Abstract

Usually a hologram is produced by means of an interference experiment. Here, however, we let a computer-guided plotter draw the hologram. The plot, which has to be minified and recorded on film, contains no grey, only binary transmittance values. Our binary holograms yield reconstructed images of a quality equal to that of images obtained from usual holograms of comparable dimensions. When a Fourier hologram is inserted into the Fraunhofer plane of a coherent image forming system, it acts as a special type of a spatial filter, a so-called optical matched filter. Our binary matched filter is suitable for optical character recognition, the same as the usual optical matched filter introduced by Vander Lugt.

© 1966 Optical Society of America

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References

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  1. O. Lummer, F. Reiche, Die Lehre von der Bildentstehung im Mikroskop (von Ernst Abbe, Braunschweig1910); A. B. Porter, Phil. Mag. 11, 154 (1906); M. Wolfke, Ann. Physik 34, 277 (1911); Ann. Physik37, 96; Ann. Physik38, 385; Ann. Physik 39, 569 (1912); Ann. Physik 40, 194 (1913).
    [CrossRef]
  2. A. Vander Lugt, Proc. IEEE IT-10, 139 (1964): A. Kozma, D. L. Kelly, Appl. Opt. 4, 387 (1965): A. Vander Lugt, F. B. Rotz, A. Klooster, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanderburgh, Eds. (MIT Press, Cambridge, Mass., 1965), p. 125: E. N. Leith, A. Kozma, J. Upatneiks, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanderburgh, Eds. (MIT Press, Cambridge, Mass., 1965), p. 143.
    [CrossRef]
  3. A. Marechal, P. Croce, Compt. Rend. Acad. Sci. (Paris) 237, 607 (1953); E. L. O’Neill, Proc. Inst. Radio Engrs. IT-2, 56 (1956); and J. Tsujiuchi, in Progress in Optics, E. Wolf, Ed., Vol. 2, p. 133 (1963).
    [CrossRef]
  4. D. Hauk, A. Lohmann, Optik 15, 275 (1958).
  5. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962); J. Opt. Soc. Am. 53, 1377 (1963); J. Opt. Soc. Am. 54, 1295 (1964).
    [CrossRef]
  6. H. S. Black, Modulation Theory (D. Van Nostrand Co., Inc., New York, 1953).

1964 (1)

A. Vander Lugt, Proc. IEEE IT-10, 139 (1964): A. Kozma, D. L. Kelly, Appl. Opt. 4, 387 (1965): A. Vander Lugt, F. B. Rotz, A. Klooster, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanderburgh, Eds. (MIT Press, Cambridge, Mass., 1965), p. 125: E. N. Leith, A. Kozma, J. Upatneiks, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanderburgh, Eds. (MIT Press, Cambridge, Mass., 1965), p. 143.
[CrossRef]

1962 (1)

1958 (1)

D. Hauk, A. Lohmann, Optik 15, 275 (1958).

1953 (1)

A. Marechal, P. Croce, Compt. Rend. Acad. Sci. (Paris) 237, 607 (1953); E. L. O’Neill, Proc. Inst. Radio Engrs. IT-2, 56 (1956); and J. Tsujiuchi, in Progress in Optics, E. Wolf, Ed., Vol. 2, p. 133 (1963).
[CrossRef]

Black, H. S.

H. S. Black, Modulation Theory (D. Van Nostrand Co., Inc., New York, 1953).

Croce, P.

A. Marechal, P. Croce, Compt. Rend. Acad. Sci. (Paris) 237, 607 (1953); E. L. O’Neill, Proc. Inst. Radio Engrs. IT-2, 56 (1956); and J. Tsujiuchi, in Progress in Optics, E. Wolf, Ed., Vol. 2, p. 133 (1963).
[CrossRef]

Hauk, D.

D. Hauk, A. Lohmann, Optik 15, 275 (1958).

Leith, E. N.

Lohmann, A.

D. Hauk, A. Lohmann, Optik 15, 275 (1958).

Lummer, O.

O. Lummer, F. Reiche, Die Lehre von der Bildentstehung im Mikroskop (von Ernst Abbe, Braunschweig1910); A. B. Porter, Phil. Mag. 11, 154 (1906); M. Wolfke, Ann. Physik 34, 277 (1911); Ann. Physik37, 96; Ann. Physik38, 385; Ann. Physik 39, 569 (1912); Ann. Physik 40, 194 (1913).
[CrossRef]

Marechal, A.

A. Marechal, P. Croce, Compt. Rend. Acad. Sci. (Paris) 237, 607 (1953); E. L. O’Neill, Proc. Inst. Radio Engrs. IT-2, 56 (1956); and J. Tsujiuchi, in Progress in Optics, E. Wolf, Ed., Vol. 2, p. 133 (1963).
[CrossRef]

Reiche, F.

O. Lummer, F. Reiche, Die Lehre von der Bildentstehung im Mikroskop (von Ernst Abbe, Braunschweig1910); A. B. Porter, Phil. Mag. 11, 154 (1906); M. Wolfke, Ann. Physik 34, 277 (1911); Ann. Physik37, 96; Ann. Physik38, 385; Ann. Physik 39, 569 (1912); Ann. Physik 40, 194 (1913).
[CrossRef]

Upatnieks, J.

Vander Lugt, A.

A. Vander Lugt, Proc. IEEE IT-10, 139 (1964): A. Kozma, D. L. Kelly, Appl. Opt. 4, 387 (1965): A. Vander Lugt, F. B. Rotz, A. Klooster, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanderburgh, Eds. (MIT Press, Cambridge, Mass., 1965), p. 125: E. N. Leith, A. Kozma, J. Upatneiks, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanderburgh, Eds. (MIT Press, Cambridge, Mass., 1965), p. 143.
[CrossRef]

Compt. Rend. Acad. Sci. (Paris) (1)

A. Marechal, P. Croce, Compt. Rend. Acad. Sci. (Paris) 237, 607 (1953); E. L. O’Neill, Proc. Inst. Radio Engrs. IT-2, 56 (1956); and J. Tsujiuchi, in Progress in Optics, E. Wolf, Ed., Vol. 2, p. 133 (1963).
[CrossRef]

J. Opt. Soc. Am. (1)

Optik (1)

D. Hauk, A. Lohmann, Optik 15, 275 (1958).

Proc. IEEE (1)

A. Vander Lugt, Proc. IEEE IT-10, 139 (1964): A. Kozma, D. L. Kelly, Appl. Opt. 4, 387 (1965): A. Vander Lugt, F. B. Rotz, A. Klooster, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanderburgh, Eds. (MIT Press, Cambridge, Mass., 1965), p. 125: E. N. Leith, A. Kozma, J. Upatneiks, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanderburgh, Eds. (MIT Press, Cambridge, Mass., 1965), p. 143.
[CrossRef]

Other (2)

O. Lummer, F. Reiche, Die Lehre von der Bildentstehung im Mikroskop (von Ernst Abbe, Braunschweig1910); A. B. Porter, Phil. Mag. 11, 154 (1906); M. Wolfke, Ann. Physik 34, 277 (1911); Ann. Physik37, 96; Ann. Physik38, 385; Ann. Physik 39, 569 (1912); Ann. Physik 40, 194 (1913).
[CrossRef]

H. S. Black, Modulation Theory (D. Van Nostrand Co., Inc., New York, 1953).

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Figures (6)

Fig. 1
Fig. 1

Fraunhofer diffraction with the complex filter F as diffraction object and μ as diffraction pattern. This setup can serve also for the readout of the Fraunhofer hologram F, yielding a reconstructed image μ.

Fig. 2
Fig. 2

The detour phase. The two lower grating slits are slightly out of position. Therefore, the complex amplitudes in these slits lag behind in phase, causing a deformation of the wave front.

Fig. 3
Fig. 3

Three ways for constructing the cell (n,m). The parameters W and p that control amplitude and phase of the light emerging from this cell carry indices (n,m). The slit width c is a constant. Cases b and c are particularly suitable for automatic plotting.

Fig. 4
Fig. 4

Two matched filters or Fraunhofer holograms for E: (a) according to Fig. 3(a); (b) according to Fig. 3(b).

Fig. 5
Fig. 5

Filter output or image reconstruction from filter in Fig. 4(a).

Fig. 6
Fig. 6

Character recognition by matched filtering with nine input letters and E filter from Fig. 4(a). The B–E correlation was measured to be 81% of the E–E autocorrelation.

Equations (3)

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F ( ν x , ν y ) = u ( x , y ) e - 2 π i ( x ν x + y ν y ) d x d y .
( m + τ ) Δ ν ( m + 1 2 ) Δ ν d ν y ( n + p - W / 2 ) Δ ν ( n + p + W / 2 ) Δ ν e - 2 π i x 0 ν x d ν x = Δ ν / π x 0 sin ( π x 0 W Δ ν ) e - 2 π i x 0 ( n + p ) Δ ν .
A = [ ( Δ ν ) 2 / π N ] 2 sin ( π N c ) cos ( π N W )             [ to Fig . 3 ( b ) ] A = [ ( Δ ν ) 2 / π N ] W sin ( π N c )             [ to Fig . 3 ( c ) ] .

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