Abstract

We use an adaptive photodetector for measuring the visibility of the Fresnel diffraction patterns generated by a grating. Visibility is measured in real time, with high spatial resolution, and without any signal processing. This method is well suited for analyzing the Talbot effect and its many applications.

© 2008 Optical Society of America

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References

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  1. A. W. Lohmann and D. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413-415 (1971).
    [CrossRef]
  2. S. Yokozeki and T. Suzuki, “Shearing interferometer using the grating as the beam splitter,” Appl. Opt. 10, 1575-1580 (1971).
    [CrossRef] [PubMed]
  3. P. Chavel and T. C. Strand, “Range measurement using Talbot diffraction imaging of gratings,” Appl. Opt. 23, 862-871(1984).
    [CrossRef] [PubMed]
  4. G. Schirripa Spagnolo, D. Ambrosini, and D. Paoleti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A Pure Appl. Opt. 4, S376-S380 (2002).
    [CrossRef]
  5. C.-F. Kao and M.-H. Lu, “Optical encoder based on the fractional Talbot effect,” Opt. Commun. 250, 16-23 (2005).
    [CrossRef]
  6. Shashi Prakash, Sanjay Upadhyay, and Chandra Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 33, 251-259(2000).
    [CrossRef]
  7. S. A. Benton and D. P. Merrill, “Simplified Talbot interferometer for lens testing,” Opt. Eng. 15, 328-331 (1976).
  8. Y. Nakano and K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24, 3162-3166 (1985).
    [CrossRef] [PubMed]
  9. P. Andrés, J. C. Barreiro, and J. Ojeda-Castaneda, “Focal length measuring technique using the Talbot effect,” Proc. SPIE 0701, 273-275 (1986).
  10. M. Tebaldi, G. Forte, R. Torroba, N. Bolognini, and A. Tagliaferri, “Self-imaging pitch variation applied to focal length digital measurements,” Opt. Commun. 250, 10-15(2005).
    [CrossRef]
  11. M. P. Kothiyal and R. S. Sirohi, “Improved collimation testing using Talbot interferometry,” Appl. Opt. 26, 4056-4057 (1987).
    [CrossRef] [PubMed]
  12. A. R. Ganesan and P. Venkateswarlu, “Laser beam collimation using Talbot interferometry,” Appl. Opt. 32, 2918-2920 (1993).
    [CrossRef] [PubMed]
  13. A. W. Lohmann, “A new Fourier spectrometer consisting of a two-gratings-interferometer,” in Proceedings of the Conference on Optical Instruments and Techniques, K. J. Habell, ed. (Chapman and Hall, 1961), pp. 58-61.
  14. H. L. Kung, A. Bhatnagar, and D. A. B. Miller, “Transform spectrometer based on measuring the periodicity of Talbot self-images,” Opt. Lett. 26, 1645-1647 (2001).
    [CrossRef]
  15. J. Ojeda-Castañeda and E. E. Sicre, “Tunable bandstop filter for binary objects: a self-imaging technique,” Opt. Commun. 47, 183-186 (1983).
    [CrossRef]
  16. A. W. Lohmann, J. Ojeda-Castañeda, and E. E. Sicre, “Multiple interaction bandstop filters based on the Talbot effect,” Opt. Commun. 49, 388-392 (1984).
    [CrossRef]
  17. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156-160 (1981).
    [CrossRef]
  18. R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Positioning method based on digital Moiré,” Opt. Commun. 209, 1-6 (2002).
    [CrossRef]
  19. S. Stepanov, “Photo-electromotive force in semiconductors,” in Handbook of Avanced Electronic and Photonics Materials and Devices, H. S. Nalwa, ed. (Academic, 2001), Vol. 2, pp. 205-272.
    [CrossRef]
  20. M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216-2225 (1990).
    [CrossRef]
  21. N. Korneev, S. Mansurova, P. Rodríguez, and S. Stepanov, “Fast and slow processes in the dynamics of near-surface charge grating formation in GaAs,” J. Opt. Soc. Am. B 14, 396-399 (1997).
    [CrossRef]
  22. S. Stepanov, P. Rodriguez, S. Trivedi, and C. C. Wang, “Effective broadband detection of nanometer laser-induced ultrasonic surface displacements by CdTe:V adaptive photoelectromotive force detector,” Appl. Phys. Lett. 84, 446-448 (2004).
    [CrossRef]
  23. Y. Ding, I. Lahiri, D. Nolte, G. J. Dunning, and D. M. Pepper, “Electric-field correlation of femtosecond pulses by use of a photoelectromotive force detector,” J. Opt. Soc. Am. B 15, 2013-2017 (1998).
    [CrossRef]
  24. M. L. Arroyo-Carrasco, P. Rodriguez-Montero, and S. Stepanov, “Measurement of the coherence length of diffusely scattered laser beams with adaptive photodetectors,” Opt. Commun. 157, 105-110 (1998).
    [CrossRef]
  25. J. Ibarra and J. Ojeda-Castaneda, “Talbot interferometry: a new geometry,” Opt. Commun. 96, 294-301 (1993).
    [CrossRef]

2005 (2)

C.-F. Kao and M.-H. Lu, “Optical encoder based on the fractional Talbot effect,” Opt. Commun. 250, 16-23 (2005).
[CrossRef]

M. Tebaldi, G. Forte, R. Torroba, N. Bolognini, and A. Tagliaferri, “Self-imaging pitch variation applied to focal length digital measurements,” Opt. Commun. 250, 10-15(2005).
[CrossRef]

2004 (1)

S. Stepanov, P. Rodriguez, S. Trivedi, and C. C. Wang, “Effective broadband detection of nanometer laser-induced ultrasonic surface displacements by CdTe:V adaptive photoelectromotive force detector,” Appl. Phys. Lett. 84, 446-448 (2004).
[CrossRef]

2002 (2)

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Positioning method based on digital Moiré,” Opt. Commun. 209, 1-6 (2002).
[CrossRef]

G. Schirripa Spagnolo, D. Ambrosini, and D. Paoleti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A Pure Appl. Opt. 4, S376-S380 (2002).
[CrossRef]

2001 (1)

2000 (1)

Shashi Prakash, Sanjay Upadhyay, and Chandra Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 33, 251-259(2000).
[CrossRef]

1998 (2)

Y. Ding, I. Lahiri, D. Nolte, G. J. Dunning, and D. M. Pepper, “Electric-field correlation of femtosecond pulses by use of a photoelectromotive force detector,” J. Opt. Soc. Am. B 15, 2013-2017 (1998).
[CrossRef]

M. L. Arroyo-Carrasco, P. Rodriguez-Montero, and S. Stepanov, “Measurement of the coherence length of diffusely scattered laser beams with adaptive photodetectors,” Opt. Commun. 157, 105-110 (1998).
[CrossRef]

1997 (1)

1993 (2)

A. R. Ganesan and P. Venkateswarlu, “Laser beam collimation using Talbot interferometry,” Appl. Opt. 32, 2918-2920 (1993).
[CrossRef] [PubMed]

J. Ibarra and J. Ojeda-Castaneda, “Talbot interferometry: a new geometry,” Opt. Commun. 96, 294-301 (1993).
[CrossRef]

1990 (1)

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216-2225 (1990).
[CrossRef]

1987 (1)

1986 (1)

P. Andrés, J. C. Barreiro, and J. Ojeda-Castaneda, “Focal length measuring technique using the Talbot effect,” Proc. SPIE 0701, 273-275 (1986).

1985 (1)

1984 (2)

P. Chavel and T. C. Strand, “Range measurement using Talbot diffraction imaging of gratings,” Appl. Opt. 23, 862-871(1984).
[CrossRef] [PubMed]

A. W. Lohmann, J. Ojeda-Castañeda, and E. E. Sicre, “Multiple interaction bandstop filters based on the Talbot effect,” Opt. Commun. 49, 388-392 (1984).
[CrossRef]

1983 (1)

J. Ojeda-Castañeda and E. E. Sicre, “Tunable bandstop filter for binary objects: a self-imaging technique,” Opt. Commun. 47, 183-186 (1983).
[CrossRef]

1981 (1)

1976 (1)

S. A. Benton and D. P. Merrill, “Simplified Talbot interferometer for lens testing,” Opt. Eng. 15, 328-331 (1976).

1971 (2)

A. W. Lohmann and D. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

S. Yokozeki and T. Suzuki, “Shearing interferometer using the grating as the beam splitter,” Appl. Opt. 10, 1575-1580 (1971).
[CrossRef] [PubMed]

Ambrosini, D.

G. Schirripa Spagnolo, D. Ambrosini, and D. Paoleti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A Pure Appl. Opt. 4, S376-S380 (2002).
[CrossRef]

Andrés, P.

P. Andrés, J. C. Barreiro, and J. Ojeda-Castaneda, “Focal length measuring technique using the Talbot effect,” Proc. SPIE 0701, 273-275 (1986).

Arroyo-Carrasco, M. L.

M. L. Arroyo-Carrasco, P. Rodriguez-Montero, and S. Stepanov, “Measurement of the coherence length of diffusely scattered laser beams with adaptive photodetectors,” Opt. Commun. 157, 105-110 (1998).
[CrossRef]

Barreiro, J. C.

P. Andrés, J. C. Barreiro, and J. Ojeda-Castaneda, “Focal length measuring technique using the Talbot effect,” Proc. SPIE 0701, 273-275 (1986).

Benton, S. A.

S. A. Benton and D. P. Merrill, “Simplified Talbot interferometer for lens testing,” Opt. Eng. 15, 328-331 (1976).

Bhatnagar, A.

Bolognini, N.

M. Tebaldi, G. Forte, R. Torroba, N. Bolognini, and A. Tagliaferri, “Self-imaging pitch variation applied to focal length digital measurements,” Opt. Commun. 250, 10-15(2005).
[CrossRef]

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Positioning method based on digital Moiré,” Opt. Commun. 209, 1-6 (2002).
[CrossRef]

Chavel, P.

Ding, Y.

Dunning, G. J.

Forte, G.

M. Tebaldi, G. Forte, R. Torroba, N. Bolognini, and A. Tagliaferri, “Self-imaging pitch variation applied to focal length digital measurements,” Opt. Commun. 250, 10-15(2005).
[CrossRef]

Ganesan, A. R.

Ibarra, J.

J. Ibarra and J. Ojeda-Castaneda, “Talbot interferometry: a new geometry,” Opt. Commun. 96, 294-301 (1993).
[CrossRef]

Ina, H.

Kao, C.-F.

C.-F. Kao and M.-H. Lu, “Optical encoder based on the fractional Talbot effect,” Opt. Commun. 250, 16-23 (2005).
[CrossRef]

Kobayashi, S.

Korneev, N.

Kothiyal, M. P.

Kung, H. L.

Lahiri, I.

Lohmann, A. W.

A. W. Lohmann, J. Ojeda-Castañeda, and E. E. Sicre, “Multiple interaction bandstop filters based on the Talbot effect,” Opt. Commun. 49, 388-392 (1984).
[CrossRef]

A. W. Lohmann and D. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

A. W. Lohmann, “A new Fourier spectrometer consisting of a two-gratings-interferometer,” in Proceedings of the Conference on Optical Instruments and Techniques, K. J. Habell, ed. (Chapman and Hall, 1961), pp. 58-61.

Lu, M.-H.

C.-F. Kao and M.-H. Lu, “Optical encoder based on the fractional Talbot effect,” Opt. Commun. 250, 16-23 (2005).
[CrossRef]

Mansurova, S.

Merrill, D. P.

S. A. Benton and D. P. Merrill, “Simplified Talbot interferometer for lens testing,” Opt. Eng. 15, 328-331 (1976).

Miller, D. A. B.

Murata, K.

Nakano, Y.

Nolte, D.

Ojeda-Castaneda, J.

J. Ibarra and J. Ojeda-Castaneda, “Talbot interferometry: a new geometry,” Opt. Commun. 96, 294-301 (1993).
[CrossRef]

P. Andrés, J. C. Barreiro, and J. Ojeda-Castaneda, “Focal length measuring technique using the Talbot effect,” Proc. SPIE 0701, 273-275 (1986).

Ojeda-Castañeda, J.

A. W. Lohmann, J. Ojeda-Castañeda, and E. E. Sicre, “Multiple interaction bandstop filters based on the Talbot effect,” Opt. Commun. 49, 388-392 (1984).
[CrossRef]

J. Ojeda-Castañeda and E. E. Sicre, “Tunable bandstop filter for binary objects: a self-imaging technique,” Opt. Commun. 47, 183-186 (1983).
[CrossRef]

Paoleti, D.

G. Schirripa Spagnolo, D. Ambrosini, and D. Paoleti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A Pure Appl. Opt. 4, S376-S380 (2002).
[CrossRef]

Pepper, D. M.

Petrov, M. P.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216-2225 (1990).
[CrossRef]

Prakash, Shashi

Shashi Prakash, Sanjay Upadhyay, and Chandra Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 33, 251-259(2000).
[CrossRef]

Rodriguez, P.

S. Stepanov, P. Rodriguez, S. Trivedi, and C. C. Wang, “Effective broadband detection of nanometer laser-induced ultrasonic surface displacements by CdTe:V adaptive photoelectromotive force detector,” Appl. Phys. Lett. 84, 446-448 (2004).
[CrossRef]

Rodríguez, P.

Rodriguez-Montero, P.

M. L. Arroyo-Carrasco, P. Rodriguez-Montero, and S. Stepanov, “Measurement of the coherence length of diffusely scattered laser beams with adaptive photodetectors,” Opt. Commun. 157, 105-110 (1998).
[CrossRef]

Shakher, Chandra

Shashi Prakash, Sanjay Upadhyay, and Chandra Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 33, 251-259(2000).
[CrossRef]

Sicre, E. E.

A. W. Lohmann, J. Ojeda-Castañeda, and E. E. Sicre, “Multiple interaction bandstop filters based on the Talbot effect,” Opt. Commun. 49, 388-392 (1984).
[CrossRef]

J. Ojeda-Castañeda and E. E. Sicre, “Tunable bandstop filter for binary objects: a self-imaging technique,” Opt. Commun. 47, 183-186 (1983).
[CrossRef]

Silva, D.

A. W. Lohmann and D. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

Sirohi, R. S.

Sokolov, I. A.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216-2225 (1990).
[CrossRef]

Spagnolo, G. Schirripa

G. Schirripa Spagnolo, D. Ambrosini, and D. Paoleti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A Pure Appl. Opt. 4, S376-S380 (2002).
[CrossRef]

Stepanov, S.

S. Stepanov, P. Rodriguez, S. Trivedi, and C. C. Wang, “Effective broadband detection of nanometer laser-induced ultrasonic surface displacements by CdTe:V adaptive photoelectromotive force detector,” Appl. Phys. Lett. 84, 446-448 (2004).
[CrossRef]

M. L. Arroyo-Carrasco, P. Rodriguez-Montero, and S. Stepanov, “Measurement of the coherence length of diffusely scattered laser beams with adaptive photodetectors,” Opt. Commun. 157, 105-110 (1998).
[CrossRef]

N. Korneev, S. Mansurova, P. Rodríguez, and S. Stepanov, “Fast and slow processes in the dynamics of near-surface charge grating formation in GaAs,” J. Opt. Soc. Am. B 14, 396-399 (1997).
[CrossRef]

S. Stepanov, “Photo-electromotive force in semiconductors,” in Handbook of Avanced Electronic and Photonics Materials and Devices, H. S. Nalwa, ed. (Academic, 2001), Vol. 2, pp. 205-272.
[CrossRef]

Stepanov, S. I.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216-2225 (1990).
[CrossRef]

Strand, T. C.

Suzuki, T.

Tagliaferri, A.

M. Tebaldi, G. Forte, R. Torroba, N. Bolognini, and A. Tagliaferri, “Self-imaging pitch variation applied to focal length digital measurements,” Opt. Commun. 250, 10-15(2005).
[CrossRef]

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Positioning method based on digital Moiré,” Opt. Commun. 209, 1-6 (2002).
[CrossRef]

Takeda, M.

Tebaldi, M.

M. Tebaldi, G. Forte, R. Torroba, N. Bolognini, and A. Tagliaferri, “Self-imaging pitch variation applied to focal length digital measurements,” Opt. Commun. 250, 10-15(2005).
[CrossRef]

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Positioning method based on digital Moiré,” Opt. Commun. 209, 1-6 (2002).
[CrossRef]

Torroba, R.

M. Tebaldi, G. Forte, R. Torroba, N. Bolognini, and A. Tagliaferri, “Self-imaging pitch variation applied to focal length digital measurements,” Opt. Commun. 250, 10-15(2005).
[CrossRef]

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Positioning method based on digital Moiré,” Opt. Commun. 209, 1-6 (2002).
[CrossRef]

Trivedi, S.

S. Stepanov, P. Rodriguez, S. Trivedi, and C. C. Wang, “Effective broadband detection of nanometer laser-induced ultrasonic surface displacements by CdTe:V adaptive photoelectromotive force detector,” Appl. Phys. Lett. 84, 446-448 (2004).
[CrossRef]

Trofimov, G. S.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216-2225 (1990).
[CrossRef]

Upadhyay, Sanjay

Shashi Prakash, Sanjay Upadhyay, and Chandra Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 33, 251-259(2000).
[CrossRef]

Venkateswarlu, P.

Wang, C. C.

S. Stepanov, P. Rodriguez, S. Trivedi, and C. C. Wang, “Effective broadband detection of nanometer laser-induced ultrasonic surface displacements by CdTe:V adaptive photoelectromotive force detector,” Appl. Phys. Lett. 84, 446-448 (2004).
[CrossRef]

Yokozeki, S.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

S. Stepanov, P. Rodriguez, S. Trivedi, and C. C. Wang, “Effective broadband detection of nanometer laser-induced ultrasonic surface displacements by CdTe:V adaptive photoelectromotive force detector,” Appl. Phys. Lett. 84, 446-448 (2004).
[CrossRef]

J. Appl. Phys. (1)

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216-2225 (1990).
[CrossRef]

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

G. Schirripa Spagnolo, D. Ambrosini, and D. Paoleti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A Pure Appl. Opt. 4, S376-S380 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (8)

M. L. Arroyo-Carrasco, P. Rodriguez-Montero, and S. Stepanov, “Measurement of the coherence length of diffusely scattered laser beams with adaptive photodetectors,” Opt. Commun. 157, 105-110 (1998).
[CrossRef]

J. Ibarra and J. Ojeda-Castaneda, “Talbot interferometry: a new geometry,” Opt. Commun. 96, 294-301 (1993).
[CrossRef]

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Positioning method based on digital Moiré,” Opt. Commun. 209, 1-6 (2002).
[CrossRef]

J. Ojeda-Castañeda and E. E. Sicre, “Tunable bandstop filter for binary objects: a self-imaging technique,” Opt. Commun. 47, 183-186 (1983).
[CrossRef]

A. W. Lohmann, J. Ojeda-Castañeda, and E. E. Sicre, “Multiple interaction bandstop filters based on the Talbot effect,” Opt. Commun. 49, 388-392 (1984).
[CrossRef]

M. Tebaldi, G. Forte, R. Torroba, N. Bolognini, and A. Tagliaferri, “Self-imaging pitch variation applied to focal length digital measurements,” Opt. Commun. 250, 10-15(2005).
[CrossRef]

C.-F. Kao and M.-H. Lu, “Optical encoder based on the fractional Talbot effect,” Opt. Commun. 250, 16-23 (2005).
[CrossRef]

A. W. Lohmann and D. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

Opt. Eng. (1)

S. A. Benton and D. P. Merrill, “Simplified Talbot interferometer for lens testing,” Opt. Eng. 15, 328-331 (1976).

Opt. Lasers Eng. (1)

Shashi Prakash, Sanjay Upadhyay, and Chandra Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 33, 251-259(2000).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

P. Andrés, J. C. Barreiro, and J. Ojeda-Castaneda, “Focal length measuring technique using the Talbot effect,” Proc. SPIE 0701, 273-275 (1986).

Other (2)

A. W. Lohmann, “A new Fourier spectrometer consisting of a two-gratings-interferometer,” in Proceedings of the Conference on Optical Instruments and Techniques, K. J. Habell, ed. (Chapman and Hall, 1961), pp. 58-61.

S. Stepanov, “Photo-electromotive force in semiconductors,” in Handbook of Avanced Electronic and Photonics Materials and Devices, H. S. Nalwa, ed. (Academic, 2001), Vol. 2, pp. 205-272.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematics of the optical setup for implementing the pEMF effect. We use the following notation. BS, beam splitter; F. G, function generator; PM, phase modulator; J Ω is the pEMF current; and U Ω is the voltage across the load resistor R L .

Fig. 2
Fig. 2

Experimental results of J Ω versus visibility of the interfering beams. The value of the average intensity is I 0 3 μW / mm 2 . The modulation frequency is f = 4 KHz , the amplitude of the phase modulation is Δ 300 mrad , and the period of the interfering beams is Λ 100 μm . The solid line is the best linear fit in the complete interval (0, 1).

Fig. 3
Fig. 3

Spatial transfer function: normalized values of J Ω as a function of the spatial frequency, ν, of the interference pattern. Solid lines represent the approximated linear mappings.

Fig. 4
Fig. 4

Schematics of the optical setup for measuring the visibility of the self-images.

Fig. 5
Fig. 5

Experimental results of J Ω versus axial distance in steps of 250 μm . The visibility is measured between the fifth self-imaging plane and the sixth self-imaging plane. The reference signal is the theoretical visibility curve versus axial displacement.

Fig. 6
Fig. 6

Fourier spectrum of the visibility curve versus axial displacement, shown in Fig. 5.

Fig. 7
Fig. 7

Extended views of the signal variations in the neighborhood of zero visibility. Each experimental point is separated by 50 μm .

Fig. 8
Fig. 8

Signal at the oscilloscope obtained when the adaptive photodetector is mounted in a motorized translation stage. The experimental conditions are similar to those in Fig. 5.

Equations (22)

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

m = 2 I 1 I 2 ( I 1 + I 2 )
J Ω = ( Δ σ 0 π k B T e ) m 2 F ( ν ) G ( Ω ) .
F ( ν ) = ν 1 + ν 2 ( 2 π L D ) 2 ,
G ( Ω ) = i Ω / Ω 0 1 + i Ω / Ω 0 = { Ω / Ω 0 [ 1 + ( Ω / Ω 0 ) 2 ] 1 / 2 } exp [ i φ ( Ω ) ] ,
tan [ φ ( Ω ) ] = Ω 0 / Ω .
J Ω = 403 m 2 9 , with     correlation coefficient R = 0.99 .
J Ω = 423 m 2 17 , with     R = 0.99 .
log ( J Ω ) = 3 . 32 0 . 87 log ( ν ) with     correlation coefficient   R = 0.99
J Ω = 2090 / ν 0 . 86 .
U n ( x ) = I n exp ( i φ n ) .
I ( x ) = I 1 + I 2 + 2 I 1 I 2 cos ( φ 2 φ 1 ) .
I max = I 1 + I 2 + 2 I 1 I 2 , I min = I 1 + I 2 2 I 1 I 2 ,
m = ( I max I min ) / ( I max + I min ) = 2 I 1 I 2 / ( I 1 + I 2 ) .
T ( x ) = n = C n exp ( i 2 π x n / Λ ) .
C n = ( 1 / 2 ) sinc ( n / 2 ) .
T ( x ) ( 1 / 2 ) + ( 2 / π ) cos ( 2 π x / Λ ) .
U ( x , z ) 1 2 + 2 π exp ( i π λ z Λ 2 ) cos ( 2 π x Λ ) .
I ( x , z ) 1 4 + 2 π cos ( π λ z Λ 2 ) cos ( 2 π x Λ ) + ( 4 π 2 ) cos 2 ( 2 π x Λ ) ,
I ( x , z ) 1 4 + 2 π 2 + 2 π cos ( π λ z Λ 2 ) cos ( 2 π x Λ ) + ( 2 π 2 ) cos ( 4 π x Λ ) .
I max = I ( 0 , z ) = 1 4 + 2 π 2 + 2 π cos ( π λ z Λ 2 ) + ( 2 π 2 ) .
I min = I ( Λ 2 , z ) = 1 4 + 2 π 2 2 π cos ( π λ z Λ 2 ) + 2 π 2 .
m = 8 π / ( 16 + π 2 ) cos ( π λ z / Λ 2 ) .

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