Abstract

Past and present approaches to the concept of optical resolution are reviewed.

© 1997 Optical Society of America

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  53. G. Toralod di Francia, “Resolving power and information,” J. Opt. Soc. Am. 45, 497–501 (1955).
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  57. S. A. Basinger, E. Michielssen, D. J. Brady, “Degrees of freedom of polychromatic images,” J. Opt. Soc. Am. A 12, 704–714 (1995).
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  58. M. von Laue, “Die Freiheitsgrade von Strahlenbündeln,” Ann. Physik 44, 1197–1212 (1914).
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  61. C. W. Helstrom, “Detection and resolution of incoherent objects by a background-limited optical system,” J. Opt. Soc. Am. 59, 164–175 (1969).
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  62. D. R. Cunningham, R. D. Laramore, “Detection in image dependent noise,” IEEE Trans. Inf. Theory IT-22, 603–610 (1976).
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  63. D. A. Nahrstedt, L. C. Schooley, “Alternative approach in decision theory as applied to the resolution of two point images,” J. Opt. Soc. Am. 69, 910–912 (1979).
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  66. J. H. Dunn, D. D. Howard, K. B. Pendleton, “Tracking radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1970), Chap. 21, pp. 21–32.
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  75. T. Orhaug, “On the resolution of imaging systems,” Opt. Acta 16, 75–84 (1969).
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  76. W. T. Cathey, B. R. Frieden, W. T. Rhodes, C. K. Rushforth, “Image gathering and processing for enhanced resolution,” J. Opt. Soc. Am. A 1, 241–250 (1984).
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  77. E. J. Kelly, I. S. Reed, W. L. Root, “The detection of radar echoes in noise. II,” J. Soc. Indust. Appl. Math. 8, 481–507 (1960).
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  78. W. L. Root, “Radar resolution of closely spaced targets,” IRE Trans. Mil. Electron. MIL-6, 197–204 (1962).
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  80. A. van den Bos, “Optical resolution: an analysis based on catastrophe theory,” J. Opt. Soc. Am. A 4, 1402–1406 (1987).
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  81. A. van den Bos, “Ultimate resolution: a mathematical framework,” Ultramicroscopy 47, 298–306 (1992).
    [CrossRef]
  82. A. van den Bos, A. J. den Dekker, “Ultimate resolution in the presence of coherence,” Ultramicroscopy 60, 345–348 (1995).
    [CrossRef]
  83. A. van den Bos, A. J. den Dekker, “Coherent model-based optical resolution,” J. Opt. Soc. Am. A 13, 1667–1669 (1996).
    [CrossRef]
  84. V. I. Arnol’d, Catastrophe Theory (Springer-Verlag, Berlin, 1992).
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    [CrossRef]
  86. A. J. den Dekker, “Model-based optical two-point resolution,” in Proceedings of ICASSP’96, the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 2395–2398.

1996 (1)

1995 (2)

S. A. Basinger, E. Michielssen, D. J. Brady, “Degrees of freedom of polychromatic images,” J. Opt. Soc. Am. A 12, 704–714 (1995).
[CrossRef]

A. van den Bos, A. J. den Dekker, “Ultimate resolution in the presence of coherence,” Ultramicroscopy 60, 345–348 (1995).
[CrossRef]

1994 (1)

1993 (1)

A. van den Bos, J. H. Swarte, “Resolvability of the parameters of multiexponentials and other sum models,” IEEE Trans. Signal Process. 41, 313–322 (1993).
[CrossRef]

1992 (3)

1987 (1)

1986 (1)

1984 (2)

1983 (1)

1980 (1)

1979 (2)

1978 (1)

1976 (2)

D. R. Cunningham, R. D. Laramore, “Detection in image dependent noise,” IEEE Trans. Inf. Theory IT-22, 603–610 (1976).
[CrossRef]

C. Pask, “Simple optical theory of super-resolution,” J. Opt. Soc. Am.: letters 66, 68–70 (1976).
[CrossRef]

1975 (1)

1974 (2)

1972 (3)

1970 (2)

1969 (4)

C. W. Helstrom, “Detection and resolution of incoherent objects by a background-limited optical system,” J. Opt. Soc. Am. 59, 164–175 (1969).
[CrossRef]

G. Toraldo di Francia, “Degrees of freedom of an image,” J. Opt. Soc. Am. 59, 799–804 (1969).
[CrossRef] [PubMed]

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

T. Orhaug, “On the resolution of imaging systems,” Opt. Acta 16, 75–84 (1969).
[CrossRef]

1968 (1)

1967 (4)

1966 (3)

1965 (2)

R. Barakat, “Rayleigh wavefront criterion,” J. Opt. Soc. Am. 55, 572–573 (1965).
[CrossRef]

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

1964 (4)

P. Swerlin, “Parameter estimation accuracy formulas,” IRE Trans. Inf. Theory 10, 302–314 (1964).
[CrossRef]

C. W. Helstrom, “The detection and resolution of optical signals,” IEEE Trans. Inf. Theory IT-10, 275–287 (1964).
[CrossRef]

J. L. Harris, “Diffraction and resolving power,” J. Opt. Soc. Am. 54, 931–936 (1964).
[CrossRef]

O. Falconi, “Maximum sensitivities of optical direction and twist measuring instruments,” J. Opt. Soc. Am. 54, 1315–1320 (1964).
[CrossRef]

1963 (1)

1962 (2)

1961 (2)

D. Slepian, H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty: I,” Bell Syst. Tech. J. 40, 43–64 (1961).
[CrossRef]

V. Ronchi, “Resolving power of calculated and detected images,” J. Opt. Soc. Am. 51, 458–460 (1961).
[CrossRef]

1960 (1)

E. J. Kelly, I. S. Reed, W. L. Root, “The detection of radar echoes in noise. II,” J. Soc. Indust. Appl. Math. 8, 481–507 (1960).
[CrossRef]

1955 (2)

P. B. Fellgett, E. H. Linfoot, “On the assessment of op-tical images,” Phil. Trans. R. Soc. London Ser. A 247, 369–407 (1955).
[CrossRef]

G. Toralod di Francia, “Resolving power and information,” J. Opt. Soc. Am. 45, 497–501 (1955).
[CrossRef]

1951 (2)

E. Wolf, “The diffraction theory of aberrations,” Rep. Prog. Phys. 14, 95–120 (1951).
[CrossRef]

H. H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London, Ser. A 208, 263–277 (1951).
[CrossRef]

1950 (3)

H. H. Hopkins, P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. London 63(10), no. 370B, 737–744 (1950).
[CrossRef]

J. E. Wilkins, “The resolving power of a coated objective,” J. Opt. Soc. Am. 40, 222–224 (1950).
[CrossRef]

H. Osterberg, “Microscope imagery and interpretations,” J. Opt. Soc. Am. 40, 295 (1950).
[CrossRef]

1949 (2)

1941 (1)

1938 (1)

F. Zernike, “The concept of degree of coherence and its applications to optical problems,” Physica 5, 785–795 (1938).
[CrossRef]

1937 (1)

A. Buxton, “Note on optical resolution,” Philos. Mag. 23, 440–442 (1937).

1927 (1)

W. V. Houston, “A compound interferometer for fine structure work,” Phys. Rev. 29, 478–484 (1927).
[CrossRef]

1916 (1)

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J. 44, 76–86 (1916).
[CrossRef]

1914 (1)

M. von Laue, “Die Freiheitsgrade von Strahlenbündeln,” Ann. Physik 44, 1197–1212 (1914).

1880 (1)

Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 9, 40–55 (1880), (continued from Vol. 8, p. 486).
[CrossRef]

1879 (1)

Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 261–274, 403–411, 477–486 (1879).
[CrossRef]

1874 (1)

Lord Rayleigh, “On the manufacture and theory of diffraction-gratings,” Philos. Mag. 47, 81–93, 193–205 (1874).

Arnol’d, V. I.

V. I. Arnol’d, Catastrophe Theory (Springer-Verlag, Berlin, 1992).

Arsenault,

Barakat, R.

Barham, P. M.

H. H. Hopkins, P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. London 63(10), no. 370B, 737–744 (1950).
[CrossRef]

Barnes, C. W.

Basinger, S. A.

Biraud, Y.

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

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Brady, D. J.

Burke, J. J.

Buxton, A.

A. Buxton, “Note on optical resolution,” Philos. Mag. 23, 440–442 (1937).

Castleman, K. R.

K. R. Castleman, Digital Image Processing (Prentice-Hall International, London, 1979).

Cathey, W. T.

Clements, A. M.

Cleveland, E. L.

Cox, I. J.

Cunningham, D. R.

D. R. Cunningham, R. D. Laramore, “Detection in image dependent noise,” IEEE Trans. Inf. Theory IT-22, 603–610 (1976).
[CrossRef]

den Dekker, A. J.

A. van den Bos, A. J. den Dekker, “Coherent model-based optical resolution,” J. Opt. Soc. Am. A 13, 1667–1669 (1996).
[CrossRef]

A. van den Bos, A. J. den Dekker, “Ultimate resolution in the presence of coherence,” Ultramicroscopy 60, 345–348 (1995).
[CrossRef]

A. J. den Dekker, “Model-based optical two-point resolution,” in Proceedings of ICASSP’96, the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 2395–2398.

Dunn, J. H.

J. H. Dunn, D. D. Howard, K. B. Pendleton, “Tracking radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1970), Chap. 21, pp. 21–32.

Falconi, O.

Farrell, E. J.

Fellgett, P. B.

P. B. Fellgett, E. H. Linfoot, “On the assessment of op-tical images,” Phil. Trans. R. Soc. London Ser. A 247, 369–407 (1955).
[CrossRef]

Fried, D. L.

Frieden, B. R.

Gerchberg, R. W.

R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer Verlag, New York, 1984), pp. 9–75.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 85–98.

Grimes, D.

Harris, J. L.

Harris, R. W.

Helstrom, C. W.

Hopkins, H. H.

H. H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London, Ser. A 208, 263–277 (1951).
[CrossRef]

H. H. Hopkins, P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. London 63(10), no. 370B, 737–744 (1950).
[CrossRef]

Houston, W. V.

W. V. Houston, “A compound interferometer for fine structure work,” Phys. Rev. 29, 478–484 (1927).
[CrossRef]

Howard, D. D.

J. H. Dunn, D. D. Howard, K. B. Pendleton, “Tracking radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1970), Chap. 21, pp. 21–32.

Idell, P. S.

Jacquinot, P.

P. Jacquinot, B. Roizen-Dossier, “Apodisation,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3, pp. 29–186.

Kelly, E. J.

E. J. Kelly, I. S. Reed, W. L. Root, “The detection of radar echoes in noise. II,” J. Soc. Indust. Appl. Math. 8, 481–507 (1960).
[CrossRef]

Kibe, J. N.

Koppius, O. T.

Laramore, R. D.

D. R. Cunningham, R. D. Laramore, “Detection in image dependent noise,” IEEE Trans. Inf. Theory IT-22, 603–610 (1976).
[CrossRef]

Leith, E. N.

Levi, L.

L. Levi, Applied Optics, A Guide to Optical System Design (Wiley, New York, 1980), Vol. 2.

Levin, E.

Linfoot, E. H.

P. B. Fellgett, E. H. Linfoot, “On the assessment of op-tical images,” Phil. Trans. R. Soc. London Ser. A 247, 369–407 (1955).
[CrossRef]

Lowenthal, S.

Lukosz, W.

Lummer, O.

O. Lummer, F. Reiche, Die Lehre von der Bildentstehung im Mikroskop von Ernst Abbe (Vieweg, Braunschweig, Germany, 1910).

Luneberg, R. K.

R. K. Luneberg, Mathematical Theory of Optics (Brown U. Press, Providence R.I., 1944), p. 390.

McKechnie, T. S.

T. S. McKechnie, “The effect of condenser obstruction on the two-point resolution of a microscope,” Opt. Acta 19, 729–737 (1972).
[CrossRef]

Michielssen, E.

Nahrstedt, D. A.

Nayyar, V. P.

Nielsen-Delaney, P. A.

Ord, K.

A. Stuart, K. Ord, Kendall’s Advanced Theory of Statistics (Arnold, London, 1994).

Orhaug, T.

T. Orhaug, “On the resolution of imaging systems,” Opt. Acta 16, 75–84 (1969).
[CrossRef]

Osterberg, H.

Pask, C.

C. Pask, “Simple optical theory of super-resolution,” J. Opt. Soc. Am.: letters 66, 68–70 (1976).
[CrossRef]

Pendleton, K. B.

J. H. Dunn, D. D. Howard, K. B. Pendleton, “Tracking radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1970), Chap. 21, pp. 21–32.

Pollak, H. O.

D. Slepian, H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty: I,” Bell Syst. Tech. J. 40, 43–64 (1961).
[CrossRef]

Ramsay, B. P.

Rayleigh, Baron

J. W. Strutt (Baron Rayleigh), “Investigations in optics, with special reference to the spectroscope,” in Scientific Papers by John William Strutt, Baron Rayleigh (Cambridge U. Press, Cambridge, 1899), Vol. I, 1869–1881, pp. 416–459; originally published in Philos. Mag. 8 and 9 (1879 and 1880).

J. W. Strutt (Baron Rayleigh), “Wave theory of light,” in Scientific Papers by John William Strutt, Baron Rayleigh (Cambridge U. Press, Cambridge, 1902), Vol. III, 1887–1892, p. 47–189; originally published in Encyclopedia Britannica, XXIV, 1888.

Rayleigh, Lord

Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 9, 40–55 (1880), (continued from Vol. 8, p. 486).
[CrossRef]

Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 261–274, 403–411, 477–486 (1879).
[CrossRef]

Lord Rayleigh, “On the manufacture and theory of diffraction-gratings,” Philos. Mag. 47, 81–93, 193–205 (1874).

Reed, I. S.

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Appl. Opt. (2)

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A. Stuart, K. Ord, Kendall’s Advanced Theory of Statistics (Arnold, London, 1994).

B. R. Frieden, “Image enhancement and restoration,” in Picture Processing and Digital Filtering, T. S. Huang, ed. (Springer-Verlag, New York, 1975), Vol. 6, pp. 177–248.

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P. Jacquinot, B. Roizen-Dossier, “Apodisation,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3, pp. 29–186.

J. W. Strutt (Baron Rayleigh), “Wave theory of light,” in Scientific Papers by John William Strutt, Baron Rayleigh (Cambridge U. Press, Cambridge, 1902), Vol. III, 1887–1892, p. 47–189; originally published in Encyclopedia Britannica, XXIV, 1888.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 85–98.

J. W. Strutt (Baron Rayleigh), “Investigations in optics, with special reference to the spectroscope,” in Scientific Papers by John William Strutt, Baron Rayleigh (Cambridge U. Press, Cambridge, 1899), Vol. I, 1869–1881, pp. 416–459; originally published in Philos. Mag. 8 and 9 (1879 and 1880).

A. Schuster, Theory of Optics (Arnold, London, 1924), p. 158.

A. J. den Dekker, “Model-based optical two-point resolution,” in Proceedings of ICASSP’96, the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 2395–2398.

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Equations (6)

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NF=2(1+LxBx)(1+LyBy)(1+TBT),
N=(1+2LxBx)(1+2LyBy)(1+2LzBz)×(1+2TBT)log(1+SNR),
SNR=-(ΔS/ΔN)2dθ,
SNR D(f)=|E[D(f)]|[Var{D(f)}]½,
wn=g(xn, yn; θ)+en,n=1, , N,
g(xn, yn; θ)=α1f2(xn-βx1, yn-βy1)+α2×f2(xn-βx2, yn-βy2)+2ρα1α2×f(xn-βx1, yn-βy1)×f(xn-βx2, yn-βy2),

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