Abstract

A four-step phase-restoration procedure that provides faithful reconstructions of images consisting of faint detail superimposed upon bright, broad backgrounds is presented. Such images tend to cause existing phase-retrieval algorithms considerable difficulty. The two middle steps consist of the simplest of our recently reported phaserestoration schemes and of Fienup's algorithm. The first and crucial step is to subtract a fraction of the central lobe of the given intensity of the Fourier transform of the image. The image is then reconstructed in two parts, which are combined in the final step. Encouraging computational results are presented.

© 1983 Optical Society of America

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  1. Y. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979).
  2. W. Lawton, "A numerical algorithm for 2-D wavefront reconstruction from intensity measurements in a single plane," Proc. Soc. Photo-Opt. Instrum. Eng. 231, 94–98 (1980).
  3. R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: I: underlying theory," Optik 61, 247–262 (1982).
  4. C. van Schooneveld, ed., Image Formation from Coherence Functions in Astronomy (Reidel, Dordrecht, The Netherlands, 1979), Part V.
  5. J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 3,27–29 (1978); "Space object imaging through the turbulent atmosphere," Opt. Eng. 18, 529–534 (1979); "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758–2769 (1982).
  6. W. R. Fright and R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: III: computational examples for two dimensions," Optik (to be published).
  7. K. L. Garden and R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: II: one-dimensional considerations," Optik (to be published).
  8. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
  9. K. T. Knox and B. J. Thompson, "Recovery of images from atmospherically- degraded short-exposure photographs," Astrophys. J. 193, L45–L48 (1974).
  10. R. H. T. Bates and W. R. Fright, "Towards imaging with a speckle-interferometric optical synthesis telescope," Mon. Not. R. Astron. Soc. 198, 1017–1031 (1982).

1982

R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: I: underlying theory," Optik 61, 247–262 (1982).

R. H. T. Bates and W. R. Fright, "Towards imaging with a speckle-interferometric optical synthesis telescope," Mon. Not. R. Astron. Soc. 198, 1017–1031 (1982).

1980

W. Lawton, "A numerical algorithm for 2-D wavefront reconstruction from intensity measurements in a single plane," Proc. Soc. Photo-Opt. Instrum. Eng. 231, 94–98 (1980).

1979

Y. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979).

1974

K. T. Knox and B. J. Thompson, "Recovery of images from atmospherically- degraded short-exposure photographs," Astrophys. J. 193, L45–L48 (1974).

Bates, R. H. T.

R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: I: underlying theory," Optik 61, 247–262 (1982).

R. H. T. Bates and W. R. Fright, "Towards imaging with a speckle-interferometric optical synthesis telescope," Mon. Not. R. Astron. Soc. 198, 1017–1031 (1982).

W. R. Fright and R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: III: computational examples for two dimensions," Optik (to be published).

K. L. Garden and R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: II: one-dimensional considerations," Optik (to be published).

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Bruck, Y. M.

Y. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979).

Fienup, J. R.

J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 3,27–29 (1978); "Space object imaging through the turbulent atmosphere," Opt. Eng. 18, 529–534 (1979); "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758–2769 (1982).

Fright, W. R.

R. H. T. Bates and W. R. Fright, "Towards imaging with a speckle-interferometric optical synthesis telescope," Mon. Not. R. Astron. Soc. 198, 1017–1031 (1982).

W. R. Fright and R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: III: computational examples for two dimensions," Optik (to be published).

Garden, K. L.

K. L. Garden and R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: II: one-dimensional considerations," Optik (to be published).

Knox, K. T.

K. T. Knox and B. J. Thompson, "Recovery of images from atmospherically- degraded short-exposure photographs," Astrophys. J. 193, L45–L48 (1974).

Lawton, W.

W. Lawton, "A numerical algorithm for 2-D wavefront reconstruction from intensity measurements in a single plane," Proc. Soc. Photo-Opt. Instrum. Eng. 231, 94–98 (1980).

Sodin, L. G.

Y. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979).

Thompson, B. J.

K. T. Knox and B. J. Thompson, "Recovery of images from atmospherically- degraded short-exposure photographs," Astrophys. J. 193, L45–L48 (1974).

Astrophys. J.

K. T. Knox and B. J. Thompson, "Recovery of images from atmospherically- degraded short-exposure photographs," Astrophys. J. 193, L45–L48 (1974).

Mon. Not. R. Astron. Soc.

R. H. T. Bates and W. R. Fright, "Towards imaging with a speckle-interferometric optical synthesis telescope," Mon. Not. R. Astron. Soc. 198, 1017–1031 (1982).

Opt. Commun.

Y. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979).

Optik

R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: I: underlying theory," Optik 61, 247–262 (1982).

Proc. Soc. Photo-Opt. Instrum. Eng.

W. Lawton, "A numerical algorithm for 2-D wavefront reconstruction from intensity measurements in a single plane," Proc. Soc. Photo-Opt. Instrum. Eng. 231, 94–98 (1980).

Other

C. van Schooneveld, ed., Image Formation from Coherence Functions in Astronomy (Reidel, Dordrecht, The Netherlands, 1979), Part V.

J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 3,27–29 (1978); "Space object imaging through the turbulent atmosphere," Opt. Eng. 18, 529–534 (1979); "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758–2769 (1982).

W. R. Fright and R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: III: computational examples for two dimensions," Optik (to be published).

K. L. Garden and R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension: II: one-dimensional considerations," Optik (to be published).

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

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