Abstract

The tandem component is a holographic component which permits generation of a general complex wave front with 100% light efficiency. It consists of two phase-only elements in two Fourier conjugate planes and of a lens. Applications of this component are discussed such as complex wave front reconstruction, beam shaping, and correlation type measurements.

© 1985 Optical Society of America

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References

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  1. J. L. Horner, “Light Utilization in Optical Correlators, Appl. Opt. 21, 4511 (1982).
    [CrossRef] [PubMed]
  2. H. J. Caulfield, “Role of the Horner Efficiency in the Optimization of Spatial Filters for Optical Pattern Recognition,” Appl. Opt. 21, 4391 (1982).
    [CrossRef] [PubMed]
  3. J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
    [CrossRef] [PubMed]
  4. A. W. Lohmann, C. Thum, “Increased Light Efficiency of Coherent-Optical Matched Filters,” Appl. Opt. 23, 1503 (1984).
    [CrossRef] [PubMed]
  5. H. Bartelt, “Computer-Generated Holographic Component with Optimum Light Efficiency,” Appl. Opt. 23, 1499 (1984).
    [CrossRef] [PubMed]
  6. J. R. Fienup, “Improved Synthesis and Computational Methods for Computer-Generated Hologams,” Thesis, Stanford U., University Microfilms No. 75-255-23 (1975).
  7. D. C. Hu, J. R. Fienup, J. W. Goodman, “Multiemulsion On-Axis Computer Generated Hologram,” Appl. Opt. 12, 1386 (1973).
    [CrossRef]
  8. L. B. Lesem, P. M. Hisch, J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
    [CrossRef]
  9. D. Kermisch, “Image Reconstruction from Phase Information Only,” J. Opt. Soc. Am. 60, 15, (1970).
    [CrossRef]
  10. H. T. Buschmann, “Bleichprozesse zur Erzeugung rauscharmer, lichtstarker Phasenhologramme,” Optik Stuttgart 34, 240 (1971).
  11. H. Bartelt, S. K. Case, “High-Efficiency Hybrid Computer-Generated Holograms,” Appl. Opt. 21, 2886 (1982).
    [CrossRef] [PubMed]
  12. P. F. Grosso, A. A. Ternowski, “Electron Beam Recording on Film—Applications and Performance,” Electro-Opt. Syst. Des. 56 (Aug.1976).
  13. J. L. Freyer, R. J. Perlmutter, J. W. Goodman, “Digital Holography: Algorithms, E-Beam Lithography and 3-D Display,” Proc. Soc. Photo-Opt. Instrum. Eng. 437, 38 (1983).
  14. W. J. Dallas, “Computer-Generated Holograms,” in The Computer in Optical Research, B. R. Frieden, Ed. (Springer-Verlag, New York, 1980), Chap. 6.
  15. H. Akahori, “Comparison of Deterministic Phase Coding with Random Phase Coding in Terms of Dynamic Range,” Appl. Opt. 12, 2336 (1973).
    [CrossRef] [PubMed]
  16. R. W. Gerchberg, W. O. Saxton, “A Practical Algorithm or the Determination of Phase from Image and Diffraction Plane Pictures,” Optik Stuttgart 35, 237 (1972).
  17. M. C. Gallagher, B. Liu, “Method for Computing Kinoforms that Reduces Image Reconstruction Error,” Appl. Opt. 12, 2328 (1973).
    [CrossRef] [PubMed]
  18. J. R. Fienup, “Iterative Method Applied to Image Reconstruction and to Computer-Generated Holograms,” Opt. Eng. 19, 297 (1980).
    [CrossRef]
  19. J. R. Fienup, “Reconstruction and Synthesis Applications of an Iterative Algorithm,” Proc. Soc. Photo-Opt. Instrum. Eng. 373, 147 (1981).
  20. W. H. Lee, “Method for Converting a Gaussian Laser Beam into a Uniform Beam,” Opt. Commun. 36, 469 (1981).
    [CrossRef]
  21. C.-Y. Han, Y. Ishii, K. Murata, “Reshaping Collimated Laser Beams with Gaussian Profile to Uniform Profiles,” Appl. Opt. 22, 3644 (1983).
    [CrossRef] [PubMed]

1984 (3)

1983 (2)

J. L. Freyer, R. J. Perlmutter, J. W. Goodman, “Digital Holography: Algorithms, E-Beam Lithography and 3-D Display,” Proc. Soc. Photo-Opt. Instrum. Eng. 437, 38 (1983).

C.-Y. Han, Y. Ishii, K. Murata, “Reshaping Collimated Laser Beams with Gaussian Profile to Uniform Profiles,” Appl. Opt. 22, 3644 (1983).
[CrossRef] [PubMed]

1982 (3)

1981 (2)

J. R. Fienup, “Reconstruction and Synthesis Applications of an Iterative Algorithm,” Proc. Soc. Photo-Opt. Instrum. Eng. 373, 147 (1981).

W. H. Lee, “Method for Converting a Gaussian Laser Beam into a Uniform Beam,” Opt. Commun. 36, 469 (1981).
[CrossRef]

1980 (1)

J. R. Fienup, “Iterative Method Applied to Image Reconstruction and to Computer-Generated Holograms,” Opt. Eng. 19, 297 (1980).
[CrossRef]

1976 (1)

P. F. Grosso, A. A. Ternowski, “Electron Beam Recording on Film—Applications and Performance,” Electro-Opt. Syst. Des. 56 (Aug.1976).

1973 (3)

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A Practical Algorithm or the Determination of Phase from Image and Diffraction Plane Pictures,” Optik Stuttgart 35, 237 (1972).

1971 (1)

H. T. Buschmann, “Bleichprozesse zur Erzeugung rauscharmer, lichtstarker Phasenhologramme,” Optik Stuttgart 34, 240 (1971).

1970 (1)

1969 (1)

L. B. Lesem, P. M. Hisch, J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Akahori, H.

Bartelt, H.

Buschmann, H. T.

H. T. Buschmann, “Bleichprozesse zur Erzeugung rauscharmer, lichtstarker Phasenhologramme,” Optik Stuttgart 34, 240 (1971).

Case, S. K.

Caulfield, H. J.

Dallas, W. J.

W. J. Dallas, “Computer-Generated Holograms,” in The Computer in Optical Research, B. R. Frieden, Ed. (Springer-Verlag, New York, 1980), Chap. 6.

Fienup, J. R.

J. R. Fienup, “Reconstruction and Synthesis Applications of an Iterative Algorithm,” Proc. Soc. Photo-Opt. Instrum. Eng. 373, 147 (1981).

J. R. Fienup, “Iterative Method Applied to Image Reconstruction and to Computer-Generated Holograms,” Opt. Eng. 19, 297 (1980).
[CrossRef]

D. C. Hu, J. R. Fienup, J. W. Goodman, “Multiemulsion On-Axis Computer Generated Hologram,” Appl. Opt. 12, 1386 (1973).
[CrossRef]

J. R. Fienup, “Improved Synthesis and Computational Methods for Computer-Generated Hologams,” Thesis, Stanford U., University Microfilms No. 75-255-23 (1975).

Freyer, J. L.

J. L. Freyer, R. J. Perlmutter, J. W. Goodman, “Digital Holography: Algorithms, E-Beam Lithography and 3-D Display,” Proc. Soc. Photo-Opt. Instrum. Eng. 437, 38 (1983).

Gallagher, M. C.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A Practical Algorithm or the Determination of Phase from Image and Diffraction Plane Pictures,” Optik Stuttgart 35, 237 (1972).

Gianino, P. D.

Goodman, J. W.

J. L. Freyer, R. J. Perlmutter, J. W. Goodman, “Digital Holography: Algorithms, E-Beam Lithography and 3-D Display,” Proc. Soc. Photo-Opt. Instrum. Eng. 437, 38 (1983).

D. C. Hu, J. R. Fienup, J. W. Goodman, “Multiemulsion On-Axis Computer Generated Hologram,” Appl. Opt. 12, 1386 (1973).
[CrossRef]

Grosso, P. F.

P. F. Grosso, A. A. Ternowski, “Electron Beam Recording on Film—Applications and Performance,” Electro-Opt. Syst. Des. 56 (Aug.1976).

Han, C.-Y.

Hisch, P. M.

L. B. Lesem, P. M. Hisch, J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Horner, J. L.

Hu, D. C.

Ishii, Y.

Jordan, J. A.

L. B. Lesem, P. M. Hisch, J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Kermisch, D.

Lee, W. H.

W. H. Lee, “Method for Converting a Gaussian Laser Beam into a Uniform Beam,” Opt. Commun. 36, 469 (1981).
[CrossRef]

Lesem, L. B.

L. B. Lesem, P. M. Hisch, J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Liu, B.

Lohmann, A. W.

Murata, K.

Perlmutter, R. J.

J. L. Freyer, R. J. Perlmutter, J. W. Goodman, “Digital Holography: Algorithms, E-Beam Lithography and 3-D Display,” Proc. Soc. Photo-Opt. Instrum. Eng. 437, 38 (1983).

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A Practical Algorithm or the Determination of Phase from Image and Diffraction Plane Pictures,” Optik Stuttgart 35, 237 (1972).

Ternowski, A. A.

P. F. Grosso, A. A. Ternowski, “Electron Beam Recording on Film—Applications and Performance,” Electro-Opt. Syst. Des. 56 (Aug.1976).

Thum, C.

Appl. Opt. (10)

Electro-Opt. Syst. Des. (1)

P. F. Grosso, A. A. Ternowski, “Electron Beam Recording on Film—Applications and Performance,” Electro-Opt. Syst. Des. 56 (Aug.1976).

IBM J. Res. Dev. (1)

L. B. Lesem, P. M. Hisch, J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

W. H. Lee, “Method for Converting a Gaussian Laser Beam into a Uniform Beam,” Opt. Commun. 36, 469 (1981).
[CrossRef]

Opt. Eng. (1)

J. R. Fienup, “Iterative Method Applied to Image Reconstruction and to Computer-Generated Holograms,” Opt. Eng. 19, 297 (1980).
[CrossRef]

Optik Stuttgart (2)

R. W. Gerchberg, W. O. Saxton, “A Practical Algorithm or the Determination of Phase from Image and Diffraction Plane Pictures,” Optik Stuttgart 35, 237 (1972).

H. T. Buschmann, “Bleichprozesse zur Erzeugung rauscharmer, lichtstarker Phasenhologramme,” Optik Stuttgart 34, 240 (1971).

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

J. R. Fienup, “Reconstruction and Synthesis Applications of an Iterative Algorithm,” Proc. Soc. Photo-Opt. Instrum. Eng. 373, 147 (1981).

J. L. Freyer, R. J. Perlmutter, J. W. Goodman, “Digital Holography: Algorithms, E-Beam Lithography and 3-D Display,” Proc. Soc. Photo-Opt. Instrum. Eng. 437, 38 (1983).

Other (2)

W. J. Dallas, “Computer-Generated Holograms,” in The Computer in Optical Research, B. R. Frieden, Ed. (Springer-Verlag, New York, 1980), Chap. 6.

J. R. Fienup, “Improved Synthesis and Computational Methods for Computer-Generated Hologams,” Thesis, Stanford U., University Microfilms No. 75-255-23 (1975).

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Figures (8)

Fig. 1
Fig. 1

Principle setup of the tandem component.

Fig. 2
Fig. 2

Kinoform reconstruction: (a) object, (b) calculated mask with phase displayed as grey level, (c) reconstruction from a bleached film.

Fig. 3
Fig. 3

Reconstruction error vs iteration steps for the object in Fig. 2(a).

Fig. 4
Fig. 4

Tandem component reconstruction: (a) object, (b) Fourier transform of first filter, (c) reconstruction, (d) object function, (e) calculated squared error.

Fig. 5
Fig. 5

Beam shaping with the tandem component: (a) input beam, (b) desired output beam intensity, (c) calculated output beam intensity, (d) experimental result.

Fig. 6
Fig. 6

Correlation type operation with the tandem component: (a) input intensity, (b) calculated output intensity, (c) experimental result.

Fig. 7
Fig. 7

Portion of a periodic first filter with phase displayed as grey level for quasi-space-invariant operation with the tandem component.

Fig. 8
Fig. 8

Correlation type operation with a periodic first phase filter: (a) simulated intensity output for a centered object, (b) simulated intensity output for an object shifted by half a period in the x direction, (c) simulated intensity output for an object shifted by one period in the x direction.

Equations (13)

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| F ( υ ) | | G ( υ ) | : for perfect recontruction , | G ( υ ) | : specified Fourier amplitude , f ( x ) = exp [ i φ ( x ) ] : kinoform element F ( υ ) = | F ( υ ) | exp [ i ψ ( υ ) ] : Fourier transform of kinoform element }
2 = 1 / A A ( | F ( υ ) | a | G ( υ ) | ) 2 d υ ,
a = A F ( υ ) G ( υ ) d υ A | G ( υ ) | 2 d υ for minimum 2 .
f ( x ) = g ( x ) | g ( x ) | ,
random diffuser 2 = 5 . 4 × 10 2 per pixel , Schroeder code 2 = 5 . 0 × 10 2 per pixel , Frank code 2 = 5 . 1 × 10 2 per pixel . }
f 1 ( x , y ) = exp [ i φ 1 ( x , y ) ] : phase filter 1 , F 1 ( υ , w ) = | F 1 ( υ , w ) | exp [ i ψ 1 ( υ , w ) ] : Fourier transform of f 1 ( x , y ) , F 2 ( υ , w ) = exp [ i ψ 2 ( υ , w ) ] : phase filter 2 , g 1 ( x , y ) = exp [ σ ( x 2 + y 2 ) ] : Gaussian beam , g 2 ( x , y ) = rect ( x Δ x ) + rect ( y Δ y ) rect ( x Δ x ) rect ( y Δ y ) × rect ( x D ) rect ( y D ) : cross pattern , G 2 ( υ , w ) = FT [ g 2 ( x , y ) ] = | G 2 ( υ , w ) | × exp [ i ψ ( υ , w ) ] : Fourier transform of g 2 ( x , y ) .
| FT [ f 1 ( x , y ) g 1 ( x , υ ) ] | = | G 2 ( υ , w ) | , FT [ f 1 ( x , y ) g 1 ( x , y ) ] F 2 ( υ , w ) = G 2 ( υ , w ) , }
η H = P | f ( x , y ) g ( x , y ) | 2 d x d y A | f ( x , y ) | 2 d x d y ,
g ( x ) = | g ( x ) | exp [ i φ g ( x ) ] : object to be detected , G ( υ ) = | G ( υ ) | exp [ i φ G ( υ ) ] : Fourier transform of object , f 1 ( x ) = exp ( i φ 1 ( x ) ] : first filter ,
F 2 ( υ ) = exp [ i φ 2 ( υ ) ] : second filter ,
R ( x ) = FT { FT [ f 1 ( x ) g ( x ) ] F 2 ( υ ) } = δ ( x ) , or [ f 1 ( x ) g ( x ) ] * f 2 ( x ) = δ ( x )
r = g b ( x ) d x + 1 g b ( x ) d x g b ( x ) d x ,
F 1 ( υ ) = 0 if υ n υ 0 , with υ 0 = υ max / 8 .

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