Abstract

Increasing the resolving power of optical systems beyond the limits imposed by diffraction, or superresolution, has considerable theoretical as well as practical interest. Several schemes have been proposed to achieve superresolution with reasonable success, but there are no criteria that enable one to determine what improvement can ultimately be attained for a certain level of resolution. We have determined fundamental limits imposed on the performance of any superresolution strategy. A brief analysis indicates that current optical-superresolution techniques can still have their performance considerably augmented.

© 1997 Optical Society of America

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References

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  1. G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
    [CrossRef]
  2. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  3. I. J. Cox, Appl. Opt. 23, 3260 (1984).
    [CrossRef] [PubMed]
  4. T. Wilson, Confocal Microscopy (Academic, London, 1990).
  5. J. J. E. Wilkins, J. Opt. Soc. Am. 40, 222 (1950).
    [CrossRef]
  6. C. J. R. Sheppard, Optik 48, 329 (1977).
  7. R. Boivin and A. Boivin, Opt. Acta 27, 587 (1980).
    [CrossRef]
  8. Z. S. Hegedus, Opt. Acta 32, 815 (1985).
    [CrossRef]
  9. T. R. M. Sales and G. M. Morris, in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.
  10. W. Lukosz, J. Opt. Soc. Am. 56, 1463 (1966).
    [CrossRef]
  11. Z. S. Hegedus and V. Sarafis, J. Opt. Soc. Am. A 3, 1892 (1982).
    [CrossRef]
  12. I. J. Cox, C. J. R. Sheppard, and T. Wilson, J. Opt. Soc. Am. 72, 1287 (1982).
    [CrossRef]

1985 (1)

Z. S. Hegedus, Opt. Acta 32, 815 (1985).
[CrossRef]

1984 (1)

1982 (2)

1980 (1)

R. Boivin and A. Boivin, Opt. Acta 27, 587 (1980).
[CrossRef]

1977 (1)

C. J. R. Sheppard, Optik 48, 329 (1977).

1966 (1)

1952 (1)

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

1950 (1)

Boivin, A.

R. Boivin and A. Boivin, Opt. Acta 27, 587 (1980).
[CrossRef]

Boivin, R.

R. Boivin and A. Boivin, Opt. Acta 27, 587 (1980).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Cox, I. J.

Hegedus, Z. S.

Lukosz, W.

Morris, G. M.

T. R. M. Sales and G. M. Morris, in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.

Sales, T. R. M.

T. R. M. Sales and G. M. Morris, in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.

Sarafis, V.

Sheppard, C. J. R.

Toraldo di Francia, G.

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

Wilkins, J. J. E.

Wilson, T.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Nuovo Cimento Suppl. (1)

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

Opt. Acta (2)

R. Boivin and A. Boivin, Opt. Acta 27, 587 (1980).
[CrossRef]

Z. S. Hegedus, Opt. Acta 32, 815 (1985).
[CrossRef]

Optik (1)

C. J. R. Sheppard, Optik 48, 329 (1977).

Other (3)

T. R. M. Sales and G. M. Morris, in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

T. Wilson, Confocal Microscopy (Academic, London, 1990).

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Figures (2)

Fig. 1
Fig. 1

(a) Conventional imaging mode where the laser illumination (LI) is incident upon a lens (L) and focused onto an observation plane (OP). A superresolution filter (SF) is used to increase the resolution of the system. The confocal mode (b) is composed of an imaging lens (IL) and a collector lens (CL) to image onto a point detector (PD). PS, point source.

Fig. 2
Fig. 2

Upper bound for the Strehl ratio Su when conventional imaging is used. The solid curve corresponds to the solution obtained with the series expansion for Su, and the inset shows the same data on a logarithmic scale. The dashed curve is a better estimate of the upper bound in the region G(0.461].

Tables (1)

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Table 1 Performance of a Two-Zone Phase-Only Binary Filtera

Equations (6)

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Ψη=201ArexpiΦrJ0ηrrdr,
Ψη=201ArexpiΦrrdr+201ArexpiΦr×p=1cpη2pr2prdr,
201ArexpiΦrrdr=S1/2=2p=1cpη12p01ArexpiΦrr2p+1dr,
S1/22p=1cpη12p01Arr2p+1dr,
SA¯p=1η1A2p22pp+1p!2G2p2.
SkGν,

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