Abstract

For the first time to the authors’ knowledge, the Talbot effect has been observed and investigated in digital holography. By numerical reconstruction of holograms, the Talbot self-imaging phenomenon is observed by reconstruction of the amplitude of the image at different distances and (or) wavelengths. A simple spectrometer based on Talbot self-imaging in digital holography is proposed and demonstrated.

© 2004 Optical Society of America

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References

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  1. O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1990).
  2. K. Patorski, The Moiré Technique (Elsevier, Amsterdam, 1993).
  3. A. Maripov and Y. Ismanov, J. Opt. 26, 25 (1995).
    [Crossref]
  4. U. Schnars and W. Juptner, Meas. Sci. Technol. 13, R85 (2002).
    [Crossref]
  5. S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, Opt. Express 9, 294 (2001), http://www.opticsexpress.org .
    [Crossref] [PubMed]
  6. A. W. Lohmann, in Proceedings of the Conference on Optical Instruments and Techniques, London (Wiley, New York, 1961), p. 58.
  7. H. L. Kung, A. Bhatnagar, and D. A. B. Miller, Opt. Lett. 26, 1645 (2001).
    [Crossref]
  8. H. L. Kung and D. A. B. Miller, “Miniaturized Talbot spectrometer,” U.S. patent6,525,815 (February25, 2003).

2002 (1)

U. Schnars and W. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[Crossref]

2001 (2)

1995 (1)

A. Maripov and Y. Ismanov, J. Opt. 26, 25 (1995).
[Crossref]

Bhatnagar, A.

De Nicola, S.

Ferraro, P.

Finizio, A.

Glatt, I.

O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1990).

Grilli, S.

Ismanov, Y.

A. Maripov and Y. Ismanov, J. Opt. 26, 25 (1995).
[Crossref]

Juptner, W.

U. Schnars and W. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[Crossref]

Kafri, O.

O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1990).

Kung, H. L.

H. L. Kung, A. Bhatnagar, and D. A. B. Miller, Opt. Lett. 26, 1645 (2001).
[Crossref]

H. L. Kung and D. A. B. Miller, “Miniaturized Talbot spectrometer,” U.S. patent6,525,815 (February25, 2003).

Lohmann, A. W.

A. W. Lohmann, in Proceedings of the Conference on Optical Instruments and Techniques, London (Wiley, New York, 1961), p. 58.

Maripov, A.

A. Maripov and Y. Ismanov, J. Opt. 26, 25 (1995).
[Crossref]

Meucci, R.

Miller, D. A. B.

H. L. Kung, A. Bhatnagar, and D. A. B. Miller, Opt. Lett. 26, 1645 (2001).
[Crossref]

H. L. Kung and D. A. B. Miller, “Miniaturized Talbot spectrometer,” U.S. patent6,525,815 (February25, 2003).

Patorski, K.

K. Patorski, The Moiré Technique (Elsevier, Amsterdam, 1993).

Pierattini, G.

Schnars, U.

U. Schnars and W. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[Crossref]

J. Opt. (1)

A. Maripov and Y. Ismanov, J. Opt. 26, 25 (1995).
[Crossref]

Meas. Sci. Technol. (1)

U. Schnars and W. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Other (4)

H. L. Kung and D. A. B. Miller, “Miniaturized Talbot spectrometer,” U.S. patent6,525,815 (February25, 2003).

O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1990).

K. Patorski, The Moiré Technique (Elsevier, Amsterdam, 1993).

A. W. Lohmann, in Proceedings of the Conference on Optical Instruments and Techniques, London (Wiley, New York, 1961), p. 58.

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Figures (8)

Fig. 1
Fig. 1

DH setup: BE, beam expander; M, mirrors; BS, beam splitters.

Fig. 2
Fig. 2

Amplitude reconstruction of a grating.

Fig. 3
Fig. 3

Numerical reconstruction at a fixed λr at various distances zr. Left inset, FFT spectrum for each reconstruction distance; right inset, small portion of the reconstruction.

Fig. 4
Fig. 4

Plot of the FFT spectrum along line L of Fig. 3 for two reconstruction wavelengths: 532 and 560 nm.

Fig. 5
Fig. 5

Spectrogram obtained by numerical reconstruction at fixed distance zr=325 mm.

Fig. 6
Fig. 6

Qualitative spectrograms for two gratings, of pitches (a) p1 and (b) p2, and (c) their product.

Fig. 7
Fig. 7

Reconstruction at zr=z0=295 mm of a hologram with two gratings, recorded with a single wavelength, (a) λr=λ0=532 nm or (b) λr=λ0=632.8 nm; with two wavelengths (c) λ01=532 nm and λ02=632.8 nm combined but reconstructed at λr=532 nm; and (d) with λr=632.8 nm.

Fig. 8
Fig. 8

Spectrograms obtained by use of λ0=532 nm and λ0=632.8 nm separately and together.

Equations (7)

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Orecξ,η,zr,λr=-1izrλrexp-iπλrzrξ2+η2×Ox,y,z0,λ0×exp-iπλrzrx2+y2+i2πλrzrxξ+yηdxdy,
Ox,y,z0,λ0=expi2π/λ0z0x2+y2iλ0z0×Gxg,yg×exp-iπλ0z0xg2+yg2+i2πλ0z0xxg+yygdxgdyg,
Gxg,yg=m=042m+1πsin2πp2m+1xg.
Orecξ,η,zr,λr=m=042m+1π×exp-iπ2m+12p2λ0z0-λrzr×sin2πp2m+1ξ.
λ0z0-λrzr/p2=±2M,
zr=λ0/λr/z0MZT,
λr=z0/zrλ0NΛT.

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