Abstract

We use the coherence of a light beam to encode spatial information. We apply this principle to obtain spatial superresolution in a limited aperture system. The method is based on shaping the mutual intensity function of the illumination beam in a set of orthogonal distributions, each one carrying the information for a different frequency bandpass or spatial region of the input object. The coherence coding is analogous to time multiplexing but with multiplexing time slots that are given by the coherence time of the illumination beam. Most images are static during times much longer than this coherence time, and thus the increase of resolution in our system is obtained without any noticeable cost.

© 2005 Optical Society of America

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References

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  1. Z. Zalevsky, D. Mendlovic, and H. M. Ozaktas, J. Opt. A Pure Appl. Opt. 2, 83 (2000).
    [CrossRef]
  2. A. W. Lohmann, D. Mendlovic, and G. Shabtay, J. Opt. Soc. Am. A 16, 359 (1999).
    [CrossRef]
  3. C. Iaconis and I. A. Walmsley, Opt. Lett. 21, 1783 (1996).
    [CrossRef] [PubMed]
  4. W. D. Montgomery, Opt. Lett. 2, 120 (1978).
    [CrossRef] [PubMed]
  5. D. Mendlovic, G. Shabtay, A. W. Lohmann, and N. Konforti, Opt. Lett. 23, 1084 (1998).
    [CrossRef]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 4, p. 147.
    [CrossRef]
  7. M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction (Pergamon, 1980), Chap. 10, p 491.
  8. J. W. Goodman, Statistical Optics (Wiley Interscience, 1985), Chap. 5, p. 158; Chap. 7, p. 287.

2000 (1)

Z. Zalevsky, D. Mendlovic, and H. M. Ozaktas, J. Opt. A Pure Appl. Opt. 2, 83 (2000).
[CrossRef]

1999 (1)

1998 (1)

1996 (1)

1978 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction (Pergamon, 1980), Chap. 10, p 491.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley Interscience, 1985), Chap. 5, p. 158; Chap. 7, p. 287.

Iaconis, C.

Konforti, N.

Lohmann, A. W.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 4, p. 147.
[CrossRef]

Mendlovic, D.

Montgomery, W. D.

Ozaktas, H. M.

Z. Zalevsky, D. Mendlovic, and H. M. Ozaktas, J. Opt. A Pure Appl. Opt. 2, 83 (2000).
[CrossRef]

Shabtay, G.

Walmsley, I. A.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 4, p. 147.
[CrossRef]

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction (Pergamon, 1980), Chap. 10, p 491.

Zalevsky, Z.

Z. Zalevsky, D. Mendlovic, and H. M. Ozaktas, J. Opt. A Pure Appl. Opt. 2, 83 (2000).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

Z. Zalevsky, D. Mendlovic, and H. M. Ozaktas, J. Opt. A Pure Appl. Opt. 2, 83 (2000).
[CrossRef]

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

Opt. Lett. (3)

Other (3)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 4, p. 147.
[CrossRef]

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction (Pergamon, 1980), Chap. 10, p 491.

J. W. Goodman, Statistical Optics (Wiley Interscience, 1985), Chap. 5, p. 158; Chap. 7, p. 287.

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Figures (3)

Fig. 1
Fig. 1

Examples of three orthogonal MIFs.

Fig. 2
Fig. 2

Schematic of the optical configuration. BS, beam splitter.

Fig. 3
Fig. 3

(a). Overall optical output of the system showing the interference between both paths. (b) Output of the anamorphic optical path. (c) Output of the spherical optical path. (d) Superresolved image obtained after applying the proposed method.

Equations (5)

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Γ ( x 1 , x 2 ) = u ( x 1 , t ) u * ( x 2 , t ) ,
Γ n ( x 1 , x 2 ) = [ δ ( x 1 x 2 ) + δ ( x 1 x 2 n α ) + δ ( x 1 x 2 + n α ) ] rect ( x 1 Δ x ) rect ( x 2 Δ x ) ,
u t ( x ) = u ( x 1 ) B ( x 1 , x ) d x 1 ,
Γ t ( x 1 , x 2 ) = u t ( x 1 , t ) u t * ( x 2 , t ) = u ( x ¯ 1 , t ) u * ( x ¯ 2 , t ) B ( x ¯ 1 , x 1 ) B * ( x ¯ 1 , x 2 ) d x ¯ 1 d x ¯ 2 ,
Γ t ( x 1 , x 2 ) = Γ ( x ¯ 1 , x ¯ 2 ) B ( x ¯ 1 , x 1 ) B * ( x ¯ 1 , x 2 ) d x ¯ 1 d x ¯ 2 .

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