Abstract

Analog spatial-filtering techniques are applied to the restoration of images degraded by propagation through random media. The image-forming system is assumed to be linear and stationary so that optically dividing the degraded image spectrum by the degrading transfer function suppresses the degradation. Images are stored and filters fabricated by controlled photographic methods. Preliminary experimental results have successfully demonstrated the feasibility of this filtering technique. In particular, degradations produced by cosine fringes and hot turbulent air were suppressed and enhanced images obtained.

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  1. J. L. Harris, J. Opt. Soc. Am. 54, 606 (1964).
  2. J. L. Harris, J. Opt. Soc. Am. 54, 931 (1964).
  3. J. L. Harris, J. Opt. Soc. Am. 56, 569 (1966).
  4. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
  5. G. O. Reynolds and T. J. Skinner, J. Opt. Soc. Am. 54, 1302 (1964).
  6. G. B. Parrent, Jr., R. A. Shore, and T. J. Skinner, J. Math. Phys. 34, 678 (1962).
  7. M. J. Beran, J. Opt. Soc. Am. 56, 1475 (1966).
  8. M. J. Beran and G. B. Parrent, Jr., The Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964).
  9. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Npw York, 1964), 2nd ed., Ch. 10,
  10. L. R. Baker, Proc. Phys. Soc. (London) B66, 975 (1953).
  11. B. J. Thompson and E. Wolf, J. Opt. Soc. Am. 47, 895 (1957); 48, 95 (1958).
  12. E. L. Bouche and P. F. Kellen, J. Opt. Soc. Am. 53, 1350A (1963).
  13. E. L. O'Neill, IRE Trans. Information Theory IT-2, 56 (1956).
  14. A. Maréchal and P. Croce, Compt. Rend. 237, 607 (1953).
  15. J. Tsujiuchi, in Progress in Optics II, E. Wolf, Ed. (North-Holland Publishing Co., Amsterdam, 1963).
  16. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill Book Co., New York, 1962), p. 37.
  17. L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, IRE Trans. Inform. Theory IT-6, 386 (1960).
  18. A. Vander Lugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).
  19. The illumination need be spatially coherent only over intervals larger than the impulse response.
  20. The delta functions used here are not rigorously justified because, strictly speaking, the integration could not proceed over infinite limits since the cosine field is limited by the lens aperture. Thus, the lens spread function should actually be convolved about each delta function. Omitting this step keeps the notation simple without sacrificing any vital information.
  21. D. G. Falconer, Phot. Sci. Eng. 10, 133 (1966).
  22. R. F. van Ligten, J. Opt. Soc. Am. 56, 1 (1966).

van Ligten, R. F.

R. F. van Ligten, J. Opt. Soc. Am. 56, 1 (1966).

Vander Lugt, A.

A. Vander Lugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).

Baker, L. R.

L. R. Baker, Proc. Phys. Soc. (London) B66, 975 (1953).

Beran, M. J.

M. J. Beran, J. Opt. Soc. Am. 56, 1475 (1966).

M. J. Beran and G. B. Parrent, Jr., The Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Npw York, 1964), 2nd ed., Ch. 10,

Bouche, E. L.

E. L. Bouche and P. F. Kellen, J. Opt. Soc. Am. 53, 1350A (1963).

Croce, P.

A. Maréchal and P. Croce, Compt. Rend. 237, 607 (1953).

Cutrona, L. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, IRE Trans. Inform. Theory IT-6, 386 (1960).

Falconer, D. G.

D. G. Falconer, Phot. Sci. Eng. 10, 133 (1966).

Harris, J. L.

J. L. Harris, J. Opt. Soc. Am. 54, 606 (1964).

J. L. Harris, J. Opt. Soc. Am. 54, 931 (1964).

J. L. Harris, J. Opt. Soc. Am. 56, 569 (1966).

Hufnagel, R. E.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Kellen, P. F.

E. L. Bouche and P. F. Kellen, J. Opt. Soc. Am. 53, 1350A (1963).

Leith, E. N.

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, IRE Trans. Inform. Theory IT-6, 386 (1960).

Maréchal, A.

A. Maréchal and P. Croce, Compt. Rend. 237, 607 (1953).

O’Neill, E. L.

E. L. O'Neill, IRE Trans. Information Theory IT-2, 56 (1956).

Palermo, C. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, IRE Trans. Inform. Theory IT-6, 386 (1960).

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill Book Co., New York, 1962), p. 37.

Parrent, Jr., G. B.

M. J. Beran and G. B. Parrent, Jr., The Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964).

G. B. Parrent, Jr., R. A. Shore, and T. J. Skinner, J. Math. Phys. 34, 678 (1962).

Porcello, L. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, IRE Trans. Inform. Theory IT-6, 386 (1960).

Reynolds, G. O.

G. O. Reynolds and T. J. Skinner, J. Opt. Soc. Am. 54, 1302 (1964).

Shore, R. A.

G. B. Parrent, Jr., R. A. Shore, and T. J. Skinner, J. Math. Phys. 34, 678 (1962).

Skinner, T. J.

G. B. Parrent, Jr., R. A. Shore, and T. J. Skinner, J. Math. Phys. 34, 678 (1962).

G. O. Reynolds and T. J. Skinner, J. Opt. Soc. Am. 54, 1302 (1964).

Stanley, N. R.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Thompson, B. J.

B. J. Thompson and E. Wolf, J. Opt. Soc. Am. 47, 895 (1957); 48, 95 (1958).

Tsujiuchi, J.

J. Tsujiuchi, in Progress in Optics II, E. Wolf, Ed. (North-Holland Publishing Co., Amsterdam, 1963).

Wolf, E.

B. J. Thompson and E. Wolf, J. Opt. Soc. Am. 47, 895 (1957); 48, 95 (1958).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Npw York, 1964), 2nd ed., Ch. 10,

Other

J. L. Harris, J. Opt. Soc. Am. 54, 606 (1964).

J. L. Harris, J. Opt. Soc. Am. 54, 931 (1964).

J. L. Harris, J. Opt. Soc. Am. 56, 569 (1966).

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

G. O. Reynolds and T. J. Skinner, J. Opt. Soc. Am. 54, 1302 (1964).

G. B. Parrent, Jr., R. A. Shore, and T. J. Skinner, J. Math. Phys. 34, 678 (1962).

M. J. Beran, J. Opt. Soc. Am. 56, 1475 (1966).

M. J. Beran and G. B. Parrent, Jr., The Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Npw York, 1964), 2nd ed., Ch. 10,

L. R. Baker, Proc. Phys. Soc. (London) B66, 975 (1953).

B. J. Thompson and E. Wolf, J. Opt. Soc. Am. 47, 895 (1957); 48, 95 (1958).

E. L. Bouche and P. F. Kellen, J. Opt. Soc. Am. 53, 1350A (1963).

E. L. O'Neill, IRE Trans. Information Theory IT-2, 56 (1956).

A. Maréchal and P. Croce, Compt. Rend. 237, 607 (1953).

J. Tsujiuchi, in Progress in Optics II, E. Wolf, Ed. (North-Holland Publishing Co., Amsterdam, 1963).

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill Book Co., New York, 1962), p. 37.

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, IRE Trans. Inform. Theory IT-6, 386 (1960).

A. Vander Lugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).

The illumination need be spatially coherent only over intervals larger than the impulse response.

The delta functions used here are not rigorously justified because, strictly speaking, the integration could not proceed over infinite limits since the cosine field is limited by the lens aperture. Thus, the lens spread function should actually be convolved about each delta function. Omitting this step keeps the notation simple without sacrificing any vital information.

D. G. Falconer, Phot. Sci. Eng. 10, 133 (1966).

R. F. van Ligten, J. Opt. Soc. Am. 56, 1 (1966).

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