Abstract

The superresolving filter design of Toraldo di Francia [Atti. Fond. Giorgio Ronchi <b>7</b>, 366 (1952)], which consists of an array of concentric annuli of finite width, is studied. Such a filter compares favorably with other superresolving filter designs while being considerably more simple to fabricate. In particular, for given input energy, the intensity at the focal point is usually greater than for optimized filter designs. The manufacturing tolerances of such a filter are discussed.

© 1982 Optical Society of America

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References

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  1. G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento Suppl. 9, 426–438 (1952).
  2. S. A. Schelkunoff, "A mathematical theory of linear arrays," Bell Syst. Tech. J. 22, 80–107 (1943).
  3. G. Toraldo di Francia, "Nuovo pupille superrisolvente," Atti. Fond. Giorgio Ronchi 7, 366–372 (1952).
  4. B. R. Frieden, "On arbitrary perfect imagery with a finite aperture," Opt. Acta 16, 795–807 (1969).
  5. B. R. Frieden, "Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions," in Progress in Optics, E. Wolf, ed. (Pergamon, New York, 1971), Vol. 9, pp. 311–407.
  6. G. Boyer and M. Sechaud, "Super-resolution by Taylor filters," Appl. Opt. 12, 893–894 (1973).
  7. G. R. Boyer, "Pupil filters for moderate super-resolution," Appl. Opt. 15, 3089–3093 (1976).
  8. R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field—I. Achievement of maximum central irradiance under an energy constraint," Opt. Acta 27, 587–610 (1980).
  9. R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field—II. Application of the impulse-generating filter," Opt. Acta 27, 1641–1670 (1980).
  10. J. E. Wilkins, Jr., "The resolving power of a coated objective II," J. Opt. Soc. Am. 40, 222–224 (1950).
  11. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, 1966), p. 405.

1980 (2)

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field—I. Achievement of maximum central irradiance under an energy constraint," Opt. Acta 27, 587–610 (1980).

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field—II. Application of the impulse-generating filter," Opt. Acta 27, 1641–1670 (1980).

1976 (1)

1973 (1)

1969 (1)

B. R. Frieden, "On arbitrary perfect imagery with a finite aperture," Opt. Acta 16, 795–807 (1969).

1952 (2)

G. Toraldo di Francia, "Nuovo pupille superrisolvente," Atti. Fond. Giorgio Ronchi 7, 366–372 (1952).

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento Suppl. 9, 426–438 (1952).

1950 (1)

1943 (1)

S. A. Schelkunoff, "A mathematical theory of linear arrays," Bell Syst. Tech. J. 22, 80–107 (1943).

Boivin, A.

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field—II. Application of the impulse-generating filter," Opt. Acta 27, 1641–1670 (1980).

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field—I. Achievement of maximum central irradiance under an energy constraint," Opt. Acta 27, 587–610 (1980).

Boivin, R.

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field—I. Achievement of maximum central irradiance under an energy constraint," Opt. Acta 27, 587–610 (1980).

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field—II. Application of the impulse-generating filter," Opt. Acta 27, 1641–1670 (1980).

Boyer, G.

Boyer, G. R.

di Francia, G. Toraldo

G. Toraldo di Francia, "Nuovo pupille superrisolvente," Atti. Fond. Giorgio Ronchi 7, 366–372 (1952).

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento Suppl. 9, 426–438 (1952).

Frieden, B. R.

B. R. Frieden, "On arbitrary perfect imagery with a finite aperture," Opt. Acta 16, 795–807 (1969).

B. R. Frieden, "Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions," in Progress in Optics, E. Wolf, ed. (Pergamon, New York, 1971), Vol. 9, pp. 311–407.

Schelkunoff, S. A.

S. A. Schelkunoff, "A mathematical theory of linear arrays," Bell Syst. Tech. J. 22, 80–107 (1943).

Sechaud, M.

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, 1966), p. 405.

Wilkins, Jr., J. E.

Appl. Opt. (2)

Atti. Fond. Giorgio Ronchi (1)

G. Toraldo di Francia, "Nuovo pupille superrisolvente," Atti. Fond. Giorgio Ronchi 7, 366–372 (1952).

Bell Syst. Tech. J. (1)

S. A. Schelkunoff, "A mathematical theory of linear arrays," Bell Syst. Tech. J. 22, 80–107 (1943).

J. Opt. Soc. Am. (1)

Nuovo Cimento Suppl. (1)

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento Suppl. 9, 426–438 (1952).

Opt. Acta (3)

B. R. Frieden, "On arbitrary perfect imagery with a finite aperture," Opt. Acta 16, 795–807 (1969).

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field—I. Achievement of maximum central irradiance under an energy constraint," Opt. Acta 27, 587–610 (1980).

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field—II. Application of the impulse-generating filter," Opt. Acta 27, 1641–1670 (1980).

Other (2)

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, 1966), p. 405.

B. R. Frieden, "Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions," in Progress in Optics, E. Wolf, ed. (Pergamon, New York, 1971), Vol. 9, pp. 311–407.

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