, “Facts Relating to Optical Science, No. IV,” Philos. Mag. 9, 401–407 (1836).

Phys. Status Solidi (1)

N. Streibl, M. E. Prise, “Digital Optics: Architectures and Systems Requirements,” Phys. Status Solidi 150, 447–454 (1988).
[CrossRef]

Other (2)

A. W. Lohmann, Optical Information Processing (Uttenreuth, F.R. Germany, 1986).

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

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Figures (4)

Fig. 1
Fig. 1

Fundamental principle of the Talbot AIL with a binary phase grating as the input. The fractional imaging distance is z = N · ZT + (P/Q)ZT: d, grating period; w, width of the phase step; φo, phase step of the phase grating.

Fig. 2
Fig. 2

Direct photographs showing half of the respective Talbot AIL outputs: left, configuration with 1:4 compression; right, configuration with 1:9 compression.

Fig. 3
Fig. 3

Enlarged view of Talbot AIL outputs scanned with a CCD camera. Intensity distribution along one scan line is plotted in the upper half: (a) configuration with 1:4 compression and (b) configuration with 1:9 compression.

Fig. 4
Fig. 4

Demonstration of the self-restoring effect of the Talbot AIL (using the Ronchi ruled configuration). Artificial defect is a Plexiglas rod (ϕ = 1 mm); (b) at the primary imaging plane (z = ¼ZTy = 18 cm); (c) at the third imaging plane (z = 1¼ZTy = 90 cm).

Equations (16)

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U 0 ( x ) = ( m ) C m · exp ( 2 π imx / d ) ,
D m ( z ) = C m · exp [ - 2 π i m 2 ( z / Z T ) ] .
A m = ( w / d ) sinc [ m ( w / d ) ] ,
C 0 = 1 + ( w / d ) [ exp ( i φ 0 ) - 1 ] ,
C m = ( w / d ) [ exp ( i φ 0 ) - 1 ] · sinc [ m ( w / d ) ] .
D o ( z ) = D o ( O ) = C o .
D m ( z = ¼ Z T ) = - i · C m ( m 0 ) ,
D m ( z = Z T ) = exp [ - i 2 π / 3 ] · C m ( m 0 ) .
u o ( x ) = c o + Δ u ( x ) .
u ( x , z ) = Σ D m ( z ) exp [ 2 π imx / d ] .
u ( x , ¼ Z T ) = c o - i Δ u ( x ) ,
u ( x , Z T ) = c o + exp ( - i 2 π / 3 ) Δ u ( x ) .
u ( x , ¼ Z T ) 2 = 2 or 0.
u ( x , y , ¼ Z T ) 2 = 4 or 0.
u ( x , Z T ) 2 = 3 or 0 ;
u ( x , y , Z T ) 2 = 9 or 0.

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