Abstract

The setup used in many optical data processing schemes is a coherent optical image forming system. The most important element in this setup is the complex spatial filter. It can perform a large variety of linear operations upon the object or input. In general, it is difficult to produce complex filters, since both amplitude transmission and phase delay may vary across the filter plane in a complicated manner. Our own filters which are very similar to binary holograms, consist of many little transparent rectangles on opaque background. They can easily be drawn on a large scale by a computer-guided plotter, and then photographically reduced in size. We show that our filters, despite containing only amplitude values zero and one, can perform any data processing operation which could be performed by any complex filter. After explaining the principle, we present three groups of applications. First, we describe new versions of some classical methods: schlieren observation and phase contrast. Next, we report on spatial filters which perform differential operations upon the object in order to enhance gradients or corners. Finally, we use our binary filters for signal detection.

© 1968 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Tsujiuchi, in Progress in Optics, E. Wolf, Ed. (John Wiley & Sons, Inc., New York, 1963), Vol. 2, p. 133.
    [CrossRef]
  2. E. L. O’Neill, Inst. Radio Eng. Trans. IT-2, 56 (1956).
  3. A. Vander Lugt, Opt. Acta15(1968) to be published.
  4. B. R. Brown, A. W. Lohmann, Appl. Opt. 6, 967 (1966).
    [CrossRef]
  5. A. W. Lohmann, D. P. Paris, H. W. Werlich, Appl. Opt. 6, 1139 (1967).
    [CrossRef] [PubMed]
  6. A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 1739 (1967).
    [CrossRef] [PubMed]
  7. D. Hauk, A. Lohmann, Optik 15, 275 (1958); G. Harburn, K. Walkley, C. A. Taylor, Nature 205, 1096 (1965).
    [CrossRef]
  8. H. Wolter, Ann. Phys. 7, 341 (1950); A. Kastler, Rev. Opt. 29, 308 (1950); S. Lowenthal, Y. Belvaux, Appl. Phys. Lett. 11, 49 (1967).
    [CrossRef]
  9. E. Menzel, Opt. 5, 385 (1949).
  10. P. Jacquinot, B. Roizen-Dossier, in Progress in Optics, E. Wolf, Ed. (John Wiley & Sons, Inc., New York, 1964), Vol. 3, p. 29.
    [CrossRef]
  11. M. Françon, C. R. Acad. Sci. Paris 233, 1176 (1951); Rev. Opt. 31, 65 (1952).
  12. G. Nomarski, Brev. Fr., Nr. 1057 486, 1059 123 (May1952); J. Phys. 15, 265 (1954); A. Lohmann, Opt. 11, 478 (1954).
  13. J. E. Rhodes, J. Opt. Soc. Amer. 43, 848 (1953).
    [CrossRef]
  14. E. A. Trabka, P. G. Roetling, J. Opt. Soc. Amer. 52, 454 (1962).
    [CrossRef]
  15. S. Lowenthal, Y. Belvaux, C. R. Acad. Sci. Paris B262, 413 (1966); Opt. Acta 14, 245 (1967).
  16. A. Maréchal, P. Croce, C. R. Acad. Sci. Paris 237, 607 (1953).
  17. P. F. Mueller, G. O. Reynolds, J. Opt. Soc. Amer. 56, 1438A (1966); J. Opt. Soc. Amer. 57, 1338 (1967).

1967 (2)

1966 (3)

P. F. Mueller, G. O. Reynolds, J. Opt. Soc. Amer. 56, 1438A (1966); J. Opt. Soc. Amer. 57, 1338 (1967).

B. R. Brown, A. W. Lohmann, Appl. Opt. 6, 967 (1966).
[CrossRef]

S. Lowenthal, Y. Belvaux, C. R. Acad. Sci. Paris B262, 413 (1966); Opt. Acta 14, 245 (1967).

1962 (1)

E. A. Trabka, P. G. Roetling, J. Opt. Soc. Amer. 52, 454 (1962).
[CrossRef]

1958 (1)

D. Hauk, A. Lohmann, Optik 15, 275 (1958); G. Harburn, K. Walkley, C. A. Taylor, Nature 205, 1096 (1965).
[CrossRef]

1956 (1)

E. L. O’Neill, Inst. Radio Eng. Trans. IT-2, 56 (1956).

1953 (2)

J. E. Rhodes, J. Opt. Soc. Amer. 43, 848 (1953).
[CrossRef]

A. Maréchal, P. Croce, C. R. Acad. Sci. Paris 237, 607 (1953).

1952 (1)

G. Nomarski, Brev. Fr., Nr. 1057 486, 1059 123 (May1952); J. Phys. 15, 265 (1954); A. Lohmann, Opt. 11, 478 (1954).

1951 (1)

M. Françon, C. R. Acad. Sci. Paris 233, 1176 (1951); Rev. Opt. 31, 65 (1952).

1950 (1)

H. Wolter, Ann. Phys. 7, 341 (1950); A. Kastler, Rev. Opt. 29, 308 (1950); S. Lowenthal, Y. Belvaux, Appl. Phys. Lett. 11, 49 (1967).
[CrossRef]

1949 (1)

E. Menzel, Opt. 5, 385 (1949).

Belvaux, Y.

S. Lowenthal, Y. Belvaux, C. R. Acad. Sci. Paris B262, 413 (1966); Opt. Acta 14, 245 (1967).

Brown, B. R.

B. R. Brown, A. W. Lohmann, Appl. Opt. 6, 967 (1966).
[CrossRef]

Croce, P.

A. Maréchal, P. Croce, C. R. Acad. Sci. Paris 237, 607 (1953).

Françon, M.

M. Françon, C. R. Acad. Sci. Paris 233, 1176 (1951); Rev. Opt. 31, 65 (1952).

Hauk, D.

D. Hauk, A. Lohmann, Optik 15, 275 (1958); G. Harburn, K. Walkley, C. A. Taylor, Nature 205, 1096 (1965).
[CrossRef]

Jacquinot, P.

P. Jacquinot, B. Roizen-Dossier, in Progress in Optics, E. Wolf, Ed. (John Wiley & Sons, Inc., New York, 1964), Vol. 3, p. 29.
[CrossRef]

Lohmann, A.

D. Hauk, A. Lohmann, Optik 15, 275 (1958); G. Harburn, K. Walkley, C. A. Taylor, Nature 205, 1096 (1965).
[CrossRef]

Lohmann, A. W.

Lowenthal, S.

S. Lowenthal, Y. Belvaux, C. R. Acad. Sci. Paris B262, 413 (1966); Opt. Acta 14, 245 (1967).

Maréchal, A.

A. Maréchal, P. Croce, C. R. Acad. Sci. Paris 237, 607 (1953).

Menzel, E.

E. Menzel, Opt. 5, 385 (1949).

Mueller, P. F.

P. F. Mueller, G. O. Reynolds, J. Opt. Soc. Amer. 56, 1438A (1966); J. Opt. Soc. Amer. 57, 1338 (1967).

Nomarski, G.

G. Nomarski, Brev. Fr., Nr. 1057 486, 1059 123 (May1952); J. Phys. 15, 265 (1954); A. Lohmann, Opt. 11, 478 (1954).

O’Neill, E. L.

E. L. O’Neill, Inst. Radio Eng. Trans. IT-2, 56 (1956).

Paris, D. P.

Reynolds, G. O.

P. F. Mueller, G. O. Reynolds, J. Opt. Soc. Amer. 56, 1438A (1966); J. Opt. Soc. Amer. 57, 1338 (1967).

Rhodes, J. E.

J. E. Rhodes, J. Opt. Soc. Amer. 43, 848 (1953).
[CrossRef]

Roetling, P. G.

E. A. Trabka, P. G. Roetling, J. Opt. Soc. Amer. 52, 454 (1962).
[CrossRef]

Roizen-Dossier, B.

P. Jacquinot, B. Roizen-Dossier, in Progress in Optics, E. Wolf, Ed. (John Wiley & Sons, Inc., New York, 1964), Vol. 3, p. 29.
[CrossRef]

Trabka, E. A.

E. A. Trabka, P. G. Roetling, J. Opt. Soc. Amer. 52, 454 (1962).
[CrossRef]

Tsujiuchi, J.

J. Tsujiuchi, in Progress in Optics, E. Wolf, Ed. (John Wiley & Sons, Inc., New York, 1963), Vol. 2, p. 133.
[CrossRef]

Vander Lugt, A.

A. Vander Lugt, Opt. Acta15(1968) to be published.

Werlich, H. W.

Wolter, H.

H. Wolter, Ann. Phys. 7, 341 (1950); A. Kastler, Rev. Opt. 29, 308 (1950); S. Lowenthal, Y. Belvaux, Appl. Phys. Lett. 11, 49 (1967).
[CrossRef]

Ann. Phys. (1)

H. Wolter, Ann. Phys. 7, 341 (1950); A. Kastler, Rev. Opt. 29, 308 (1950); S. Lowenthal, Y. Belvaux, Appl. Phys. Lett. 11, 49 (1967).
[CrossRef]

Appl. Opt. (3)

Brev. Fr., Nr. 1057 486, 1059 123 (1)

G. Nomarski, Brev. Fr., Nr. 1057 486, 1059 123 (May1952); J. Phys. 15, 265 (1954); A. Lohmann, Opt. 11, 478 (1954).

C. R. Acad. Sci. Paris (3)

M. Françon, C. R. Acad. Sci. Paris 233, 1176 (1951); Rev. Opt. 31, 65 (1952).

S. Lowenthal, Y. Belvaux, C. R. Acad. Sci. Paris B262, 413 (1966); Opt. Acta 14, 245 (1967).

A. Maréchal, P. Croce, C. R. Acad. Sci. Paris 237, 607 (1953).

Inst. Radio Eng. Trans. (1)

E. L. O’Neill, Inst. Radio Eng. Trans. IT-2, 56 (1956).

J. Opt. Soc. Amer. (3)

J. E. Rhodes, J. Opt. Soc. Amer. 43, 848 (1953).
[CrossRef]

E. A. Trabka, P. G. Roetling, J. Opt. Soc. Amer. 52, 454 (1962).
[CrossRef]

P. F. Mueller, G. O. Reynolds, J. Opt. Soc. Amer. 56, 1438A (1966); J. Opt. Soc. Amer. 57, 1338 (1967).

Opt. (1)

E. Menzel, Opt. 5, 385 (1949).

Optik (1)

D. Hauk, A. Lohmann, Optik 15, 275 (1958); G. Harburn, K. Walkley, C. A. Taylor, Nature 205, 1096 (1965).
[CrossRef]

Other (3)

P. Jacquinot, B. Roizen-Dossier, in Progress in Optics, E. Wolf, Ed. (John Wiley & Sons, Inc., New York, 1964), Vol. 3, p. 29.
[CrossRef]

J. Tsujiuchi, in Progress in Optics, E. Wolf, Ed. (John Wiley & Sons, Inc., New York, 1963), Vol. 2, p. 133.
[CrossRef]

A. Vander Lugt, Opt. Acta15(1968) to be published.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1

Detour phase effect with arbitrary incidence.

Fig. 2
Fig. 2

Setup for schlieren observation.

Fig. 3
Fig. 3

Schlieren image.

Fig. 4
Fig. 4

Schlieren setup with lambda compensation.

Fig. 5
Fig. 5

Phase contrast filter.

Fig. 6
Fig. 6

Phase contrast image.

Fig. 7
Fig. 7

Filter for ∂u/∂x.

Fig. 8
Fig. 8

Image v = ∂u/∂x.

Fig. 9
Fig. 9

Filter for ∂2u/∂xy.

Fig. 10
Fig. 10

Image v = ∂2/∂xy.

Fig. 11
Fig. 11

Filter for gradient correlation.

Fig. 12
Fig. 12

Gradient correlation of E.

Fig. 13
Fig. 13

Inverse filter.

Fig. 14
Fig. 14

Output of inverse filter for E.

Fig. 15
Fig. 15

Output of inverse filter for E. This input was blurred with an E.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

v ˜ ( ν , μ ) = u ˜ ( ν , μ ) F ˜ ( ν , μ ) ,
u ˜ ( ν , μ ) = u ( x , y ) exp [ - 2 π i ( x ν + y μ ) ] d x d y .
L M = ( sin α M - sin α 0 ) d - M λ .
L M = ( sin α M - sin α 0 ) ( d + P ) .
Δ M = L M - L M = P ( sin α M - sin α 0 ) = P M λ / d .
φ M = 2 π Δ M / λ = 2 π M P / d .
F ˜ ( ν , μ ) = { 1 ; if ν 0 - 1 ; if ν < 0.
A ( ν , μ ) = 1 ; φ ( ν , μ ) = { 0 ; if ν 0 π ; if ν < 0.
P ( ν , μ ) = { 0 ; if ν 0 d / 2 ; if ν < 0 ; φ 1 ( ν , μ ) = 2 π P / d .
v ( x , y ) = u ( x + Δ x , y ) - u ( x , y ) [ u ( x , y ) / x ] Δ x .
F ˜ ( ν , μ ) = v ˜ ( ν , μ ) / u ˜ ( ν , μ ) = 2 π i ν Δ x ; A ( ν , μ ) = ν 2 π Δ x ; φ ( ν , μ ) = { + π / ν ; if ν 0 - π / 2 ; if ν < 0.
v = 2 u / x y ; F ˜ ( ν , μ ) = - ( 2 π ) 2 ν μ ,
F ˜ G ( ν , μ ) = - ( 2 π ) 2 ( ν 2 + μ 2 ) μ ˜ * ( ν , μ ) ;
v ( x , y ) = grad u ( x - x 0 , y - y 0 ) grad u * ( x - x , y - y ) d x d y .

Metrics