Abstract

A new method for continuing the Fourier spectrum of data of finite extent has been developed. Almost perfect restoration was obtained for noise-free data. Much improved resolution was obtained for error-laden data. Many forms of peak data lend themselves easily to the application of additional constraints that further enhance resolution almost to the theoretical limit.

© 1981 Optical Society of America

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References

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  1. J. L. Harris, "Diffraction and resolving power," J. Opt. Soc. Am. 54, 931–936 (1964).
  2. B. R. Frieden, in Picture Processing and Digital Filtering, T. S. Huang, ed. (Springer-Verlag, New York, 1975), Chap. 5.
  3. A. C. Schell, "Enchancing the angular resolution of incoherent sources," Radio Electron. Eng. 29, 21–26 (1965).
  4. Y. Biraud, "A new approach for increasing the resolving power by data processing," Astron. Astrophys. 1, 124–127 (1969).
  5. J. P. Burg, "Maximum entropy spectral analysis," presented at the 37th annual meeting of the Society of Exploration Geophysicists, Oklahoma City, Okla., 1967.
  6. P. A. Jansson, R. H. Hunt, and E. K. Plyler, "Resolution enhancement of spectra," J. Opt. Soc. Am. 60, 596–599 (1970).
  7. H. Wolter, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, Chap. 5.
  8. J. L. Harris, "Image evaluation and restoration," J. Opt. Soc. Am. 56, 569–574 (1966).
  9. R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709–720 (1974).
  10. C. W. Barnes, "Object restoration in a diffraction-limited imaging system," J. Opt. Soc. Am. 56, 575–578 (1966).
  11. D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-I," Bell Syst. Tech. J. 40, 43–63 (1961).
  12. J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Computation 19, 297–301 (1965).

1974 (1)

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709–720 (1974).

1970 (1)

1969 (1)

Y. Biraud, "A new approach for increasing the resolving power by data processing," Astron. Astrophys. 1, 124–127 (1969).

1966 (2)

1965 (2)

J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Computation 19, 297–301 (1965).

A. C. Schell, "Enchancing the angular resolution of incoherent sources," Radio Electron. Eng. 29, 21–26 (1965).

1964 (1)

1961 (1)

D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-I," Bell Syst. Tech. J. 40, 43–63 (1961).

Barnes, C. W.

Biraud, Y.

Y. Biraud, "A new approach for increasing the resolving power by data processing," Astron. Astrophys. 1, 124–127 (1969).

Burg, J. P.

J. P. Burg, "Maximum entropy spectral analysis," presented at the 37th annual meeting of the Society of Exploration Geophysicists, Oklahoma City, Okla., 1967.

Cooley, J. W.

J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Computation 19, 297–301 (1965).

Frieden, B. R.

B. R. Frieden, in Picture Processing and Digital Filtering, T. S. Huang, ed. (Springer-Verlag, New York, 1975), Chap. 5.

Gerchberg, R. W.

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709–720 (1974).

Harris, J. L.

Hunt, R. H.

Jansson, P. A.

Plyler, E. K.

Pollak, H. O.

D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-I," Bell Syst. Tech. J. 40, 43–63 (1961).

Schell, A. C.

A. C. Schell, "Enchancing the angular resolution of incoherent sources," Radio Electron. Eng. 29, 21–26 (1965).

Slepian, D.

D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-I," Bell Syst. Tech. J. 40, 43–63 (1961).

Tukey, J. W.

J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Computation 19, 297–301 (1965).

Wolter, H.

H. Wolter, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, Chap. 5.

Astron. Astrophys. (1)

Y. Biraud, "A new approach for increasing the resolving power by data processing," Astron. Astrophys. 1, 124–127 (1969).

Bell Syst. Tech. J. (1)

D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-I," Bell Syst. Tech. J. 40, 43–63 (1961).

J. Opt. Soc. Am. (4)

Math. Computation (1)

J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Computation 19, 297–301 (1965).

Opt. Acta (1)

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709–720 (1974).

Radio Electron. Eng. (1)

A. C. Schell, "Enchancing the angular resolution of incoherent sources," Radio Electron. Eng. 29, 21–26 (1965).

Other (3)

B. R. Frieden, in Picture Processing and Digital Filtering, T. S. Huang, ed. (Springer-Verlag, New York, 1975), Chap. 5.

J. P. Burg, "Maximum entropy spectral analysis," presented at the 37th annual meeting of the Society of Exploration Geophysicists, Oklahoma City, Okla., 1967.

H. Wolter, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, Chap. 5.

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