Abstract

The expanding use of optical communication by means of optical fibers and the situation of drastically increasing amounts of data to be transmitted urge the exploration of novel systems permitting the transmission of large amounts of spatial information by fiber with smaller spatial resolution. An optical encoding and decoding system is suggested for transmitting one- or two-dimensional images by means of a single-mode fiber. The superresolving system is based on wavelength multiplexing of the input spatial information, which is achieved with diffractive optical elements. Preliminary experimental results demonstrate the capabilities of the suggested method for the one- and two-dimensional cases.

© 1997 Optical Society of America

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References

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  1. G. Toraldo Di Francia, “Resolving power and information,” J. Opt. Soc. Am. A 45, 497–501 (1955).
    [CrossRef]
  2. G. Toraldo Di Francia, “Degrees of freedom of an image,” J. Opt. Soc. Am. A 59, 799–804 (1969).
    [CrossRef]
  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 Abbe’s limit of diffraction,” Z. Physik 174, 18 (1963).
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    [CrossRef]
  7. A. I. Kartashev, “Optical systems with enhanced resolving power,” Opt. Spectrosc. 9, 204–206 (1960).
  8. A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space–bandwidth product of optical signal and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).
    [CrossRef]
  9. D. Mendlovic, A. W. Lohmann, “Space–bandwidth product adaptation and its application for super resolution: fundamentals,” J. Opt. Soc. Am. A 15, 558–562 (1997).
    [CrossRef]
  10. D. Mendlovic, A. W. Lohmann, Z. Zalevsky, “Space–bandwidth product adaptation and its application for superresolution: examples,” J. Opt. Soc. Am. A 15, 563–567 (1997).
    [CrossRef]
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    [CrossRef]
  14. H. O. Bartelt, “Image correlation in white light by wavelength multiplexing,” Opt. Commun. 29, 37–40 (1979).
    [CrossRef]
  15. H. O. Bartelt, “One dimensional image transformation in white light,” Opt. Commun. 38, 239–242 (1981).
    [CrossRef]
  16. H. O. Bartelt, “Height contouring by wavelength multiplexing,” Opt. Commun. 49, 17–20 (1984).
    [CrossRef]
  17. E. G. Paek, C. E. Zah, K. W. Cheung, L. Curtis, “All–optical image transmission through a single mode fiber,” Opt. Lett. 17, 613–615 (1992).
    [CrossRef] [PubMed]
  18. A. A. Friesem, U. Levy, Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
    [CrossRef]

1997

D. Mendlovic, A. W. Lohmann, “Space–bandwidth product adaptation and its application for super resolution: fundamentals,” J. Opt. Soc. Am. A 15, 558–562 (1997).
[CrossRef]

D. Mendlovic, A. W. Lohmann, Z. Zalevsky, “Space–bandwidth product adaptation and its application for superresolution: examples,” J. Opt. Soc. Am. A 15, 563–567 (1997).
[CrossRef]

1996

1992

1988

1984

H. O. Bartelt, “Height contouring by wavelength multiplexing,” Opt. Commun. 49, 17–20 (1984).
[CrossRef]

1983

A. A. Friesem, U. Levy, Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
[CrossRef]

1982

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

1981

H. O. Bartelt, “One dimensional image transformation in white light,” Opt. Commun. 38, 239–242 (1981).
[CrossRef]

1979

H. O. Bartelt, “Transmission of two dimensional images by wavelength multiplexing,” Opt. Commun. 28, 45–50 (1979).
[CrossRef]

H. O. Bartelt, “Image correlation in white light by wavelength multiplexing,” Opt. Commun. 29, 37–40 (1979).
[CrossRef]

1969

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

1966

W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. A 56, 1463–1472 (1966).
[CrossRef]

1965

J. D. Armitage, A. W. Lohmann, D. P. Paris, “Superresolution image forming systems for objects with restricted lambda dependence,” Jpn. J. Appl. Phys. 4, 273–275 (1965).

1963

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

1960

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

1955

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

1952

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

Armitage, J. D.

J. D. Armitage, A. W. Lohmann, D. P. Paris, “Superresolution image forming systems for objects with restricted lambda dependence,” Jpn. J. Appl. Phys. 4, 273–275 (1965).

Bartelt, H.

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

Bartelt, H. O.

H. O. Bartelt, “Height contouring by wavelength multiplexing,” Opt. Commun. 49, 17–20 (1984).
[CrossRef]

H. O. Bartelt, “One dimensional image transformation in white light,” Opt. Commun. 38, 239–242 (1981).
[CrossRef]

H. O. Bartelt, “Image correlation in white light by wavelength multiplexing,” Opt. Commun. 29, 37–40 (1979).
[CrossRef]

H. O. Bartelt, “Transmission of two dimensional images by wavelength multiplexing,” Opt. Commun. 28, 45–50 (1979).
[CrossRef]

Cheung, K. W.

Curtis, L.

Dorsch, R. G.

Ferreira, C.

Francon, M.

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

Friesem, A. A.

A. A. Friesem, U. Levy, Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
[CrossRef]

Gartner, W.

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

Heritage, J. P.

Kartashev, A. I.

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

Kirschner, E. M.

Levy, U.

A. A. Friesem, U. Levy, Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
[CrossRef]

Lohmann, A. W.

D. Mendlovic, A. W. Lohmann, Z. Zalevsky, “Space–bandwidth product adaptation and its application for superresolution: examples,” J. Opt. Soc. Am. A 15, 563–567 (1997).
[CrossRef]

D. Mendlovic, A. W. Lohmann, “Space–bandwidth product adaptation and its application for super resolution: fundamentals,” J. Opt. Soc. Am. A 15, 558–562 (1997).
[CrossRef]

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space–bandwidth product of optical signal and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).
[CrossRef]

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

J. D. Armitage, A. W. Lohmann, D. P. Paris, “Superresolution image forming systems for objects with restricted lambda dependence,” Jpn. J. Appl. Phys. 4, 273–275 (1965).

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

Lukosz, W.

W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. A 56, 1463–1472 (1966).
[CrossRef]

Mendlovic, D.

Paek, E. G.

Paris, D. P.

J. D. Armitage, A. W. Lohmann, D. P. Paris, “Superresolution image forming systems for objects with restricted lambda dependence,” Jpn. J. Appl. Phys. 4, 273–275 (1965).

Silberberg, Y.

A. A. Friesem, U. Levy, Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
[CrossRef]

Toraldo Di Francia, G.

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

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

Weiner, A. M.

Zah, C. E.

Zalevsky, Z.

J. Opt. Soc. Am. A

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

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

W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. A 56, 1463–1472 (1966).
[CrossRef]

D. Mendlovic, A. W. Lohmann, “Space–bandwidth product adaptation and its application for super resolution: fundamentals,” J. Opt. Soc. Am. A 15, 558–562 (1997).
[CrossRef]

D. Mendlovic, A. W. Lohmann, Z. Zalevsky, “Space–bandwidth product adaptation and its application for superresolution: examples,” J. Opt. Soc. Am. A 15, 563–567 (1997).
[CrossRef]

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space–bandwidth product of optical signal and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

J. D. Armitage, A. W. Lohmann, D. P. Paris, “Superresolution image forming systems for objects with restricted lambda dependence,” Jpn. J. Appl. Phys. 4, 273–275 (1965).

Nuovo Cimento Suppl.

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

Opt. Commun.

H. O. Bartelt, “Transmission of two dimensional images by wavelength multiplexing,” Opt. Commun. 28, 45–50 (1979).
[CrossRef]

H. O. Bartelt, “Image correlation in white light by wavelength multiplexing,” Opt. Commun. 29, 37–40 (1979).
[CrossRef]

H. O. Bartelt, “One dimensional image transformation in white light,” Opt. Commun. 38, 239–242 (1981).
[CrossRef]

H. O. Bartelt, “Height contouring by wavelength multiplexing,” Opt. Commun. 49, 17–20 (1984).
[CrossRef]

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

Opt. Lett.

Opt. Spectrosc.

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

Proc. IEEE

A. A. Friesem, U. Levy, Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
[CrossRef]

Z. Physik

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

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Figures (6)

Fig. 1
Fig. 1

Illustration of the suggested optical setup: (a) The encoding part. (b) The decoding part.

Fig. 2
Fig. 2

DOE grating structure.

Fig. 3
Fig. 3

Illustration of the color distribution over the input pattern.

Fig. 4
Fig. 4

(a) Obtained reconstruction in the output plane. (b) The information carried in the green spectral range. (c) The information carried in the yellow spectral range. (d) The information carried in the orange spectral range. (e) The information carried in the red spectral range.

Fig. 5
Fig. 5

Color distribution over the input pattern obtained in the 2-D experiment.

Fig. 6
Fig. 6

(a) Input pattern. (b) The information carried by λ = 490 nm. (c) The information carried by λ = 600 nm. (d) The information carried by λ = 640 nm. (e) The information carried by λ = 710 nm. (f) The information carried in the red spectral range. (g) The information carried in the green spectral range. (h) The obtained reconstruction in the output plane.

Equations (14)

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

λ0Λ1=λ0-Δλ/2Λ2,
2λ0-Δλ/2Λ1λ0+Δλ/2Λ2;
λ0Λ2-λ0Λ1f=Lx.
u1x1, λ=Sλexp2πiλλΛx1,
u2x2, λ=Sλδx2-fλΛ,
u2x2, λ=Gx2Sλδx2-fλΛ.
u3x3, λ=- u2x2, λexp-2πix2x3λfdx2=exp-2πix3ΛGfλΛSλ.
u3x3, λ=u3x3, λexp2πix3Λ=GfλΛSλ.
u4x4, λ=δx4GfλΛSλ.
u5x5, λ=GfλΛSλ.
u5x5, λ=exp2πix5ΛGfλΛSλ.
u6x6, λ=- u5x5, λexp-2πix5x6λfdx5=GfλΛSλδx6-fλΛ.
GfλΛSλ=Gfλλ;
ΔλS  ΔλG,

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