Abstract

We demonstrate that the non-steady-state photoelectromotive force induced by a vibrating Ronchi grating has a very complicated but deterministic dependence on the propagation distance. The characteristic minima of this dependence are found at fractional values of the Talbot distance, and their width is determined by the maximal transversal spatial frequency resolved by the system. This permits high accuracy in the determination of the Talbot distance.

© 2013 Optical Society of America

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References

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  1. H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401–407 (1836).
    [CrossRef]
  2. Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–201 (1881).
    [CrossRef]
  3. K. Patorsky, “The self-imaging phenomenon and its applications,” in Vol. 27 of Progress in Optics, E. Wolf, ed., (North Holland, 1989), pp. 1–108.
  4. M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996).
    [CrossRef]
  5. W. B. Case, M. T. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot–Lau configurations,” Opt. Express 17, 20966–20974 (2009).
    [CrossRef]
  6. M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wavepackets,” Phys. Rev. A 54, R3740 (1996).
    [CrossRef]
  7. J. A. Yeazell and C. R. Stroud, “Observation of fractional revivals in the evolution of a Rydberg atomic wave packet,” Phys. Rev A 43, 5153–5156 (1991).
    [CrossRef]
  8. 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]
  9. S. Stepanov, “Photo-electromotive force in semiconductors,” In Handbook of Advanced Electronic and Photonic Materials and Devices, H. S. Nalwa, ed., (Academic, 2001), Vol. 2, pp. 205–272.
  10. S. Stepanov, P. Rodriguez, S. Mansurova, M. L. Arroyo, S. Trivedi, and C. C. Wang, “Wavelength dependence of the photo-electromotive-force effect in CdTe:V crystal with bipolar photoconductivity,” Opt. Mater. 29, 623–630 (2007).
    [CrossRef]
  11. 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]
  12. N. Korneev, P. Rodriguez, and S. Stepanov, “2D pattern matching with adaptive photodetectors,” Opt. Commun. 134, 514–520 (1997).
    [CrossRef]
  13. 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]
  14. 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]
  15. P. Rodríguez-Montero, C. M. Gómez-Sarabia, and J. Ojeda-Castañeda, “Adaptive photodetector for assisted Talbot effect,” Appl. Opt. 47, 3778–3783 (2008).
    [CrossRef]
  16. A. W. Lohmann and D. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413–415 (1971).
    [CrossRef]
  17. Y. Nakano and K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24, 3162–3166 (1985).
    [CrossRef]
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    [CrossRef]
  19. 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]
  20. P. Chavel and T. C. Strand, “Range measurement using Talbot diffraction imaging of gratings,” Appl. Opt. 23, 862–871(1984).
    [CrossRef]
  21. G. Schirripa Spagnolo, D. Ambrosini, and D. Paoleti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A. 4, S376–S380 (2002).
    [CrossRef]
  22. S. Prakash, S. Upadhyay, and C. Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 34, 251–259 (2000).
    [CrossRef]
  23. C.-F. Kao and M.-H. Lu, “Optical encoder based on the fractional Talbot effect,” Opt. Commun. 250, 16–23 (2005).
    [CrossRef]
  24. W. Gautschi, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, M. Abramowitz and I. A. Stegun, eds., (National Bureau of Standards, 1972), Chap. 7.3.
  25. R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Positioning method based on digital Moiré,” Opt. Commun. 209, 1–6 (2002).
    [CrossRef]
  26. 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 (1982).
    [CrossRef]
  27. 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]

2009 (1)

2008 (1)

2007 (1)

S. Stepanov, P. Rodriguez, S. Mansurova, M. L. Arroyo, S. Trivedi, and C. C. Wang, “Wavelength dependence of the photo-electromotive-force effect in CdTe:V crystal with bipolar photoconductivity,” Opt. Mater. 29, 623–630 (2007).
[CrossRef]

2005 (2)

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]

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. 4, S376–S380 (2002).
[CrossRef]

2001 (1)

2000 (1)

S. Prakash, S. Upadhyay, and C. Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 34, 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)

N. Korneev, P. Rodriguez, and S. Stepanov, “2D pattern matching with adaptive photodetectors,” Opt. Commun. 134, 514–520 (1997).
[CrossRef]

1996 (2)

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wavepackets,” Phys. Rev. A 54, R3740 (1996).
[CrossRef]

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996).
[CrossRef]

1991 (1)

J. A. Yeazell and C. R. Stroud, “Observation of fractional revivals in the evolution of a Rydberg atomic wave packet,” Phys. Rev A 43, 5153–5156 (1991).
[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)

1985 (1)

1984 (1)

1982 (1)

1971 (1)

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

1881 (1)

Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–201 (1881).
[CrossRef]

1836 (1)

H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401–407 (1836).
[CrossRef]

Ambrosini, D.

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

Arndt, M.

Arroyo, M. L.

S. Stepanov, P. Rodriguez, S. Mansurova, M. L. Arroyo, S. Trivedi, and C. C. Wang, “Wavelength dependence of the photo-electromotive-force effect in CdTe:V crystal with bipolar photoconductivity,” Opt. Mater. 29, 623–630 (2007).
[CrossRef]

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]

Berry, M. V.

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996).
[CrossRef]

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]

Case, W. B.

Chavel, P.

Deachapunya, S.

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]

Gautschi, W.

W. Gautschi, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, M. Abramowitz and I. A. Stegun, eds., (National Bureau of Standards, 1972), Chap. 7.3.

Gómez-Sarabia, C. M.

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]

Klein, S.

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996).
[CrossRef]

Kobayashi, S.

Korneev, N.

N. Korneev, P. Rodriguez, and S. Stepanov, “2D pattern matching with adaptive photodetectors,” Opt. Commun. 134, 514–520 (1997).
[CrossRef]

Kothiyal, M. P.

Kung, H. L.

Lahiri, I.

Lohmann, A. W.

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

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.

S. Stepanov, P. Rodriguez, S. Mansurova, M. L. Arroyo, S. Trivedi, and C. C. Wang, “Wavelength dependence of the photo-electromotive-force effect in CdTe:V crystal with bipolar photoconductivity,” Opt. Mater. 29, 623–630 (2007).
[CrossRef]

Miller, D. A. B.

Murata, K.

Nakano, Y.

Nolte, D.

Ojeda-Castañeda, J.

Paoleti, D.

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

Patorsky, K.

K. Patorsky, “The self-imaging phenomenon and its applications,” in Vol. 27 of Progress in Optics, E. Wolf, ed., (North Holland, 1989), pp. 1–108.

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, S.

S. Prakash, S. Upadhyay, and C. Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 34, 251–259 (2000).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–201 (1881).
[CrossRef]

Rodriguez, P.

S. Stepanov, P. Rodriguez, S. Mansurova, M. L. Arroyo, S. Trivedi, and C. C. Wang, “Wavelength dependence of the photo-electromotive-force effect in CdTe:V crystal with bipolar photoconductivity,” Opt. Mater. 29, 623–630 (2007).
[CrossRef]

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]

N. Korneev, P. Rodriguez, and S. Stepanov, “2D pattern matching with adaptive photodetectors,” Opt. Commun. 134, 514–520 (1997).
[CrossRef]

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]

Rodríguez-Montero, P.

Schirripa Spagnolo, G.

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

Shakher, C.

S. Prakash, S. Upadhyay, and C. Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 34, 251–259 (2000).
[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]

Stepanov, S.

S. Stepanov, P. Rodriguez, S. Mansurova, M. L. Arroyo, S. Trivedi, and C. C. Wang, “Wavelength dependence of the photo-electromotive-force effect in CdTe:V crystal with bipolar photoconductivity,” Opt. Mater. 29, 623–630 (2007).
[CrossRef]

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, P. Rodriguez, and S. Stepanov, “2D pattern matching with adaptive photodetectors,” Opt. Commun. 134, 514–520 (1997).
[CrossRef]

S. Stepanov, “Photo-electromotive force in semiconductors,” In Handbook of Advanced Electronic and Photonic Materials and Devices, H. S. Nalwa, ed., (Academic, 2001), Vol. 2, pp. 205–272.

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]

Stolow, A.

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wavepackets,” Phys. Rev. A 54, R3740 (1996).
[CrossRef]

Strand, T. C.

Stroud, C. R.

J. A. Yeazell and C. R. Stroud, “Observation of fractional revivals in the evolution of a Rydberg atomic wave packet,” Phys. Rev A 43, 5153–5156 (1991).
[CrossRef]

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.

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401–407 (1836).
[CrossRef]

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]

Tomandl, M. T.

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. Mansurova, M. L. Arroyo, S. Trivedi, and C. C. Wang, “Wavelength dependence of the photo-electromotive-force effect in CdTe:V crystal with bipolar photoconductivity,” Opt. Mater. 29, 623–630 (2007).
[CrossRef]

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, S.

S. Prakash, S. Upadhyay, and C. Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 34, 251–259 (2000).
[CrossRef]

Villeneuve, D. M.

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wavepackets,” Phys. Rev. A 54, R3740 (1996).
[CrossRef]

Vrakking, M. J. J.

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wavepackets,” Phys. Rev. A 54, R3740 (1996).
[CrossRef]

Wang, C. C.

S. Stepanov, P. Rodriguez, S. Mansurova, M. L. Arroyo, S. Trivedi, and C. C. Wang, “Wavelength dependence of the photo-electromotive-force effect in CdTe:V crystal with bipolar photoconductivity,” Opt. Mater. 29, 623–630 (2007).
[CrossRef]

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]

Yeazell, J. A.

J. A. Yeazell and C. R. Stroud, “Observation of fractional revivals in the evolution of a Rydberg atomic wave packet,” Phys. Rev A 43, 5153–5156 (1991).
[CrossRef]

Appl. Opt. (4)

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. Mod. Opt. (1)

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996).
[CrossRef]

J. Opt. A. (1)

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

J. Opt. Soc. Am. (1)

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

Opt. Commun. (6)

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, P. Rodriguez, and S. Stepanov, “2D pattern matching with adaptive photodetectors,” Opt. Commun. 134, 514–520 (1997).
[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]

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

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

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

Opt. Express (1)

Opt. Lasers Eng. (1)

S. Prakash, S. Upadhyay, and C. Shakher, “Real time out-of-plane vibration measurement/monitoring using Talbot interferometry,” Opt. Lasers Eng. 34, 251–259 (2000).
[CrossRef]

Opt. Lett. (1)

Opt. Mater. (1)

S. Stepanov, P. Rodriguez, S. Mansurova, M. L. Arroyo, S. Trivedi, and C. C. Wang, “Wavelength dependence of the photo-electromotive-force effect in CdTe:V crystal with bipolar photoconductivity,” Opt. Mater. 29, 623–630 (2007).
[CrossRef]

Philos. Mag. (2)

H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401–407 (1836).
[CrossRef]

Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–201 (1881).
[CrossRef]

Phys. Rev A (1)

J. A. Yeazell and C. R. Stroud, “Observation of fractional revivals in the evolution of a Rydberg atomic wave packet,” Phys. Rev A 43, 5153–5156 (1991).
[CrossRef]

Phys. Rev. A (1)

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wavepackets,” Phys. Rev. A 54, R3740 (1996).
[CrossRef]

Other (3)

K. Patorsky, “The self-imaging phenomenon and its applications,” in Vol. 27 of Progress in Optics, E. Wolf, ed., (North Holland, 1989), pp. 1–108.

S. Stepanov, “Photo-electromotive force in semiconductors,” In Handbook of Advanced Electronic and Photonic Materials and Devices, H. S. Nalwa, ed., (Academic, 2001), Vol. 2, pp. 205–272.

W. Gautschi, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, M. Abramowitz and I. A. Stegun, eds., (National Bureau of Standards, 1972), Chap. 7.3.

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Figures (7)

Fig. 1.
Fig. 1.

Theoretical intensity profiles for (a) z=(π/2)(π/390) and (b) z=(π/2)(π/96). The Talbot distance is normalized to z0=π.

Fig. 2.
Fig. 2.

Theoretical intensity distribution for z=π/3 (square wave) and z=(160/481)π. The Talbot distance is normalized to z0=π.

Fig. 3.
Fig. 3.

Experimental setup for measuring the photoEMF currents generated in a GaAs crystal by the diffraction of a vibrating Ronchi grating. SG, signal generator; B.S., beam splitter.

Fig. 4.
Fig. 4.

PhotoEMF calculation for a number of discrete values zq,p=πq/p. Note that the only plane where the current is zero is z=π/2 (the last point to the right). The function is highly irregular. The continuous curve is only a guide to the eye for connecting discrete points. The Talbot distance is normalized to z0=π.

Fig. 5.
Fig. 5.

Computer simulation of the photoEMF signal generated by a vibrating Ronchi grating illuminated by a wide Gaussian beam. The first (negative) self-image is at z=z0; the zero contrast point is z/z0=0.5. The detector spatial cutoff frequency is (from the lower to the upper curve) k0=5, 10, 15. The k0=10 and 15 curves are upward shifted for better visibility. Positions marked as a, b, and c in the k0=15 curve correspond to fractional distances 5/8, 2/3, and 3/4 of z0, respectively.

Fig. 6.
Fig. 6.

Experimental photoEMF current generated in a GaAs crystal by a vibrating Ronchi grating as a function of the axial distance from the grating in 1 mm steps. Positions marked a, b, and c correspond to fractional distances 5/8, 2/3, and 3/4 of z0, respectively.

Fig. 7.
Fig. 7.

PhotoEMF current as a function of the axial position around the first position of minimum contrast at two scanning steps: (a) steps of 0.5 mm and (b) 100 μm. The data were taken with 1 s time constant.

Equations (9)

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E(x,z)=1/2+n=1iπ12n+1exp(i(2n+1)2z+i(2n+1)x).
E(x,0)=1if0<x<πandE(x,0)=0ifπ<x<2π.
Δm=limε0[E(xm+ε)E(xmε)]
Δm=1ps=0p1exp(i(2s+1)2πq/p+i(2s+1)mπ/p).
Δm=1pexp(iπ4[5(pm)2p])
Δm=1pexp(iπ4[1m2p])
dE(x)dxp2πexp(iπ4[1px2/π2]).
J(δ,z)J0δππ(I(z,x)x)2dx.
J(δ)J0m(ΔIm)2,

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