Abstract

In this paper we describe a super-resolving approach based upon gray level coding of the information. Thus, the imaged object should have limited number of gray levels. The proposed approach overcomes the resolution limitations caused either by the optics or by the finite size of the detector. In contrast to other existing super resolution techniques that use time or wavelength multiplexing, in this approach one does not need to pay neither in temporal nor in wavelength degrees of freedom, but in intensity dynamic range. After the gray coding and the imaging, the high frequency spatial resolution features are decoded using the decoding gray level lookup table.

© 2006 Optical Society of America

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References

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  1. Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical systems with improved resolving power” in Progress in optics, Vol. XL and E. Wolf Ed. (Elsevier, Amsterdam1999).
  2. Z. Zalevsky and D. MendlovicOptical Super Resolution, (Springer, 2002).
  3. A. J. den Dekker and A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am A. 14, 547–557 (1997).
    [CrossRef]
  4. D. Mendlovic and A. W. Lohmann, “Space-bandwidth product adaptation and its application to superresolution: Fundamentals,” J. Opt. Soc. Am. A 14, 558–562 (1997).
    [CrossRef]
  5. W. Lukosz, “Optical systems with resolving powers exceeding classical limit,” J. Opt. Soc. Am. 56, 1463–1472 (1966).
    [CrossRef]
  6. A. I. Kartashev, “Optical systems with enhanced resolving power,” Opt. Spectry. 9, 204–206 (1960).
  7. W. Gartner and A. W. Lohmann, “Ein experiment zur uberschreitung der abbeschen auflosungsgrenze “Z. Physik 174, 18 (1963)
  8. G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–428 (1952).
    [CrossRef]
  9. F. Gray. Pulse code communication, March 17, 1953. U.S. patent no. 2,632,058

1997 (2)

1966 (1)

1960 (1)

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

1952 (1)

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–428 (1952).
[CrossRef]

den Dekker, A. J.

A. J. den Dekker and A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am A. 14, 547–557 (1997).
[CrossRef]

Gartner, W.

W. Gartner and A. W. Lohmann, “Ein experiment zur uberschreitung der abbeschen auflosungsgrenze “Z. Physik 174, 18 (1963)

Gray, F.

F. Gray. Pulse code communication, March 17, 1953. U.S. patent no. 2,632,058

Kartashev, A. I.

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

Lohmann, A. W.

D. Mendlovic and A. W. Lohmann, “Space-bandwidth product adaptation and its application to superresolution: Fundamentals,” J. Opt. Soc. Am. A 14, 558–562 (1997).
[CrossRef]

W. Gartner and A. W. Lohmann, “Ein experiment zur uberschreitung der abbeschen auflosungsgrenze “Z. Physik 174, 18 (1963)

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical systems with improved resolving power” in Progress in optics, Vol. XL and E. Wolf Ed. (Elsevier, Amsterdam1999).

Lukosz, W.

Mendlovic, D.

D. Mendlovic and A. W. Lohmann, “Space-bandwidth product adaptation and its application to superresolution: Fundamentals,” J. Opt. Soc. Am. A 14, 558–562 (1997).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical systems with improved resolving power” in Progress in optics, Vol. XL and E. Wolf Ed. (Elsevier, Amsterdam1999).

Z. Zalevsky and D. MendlovicOptical Super Resolution, (Springer, 2002).

Toraldo di Francia, G.

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–428 (1952).
[CrossRef]

van den Bos, A.

A. J. den Dekker and A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am A. 14, 547–557 (1997).
[CrossRef]

Zalevsky, Z.

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical systems with improved resolving power” in Progress in optics, Vol. XL and E. Wolf Ed. (Elsevier, Amsterdam1999).

Z. Zalevsky and D. MendlovicOptical Super Resolution, (Springer, 2002).

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

A. J. den Dekker and A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am A. 14, 547–557 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nuovo Cimento Suppl. (1)

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–428 (1952).
[CrossRef]

Opt. Spectry. (1)

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

Other (4)

W. Gartner and A. W. Lohmann, “Ein experiment zur uberschreitung der abbeschen auflosungsgrenze “Z. Physik 174, 18 (1963)

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical systems with improved resolving power” in Progress in optics, Vol. XL and E. Wolf Ed. (Elsevier, Amsterdam1999).

Z. Zalevsky and D. MendlovicOptical Super Resolution, (Springer, 2002).

F. Gray. Pulse code communication, March 17, 1953. U.S. patent no. 2,632,058

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Figures (4)

Fig. 1.
Fig. 1.

(a). The gray level coding mask. (b) The look up table relating sensed gray level and the spatial structure of the original object.

Fig. 2.
Fig. 2.

The experimental setup.

Fig. 3.
Fig. 3.

The high resolution image.

Fig. 4.
Fig. 4.

a). The experimentally grabbed image after binning and before decoding. b). The experimentally reconstructed image after gray levels decoding.

Equations (8)

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I 0 ( x , y ) = Δ x 2 Δ x 2 Δ y 2 Δ y 2 I in ( x , y ) C ( x , y ) p ( x x , y y ) dx dy n m δ ( x n δ x , y m δ y )
I o ( n δ x , m δ y ) = n m [ n δ x θ x 2 n δ x + θ x 2 m δ y θ y 2 m δ y + θ y 2 I in ( x , y ) C ( x , y ) p ( n δ x x , m δ y y ) dx dy ]
× δ ( x n δ x , y m δ y )
I in ( k 1 δ x , k 2 δ y ) = { 0 , 1 }
p ( x , y ) = rect ( x θ x , y θ y )
C ( x , y ) = [ k 1 = n N 2 n + N 2 1 k 2 = m M 2 m + M 2 1 2 k 1 + N 2 n · 2 k 2 + M 2 m rect ( x k 1 δ x δ x , y k 2 δ y δ y ) ]
* δ ( x n N δ x , y m M δ y )
I o ( n δ x , m δ y ) = k 1 = n N 2 n + N 2 1 k 2 = m M 2 m + M 2 1 I in ( k 1 δ x , k 2 δ y ) · 2 k 1 + N 2 n · 2 k 2 + M 2 m

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