Abstract

Based on the idea of the complex filters suggested by Toraldo di Francia in 1952 [Nuovo Cimento Suppl. 9, 426 (1952)], superresolved imaging has been achieved by use of interferometric image multiplication. A resolution limit of 55% of the Sparrow limit was achieved for incoherent objects.

© 2000 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. G. Toraldo di Francia, Atti Fond. Giorgio Ronchi 7, 366 (1952).
  3. B. R. Frieden, Opt. Acta 16, 795 (1969).
    [CrossRef]
  4. Z. Hegedus and V. Sarafis, J. Opt. Soc. Am. A 3, 1892 (1986).
    [CrossRef]
  5. S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics, 3rd ed. (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  6. A. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, Orlando, Fla., 1984).
  7. R. K. Luneberg, The Mathematical Theory of Optics (Cambridge U. Press, Cambridge, 1966).
  8. D. Yu. Gal’pern, Opt. Spectrosc. (USSR) 9, 291 (1960).

1986 (1)

1969 (1)

B. R. Frieden, Opt. Acta 16, 795 (1969).
[CrossRef]

1960 (1)

D. Yu. Gal’pern, Opt. Spectrosc. (USSR) 9, 291 (1960).

1952 (2)

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

G. Toraldo di Francia, Atti Fond. Giorgio Ronchi 7, 366 (1952).

Frieden, B. R.

B. R. Frieden, Opt. Acta 16, 795 (1969).
[CrossRef]

Gal’pern, D. Yu.

D. Yu. Gal’pern, Opt. Spectrosc. (USSR) 9, 291 (1960).

Hegedus, Z.

Lipson, H.

S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics, 3rd ed. (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Lipson, S. G.

S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics, 3rd ed. (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Luneberg, R. K.

R. K. Luneberg, The Mathematical Theory of Optics (Cambridge U. Press, Cambridge, 1966).

Sarafis, V.

Sheppard, C.

A. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, Orlando, Fla., 1984).

Tannhauser, D. S.

S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics, 3rd ed. (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Toraldo di Francia, G.

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

G. Toraldo di Francia, Atti Fond. Giorgio Ronchi 7, 366 (1952).

Wilson, A.

A. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, Orlando, Fla., 1984).

Atti Fond. Giorgio Ronchi (1)

G. Toraldo di Francia, Atti Fond. Giorgio Ronchi 7, 366 (1952).

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

Nuovo Cimento Suppl. (1)

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

Opt. Acta (1)

B. R. Frieden, Opt. Acta 16, 795 (1969).
[CrossRef]

Opt. Spectrosc. (USSR) (1)

D. Yu. Gal’pern, Opt. Spectrosc. (USSR) 9, 291 (1960).

Other (3)

S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics, 3rd ed. (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

A. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, Orlando, Fla., 1984).

R. K. Luneberg, The Mathematical Theory of Optics (Cambridge U. Press, Cambridge, 1966).

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Figures (5)

Fig. 1
Fig. 1

Experimental system used to implement the phase mask synthesis and interferometric multiplication: L’s, lenses; P, piezoelectrially tilted phase plate; M2a, M2b, positive and negative phase masks, respectively; M1, open-aperture mask.

Fig. 2
Fig. 2

a, Optimized mask with circular symmetry: white areas, transmission amplitude 1; gray area, amplitude 0; black areas, amplitude -1. b, Profile of the mask’s diffraction pattern. c, Product of diffraction pattern and the Airy disk function.

Fig. 3
Fig. 3

Synthetic phase mask with square symmetry used in the experiments: a, positive part M2a; b, negative part M2b; c, observed diffraction pattern of the superposition of a and b; d, interferometric product of c and the Airy disk function.

Fig. 4
Fig. 4

Profiles of images of two point sources through the full aperture and through the phase mask: in a and b the separation is 1.13, and in c and d it is 0.75 in units of 0.95λf#, which has unit value when the separation has the Sparrow resolution limit of a circular aperture.

Fig. 5
Fig. 5

Calculated appearance of the image of five dots, separated by various distances in the region of the Sparrow resolution limit (shown by the scale line, which is one unit of Fig. 4: a, as imaged by a conventional imaging system; b, with our experimentally determined PSF as shown in Fig. 3d.

Equations (3)

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p+u=pmu+p0u,
p-u=pmu-p0u.
aρ=n=1Ncn-1n-1rn2fρrn,

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