Abstract

Objects that have slow temporal variations may be superresolved with two moving masks such as pinhole or grating. The first mask is responsible for encoding the input image, and the second one performs the decoding operation. This approach is efficient for exceeding the resolving capability beyond Abbe’s limit of resolution. However, the proposed setup requires two physical gratings that should move in a synchronized manner. We propose what is believed to be a novel configuration in which the second grating responsible for the information decoding is replaced with a detector array and some postprocessing digital procedures. In this way the synchronization problem that exists when two gratings are used is simplified. Experimental results are provided for illustrating the utility of the new approach.

© 1999 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  7. D. Mendlovic, A. W. Lohmann, “Space–bandwidth product and its application to superresolution: fundamentals,” J. Opt. Soc. Am. A 14, 558–562 (1997);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]
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    [CrossRef]
  9. H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  10. D. Mendlovic, D. Farkas, Z. Zalevsky, A. W. Lohmann, “High-frequency enhancement by an optical system superresolution for of temporally restricted objects,” Opt. Lett. 23, 801–803 (1998).
    [CrossRef]

1998

1997

1996

1977

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two dimensional periodic structures,” Opt. Acta. 24, 505–515 (1977).
[CrossRef]

1971

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

1967

1964

1960

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

1952

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

Dammann, H.

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two dimensional periodic structures,” Opt. Acta. 24, 505–515 (1977).
[CrossRef]

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Dorsch, R.

Farkas, D.

Ferreira, C.

Francon, M.

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

Görtler, K.

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Kartashev, A. I.

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

Kiryuschev, I.

Klotz, E.

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two dimensional periodic structures,” Opt. Acta. 24, 505–515 (1977).
[CrossRef]

Konforti, N.

Lohmann, A. W.

Lukosz, W.

Mendlovic, D.

Paris, D. P.

Zalevsky, Z.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nouvo Climento Suppl.

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

Opt. Acta.

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two dimensional periodic structures,” Opt. Acta. 24, 505–515 (1977).
[CrossRef]

Opt. Commun.

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Opt. Lett.

Opt. Spectra

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

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Figures (6)

Fig. 1
Fig. 1

Optical system for obtaining increased effective aperture with two moving gratings.

Fig. 2
Fig. 2

Superresolution technique in the coherent case: (a) FT of the object, (b) FT of the first moving grating, (c) FT after passing the first grating, (d) FT after passing of the system finite aperture, (e) decoded spectrum after the second grating (same as the first grating) and before time averaging, (f) results after integration by time on the output intensity.

Fig. 3
Fig. 3

Objects used for the superresolution experiment: (a) grating with a basic period of 125 µm, (b) image of a digital bird (contains information in both axes).

Fig. 4
Fig. 4

Ronchi grating used in the setup with a basic period of 125 µm.

Fig. 5
Fig. 5

Computer-decoding superresolution approach under coherent illumination. With Fig. 3(a) as an object: (a) obtained output without use of the superresolution approach, (b) obtained output with the superresolution approach. With Fig. 3(b) as an object: (c) obtained output without use of the superresolution approach, (d) obtained output with the superresolution approach.

Fig. 6
Fig. 6

Same as in Fig. 5 but under noncoherent illumination.

Equations (12)

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aν=U˜0νrectν/Δν,bν=U˜0ν+v0rectν/Δν,cν=U˜0ν-v0rectν/Δν,
FTU0x=U˜0ν=bνδν+ν0+aνδν+cνδν-ν0,
U˜0ν * U˜0ν=cν * bνδν+2ν0+aν * bν+cν * aνδν+ν0+aν * aν+bν * bν+cν * cνδν+bν * aν+aν * cνδν-ν0+bν * cνδν-2ν0,
1τ-τ/2τ/2 U0x1, tU0*x2, tdt.
U˜1ν * U˜1ν=cν * bνδν+2ν0+2aν * bν+cν * aνδν+ν0+3aν * aν+bν * bν+cν * cνδν+2bν * aν+aν * cνδν-ν0+bν * cνδν-2ν0.
U˜1ν * U˜1ν=7cν * bνδν+2ν0+8aν * bν+cν * aνδν+ν0+9aν * aν+bν * bν+cν * cνδν+8bν * aν+aν * cνδν-ν0+7bν * cνδν-2ν0.
1τ-τ/2τ/2 U0x1, tU0*x2, tdt=|U0x1|2δx1-x2.
Gx, y=nxny Anx,ny exp2πjν0xx+ν0yy
Ix, y, t=u0x, y, tu0x, y, t*.
ν0x=Δνx,ν0y=Δνy,
Ix, y=1τ-τ/2τ/2Ix, y, tGx-Vxt, y-Vyt|2dt,
Icx, y=k=1MIx, y, tkGx-Vxtk, y-Vytk|2,

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