Abstract

We describe an optical setup for implementing a Talbot interferometer that uses two mutually incoherent sets of self-images to simultaneously produce interference bands due to dark and bright fields. A spatial filter can be used to visualize these fields without interference fringes. Experimental results are included.

© 1989 Optical Society of America

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References

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  1. A. W. Lohmann, “A New Fourier Spectrometer Consisting of a Two Grating Interferometer,” in Proceedings, ICO Conference on Optical Instruments, K. J. Habell, Ed. (Butterworth, London, 1961), p. 58.
  2. H. Klages, Colloque 2 Supplement and No. 3–4, J. de Physique 28, C2-C40 (1967) J. Phys (Paris) 28, C2-40 (1967).
  3. A. W. Lohmann, D. Silva, “An Interferometer Based on the Talbot Effect,” Opt. Commun. 2, 413 (1971); “A Talbot Interferometer with Circular Gratings,” Opt. Commun. 4, 326 (1972).
    [CrossRef]
  4. S. Yokozeki, T. Suzuki, “Shearing Interferometer Using the Grating as the Beam Splitter,” Appl. Opt. 10, 1575 (1971).
    [CrossRef] [PubMed]
  5. J. Ojeda-Castaneda, E. E. Sicre, “Tunable Bandstop Filter for Binary Objects: a Self Imaging Technique,” Opt. Commun. 47, 183 (1983).
    [CrossRef]
  6. A. W. Lohmann, J. Ojeda-Castaneda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 79, 388 (1984).
    [CrossRef]
  7. D. E. Silva, “Talbot Interferometer for Radial and Lateral Derivatives,” Appl. Opt. 11, 2613 (1972).
    [CrossRef] [PubMed]

1984 (1)

A. W. Lohmann, J. Ojeda-Castaneda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 79, 388 (1984).
[CrossRef]

1983 (1)

J. Ojeda-Castaneda, E. E. Sicre, “Tunable Bandstop Filter for Binary Objects: a Self Imaging Technique,” Opt. Commun. 47, 183 (1983).
[CrossRef]

1972 (1)

1971 (2)

A. W. Lohmann, D. Silva, “An Interferometer Based on the Talbot Effect,” Opt. Commun. 2, 413 (1971); “A Talbot Interferometer with Circular Gratings,” Opt. Commun. 4, 326 (1972).
[CrossRef]

S. Yokozeki, T. Suzuki, “Shearing Interferometer Using the Grating as the Beam Splitter,” Appl. Opt. 10, 1575 (1971).
[CrossRef] [PubMed]

1967 (1)

H. Klages, Colloque 2 Supplement and No. 3–4, J. de Physique 28, C2-C40 (1967) J. Phys (Paris) 28, C2-40 (1967).

Klages, H.

H. Klages, Colloque 2 Supplement and No. 3–4, J. de Physique 28, C2-C40 (1967) J. Phys (Paris) 28, C2-40 (1967).

Lohmann, A. W.

A. W. Lohmann, J. Ojeda-Castaneda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 79, 388 (1984).
[CrossRef]

A. W. Lohmann, D. Silva, “An Interferometer Based on the Talbot Effect,” Opt. Commun. 2, 413 (1971); “A Talbot Interferometer with Circular Gratings,” Opt. Commun. 4, 326 (1972).
[CrossRef]

A. W. Lohmann, “A New Fourier Spectrometer Consisting of a Two Grating Interferometer,” in Proceedings, ICO Conference on Optical Instruments, K. J. Habell, Ed. (Butterworth, London, 1961), p. 58.

Ojeda-Castaneda, J.

A. W. Lohmann, J. Ojeda-Castaneda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 79, 388 (1984).
[CrossRef]

J. Ojeda-Castaneda, E. E. Sicre, “Tunable Bandstop Filter for Binary Objects: a Self Imaging Technique,” Opt. Commun. 47, 183 (1983).
[CrossRef]

Sicre, E. E.

A. W. Lohmann, J. Ojeda-Castaneda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 79, 388 (1984).
[CrossRef]

J. Ojeda-Castaneda, E. E. Sicre, “Tunable Bandstop Filter for Binary Objects: a Self Imaging Technique,” Opt. Commun. 47, 183 (1983).
[CrossRef]

Silva, D.

A. W. Lohmann, D. Silva, “An Interferometer Based on the Talbot Effect,” Opt. Commun. 2, 413 (1971); “A Talbot Interferometer with Circular Gratings,” Opt. Commun. 4, 326 (1972).
[CrossRef]

Silva, D. E.

Suzuki, T.

Yokozeki, S.

Appl. Opt. (2)

J. de Physique (1)

H. Klages, Colloque 2 Supplement and No. 3–4, J. de Physique 28, C2-C40 (1967) J. Phys (Paris) 28, C2-40 (1967).

Opt. Commun. (3)

A. W. Lohmann, D. Silva, “An Interferometer Based on the Talbot Effect,” Opt. Commun. 2, 413 (1971); “A Talbot Interferometer with Circular Gratings,” Opt. Commun. 4, 326 (1972).
[CrossRef]

J. Ojeda-Castaneda, E. E. Sicre, “Tunable Bandstop Filter for Binary Objects: a Self Imaging Technique,” Opt. Commun. 47, 183 (1983).
[CrossRef]

A. W. Lohmann, J. Ojeda-Castaneda, E. E. Sicre, “Multiple Interaction Bandstop Filters Based on the Talbot Effect,” Opt. Commun. 79, 388 (1984).
[CrossRef]

Other (1)

A. W. Lohmann, “A New Fourier Spectrometer Consisting of a Two Grating Interferometer,” in Proceedings, ICO Conference on Optical Instruments, K. J. Habell, Ed. (Butterworth, London, 1961), p. 58.

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Figures (8)

Fig. 1
Fig. 1

Holographic recording on H of the field diffracted by coarse grating G1.

Fig. 2
Fig. 2

Set of self-images Sm that are generated by the holographic reconstructed grating G 1.

Fig. 3
Fig. 3

Two sets of mutually incoherent self-images Sm (or Sn) and Sm (or Sn).

Fig. 4
Fig. 4

Schematic representation of the Talbot interferometer that uses two complementary half-viewfields. One viewfield is set to the dark field, while the other is set to the bright field.

Fig. 5
Fig. 5

Bright field images of a phase structure: (a) the fringes are clearly present and (b) the fringes are blocked out.

Fig. 6
Fig. 6

Same as Fig. 5 but for dark field images.

Fig. 7
Fig. 7

Same as Fig. 5 but for simultaneous visualization of dark field and bright field images.

Fig. 8
Fig. 8

Same as Fig. 7 but with interchanged positions for the dark field and the bright field images.

Equations (4)

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G ( x ) = m = C m exp ( i 2 π m x / d ) ,
t ( x ) = exp [ i 2 π ϕ ( x ) ] .
u ( x ) = m = n = C m C n exp [ i ψ ( n ) ] exp [ i 2 π ϕ ( x + n λ z / d ) ] × exp { i 2 π [ ( m + n ) 2 z 2 / ( z 1 + z 2 ) + ( m + n ) x / d ] } .
| u ( x ) | 2 = 2 C 0 2 C 1 2 { 1 + cos [ 2 π ( ϕ ( x + z λ / d ) ϕ ( x ) ) ] } .

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