Abstract

This paper presents a system that exceeds the Rayleigh limit of resolution by placing three fixed gratings in predetermined positions. The proposed system works without any moving elements and is suitable for coherent or incoherent two-dimensional imaging. The three gratings are located between the input plane and the output plane, and thus the superresolved image is produced without additional imaging lenses. The generalized gratings allow us to obtain the undistorted spectral restoration of information. The trade-off for higher resolution is a smaller field of view. Experiment results validate the theoretical analysis.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Toraldo Di Francia, “Resolving power and information,” J. Opt. Soc. Am. 45, 497–501 (1955).
    [CrossRef]
  2. G. Toraldo Di Francia, “Degrees of freedom of an image,” J. Opt. Soc. Am. 59, 799–804 (1969).
    [CrossRef] [PubMed]
  3. H. Bartelt, A. W. Lohmann, “Optical processing of 1-D signals,” Opt. Commun. 42, 87–91 (1982).
    [CrossRef]
  4. W. Gartner, A. W. Lohmann, “An experiment going beyond Abbé’s limit of diffraction,” Z. Physik 174, 18–24 (1963).
  5. M. Francon, “Amélioration de résolution d’optique,” Nuovo Cimento Suppl. 9, 283–290 (1952).
  6. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. 56, 1463–1472 (1966).
    [CrossRef]
  7. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. 57, 932–941 (1967).
    [CrossRef]
  8. A. Malov, V. Morozov, I. Kompanents, Yu. Popov, “Formation of an image in a coherent synthesized-aperture system,” Sov. J. Quantum Electron. 7, 1125–1130.
  9. A. I. Kartashev, “Optical systems with enhanced resolving power,” Opt. Spectrosc. 9, 204–206 (1960).
  10. A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space–bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).
    [CrossRef]
  11. D. Mendlovic, A. W. Lohmann, “Space–bandwidth product adaptation and its application to superresolution: fundamentals,” J. Opt. Soc. Am. A 14, 558–562 (1997).
    [CrossRef]
  12. D. Mendlovic, A. W. Lohmann, Z. Zalevsky, “Space–bandwidth product adaptation and its application to superresolution: examples,” J. Opt. Soc. Am. A 14, 563–567 (1997).
    [CrossRef]
  13. D. Mendlovic, A. W. Lohmann, N. Konforti, I. Kiryuschev, Z. Zalevsky, “One-dimensional superresolution optical system for temporally restricted objects,” Appl. Opt. 36, 2353–2359 (1997).
    [CrossRef] [PubMed]
  14. D. Mendlovic, I. Kiryuschev, Z. Zalevsky, A. W. Lohmann, D. Farkas, “Two-dimensional superresolution optical system for temporally restricted objects,” Appl. Opt. 36, 6687–6691 (1997).
    [CrossRef]
  15. Z. Zalevsky, D. Mendlovic, A. W. Lohmann, “Super resolution optical systems for objects with finite sizes,” Opt. Commun. 163, 79–85 (1999).
    [CrossRef]

1999 (1)

Z. Zalevsky, D. Mendlovic, A. W. Lohmann, “Super resolution optical systems for objects with finite sizes,” Opt. Commun. 163, 79–85 (1999).
[CrossRef]

1997 (4)

1996 (1)

1982 (1)

H. Bartelt, A. W. Lohmann, “Optical processing of 1-D signals,” Opt. Commun. 42, 87–91 (1982).
[CrossRef]

1969 (1)

1967 (1)

1966 (1)

1963 (1)

W. Gartner, A. W. Lohmann, “An experiment going beyond Abbé’s limit of diffraction,” Z. Physik 174, 18–24 (1963).

1960 (1)

A. I. Kartashev, “Optical systems with enhanced resolving power,” Opt. Spectrosc. 9, 204–206 (1960).

1955 (1)

1952 (1)

M. Francon, “Amélioration de résolution d’optique,” Nuovo Cimento Suppl. 9, 283–290 (1952).

Bartelt, H.

H. Bartelt, A. W. Lohmann, “Optical processing of 1-D signals,” Opt. Commun. 42, 87–91 (1982).
[CrossRef]

Dorsch, R. G.

Farkas, D.

Ferreira, C.

Francon, M.

M. Francon, “Amélioration de résolution d’optique,” Nuovo Cimento Suppl. 9, 283–290 (1952).

Gartner, W.

W. Gartner, A. W. Lohmann, “An experiment going beyond Abbé’s limit of diffraction,” Z. Physik 174, 18–24 (1963).

Kartashev, A. I.

A. I. Kartashev, “Optical systems with enhanced resolving power,” Opt. Spectrosc. 9, 204–206 (1960).

Kiryuschev, I.

Kompanents, I.

A. Malov, V. Morozov, I. Kompanents, Yu. Popov, “Formation of an image in a coherent synthesized-aperture system,” Sov. J. Quantum Electron. 7, 1125–1130.

Konforti, N.

Lohmann, A. W.

Lukosz, W.

Malov, A.

A. Malov, V. Morozov, I. Kompanents, Yu. Popov, “Formation of an image in a coherent synthesized-aperture system,” Sov. J. Quantum Electron. 7, 1125–1130.

Mendlovic, D.

Morozov, V.

A. Malov, V. Morozov, I. Kompanents, Yu. Popov, “Formation of an image in a coherent synthesized-aperture system,” Sov. J. Quantum Electron. 7, 1125–1130.

Popov, Yu.

A. Malov, V. Morozov, I. Kompanents, Yu. Popov, “Formation of an image in a coherent synthesized-aperture system,” Sov. J. Quantum Electron. 7, 1125–1130.

Toraldo Di Francia, G.

Zalevsky, Z.

Appl. Opt. (2)

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (3)

Nuovo Cimento Suppl. (1)

M. Francon, “Amélioration de résolution d’optique,” Nuovo Cimento Suppl. 9, 283–290 (1952).

Opt. Commun. (2)

H. Bartelt, A. W. Lohmann, “Optical processing of 1-D signals,” Opt. Commun. 42, 87–91 (1982).
[CrossRef]

Z. Zalevsky, D. Mendlovic, A. W. Lohmann, “Super resolution optical systems for objects with finite sizes,” Opt. Commun. 163, 79–85 (1999).
[CrossRef]

Opt. Spectrosc. (1)

A. I. Kartashev, “Optical systems with enhanced resolving power,” Opt. Spectrosc. 9, 204–206 (1960).

Sov. J. Quantum Electron. (1)

A. Malov, V. Morozov, I. Kompanents, Yu. Popov, “Formation of an image in a coherent synthesized-aperture system,” Sov. J. Quantum Electron. 7, 1125–1130.

Z. Physik (1)

W. Gartner, A. W. Lohmann, “An experiment going beyond Abbé’s limit of diffraction,” Z. Physik 174, 18–24 (1963).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Optical setup for superresolution.

Fig. 2
Fig. 2

Experiment setup for obtaining superresolution.

Fig. 3
Fig. 3

Transparency function of the Dammann gratings.

Fig. 4
Fig. 4

Maximum size of the object (Δx) can be resolved against the distance between the first grating and the object (z0).

Fig. 5
Fig. 5

Synthetic aperture.

Fig. 6
Fig. 6

Geometrical ray’s track of the superresolution setup: (a) for an intermediate frequency in the object, (b) for an edge frequency in the object.

Fig. 7
Fig. 7

Objects used for the experiment as seen in the output plane without using a shutter: (a) Rosseta pattern with frequency range of 5–14 mm-1, (b) Ronchi pattern with frequency of 10 mm-1.

Fig. 8
Fig. 8

Images as seen in the output plane after using a square shutter with length side of 9.5 mm and without using Dammann gratings, for the objects of Figs. 7(a) and 7(b), respectively.

Fig. 9
Fig. 9

Superresolved output results obtained with the Dammann gratings: (a) and (b) present the whole output; (c) and (d) present the enlargement of the relevant regions in (a) and (b), respectively.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

u0(x, 0)u0(x, z0-)free-spacepropagationofz0.u0(x, z0-)u0(x, z0+)passingthroughgrating1.u0(x, z0+)u0(x, 0)virtualbackwardpropagation.u0(x, 0)u0(x, 2F-)opticalFouriertransformation.u0(x, 2F-)u0(x, 2F+)passingthroughanaperture.u0(x, 2F+)u0(x, 4F)opticalFouriertransformation.
u0(x, 4F)u0[x,(4F-z1)-]virtualbackwardpropagation.u0[x, (4F-z1)-]u0[x, (4F-z1)+]passingthroughgrating2.u0[x, (4F-z1)+]u0(x, 4F)free-spacepropagationofz1.u0(x, 4F)u0[x, (4F-z2)-]virtualbackwardpropagation.u0[x, (4F-z2)-]u0[x, (4F-z2)+]passingthroughgrating3.u0[x, (4F-z2)+]u0(x, 4F)free-spacepropagationofz2.
u0(x, z=0)=-u˜0(ν)exp(2πixν)dν.
u0(x, 4F)
=mnlAmBnCl-u˜0(ν)rectν+mν0Δμ/λF×exp{2πi[x(ν+mν0+nν1+lν2)+ϕt]}dν,
ϕt=ν(z0λmν0-z1λnν1-z2λlν2)+z0λ2 m2ν02-z1λmnν0ν1-z1λ2 n2ν12-z2λmlν0ν2-z2λ2 l2ν22-z2λnlνν2.
mν0+nν1+lν2=0,
z0mν0-z1nν1-z2lν2=0,
z0λ2 m2ν02-z1λmnν0ν1-z1λ2 n2ν12
-z2λmlν0ν2-z2λ2 l2ν22-z2λnlν1ν2=N,
ν0=ν1 ν2=2ν0
n=ml=-m,
z1=2Nλm2ν02-z0,z2=z1-Nλm2ν02,
u0(x, z=4F)=mAmBmC-m-u˜0(ν)rectν+mν0Δμ/λF×exp(2πixν)dν.
ν0=ΔμλF.
xm,n,l=λ(z0mν0-z1nν1-z2lν2)

Metrics