Abstract

To suppress the aperture diffraction and spectral leakage effects in the reconstruction process of the digital hologram and to maintain the original information recorded in the hologram, a novel reconstruction method based on extension and apodization of the digital hologram is presented, by which the original hologram can be extended by filling the average intensity values of the boundary, and the extended hologram is apodized by use of the constructed window function. As a sample, the digital hologram of the static particle field is recorded and numerically extended and then apodized with the appointed window. Finally, an unabridged and clear digital holographic image is reconstructed from the extended and apodized hologram. The experimental results confirm that this method cannot only eliminate the black-and-white diffraction fringes in the reconstructed image, but also attain the unabridged image with high quality.

© 2009 Optical Society of America

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References

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  1. E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation: application in digital holographic microscopy,” Opt. Commun. 182, 59-69 (2000).
    [CrossRef]
  2. R. Jóźwicki, J. Bartold, and M. Prytulak, “Application of digital hologram apodization for surface shape measurement methods,” Proc. SPIE 6254, 625415 (2006).
    [CrossRef]
  3. Y.C. Zhang, J. L. Zhao, W. Zhang, and Q. Fan, “Digital hologram apodization using Tukey-window function,” Acta Photonica Sinica 36, 2256-2260 (2007) (in Chinese).
  4. Y. C. Zhang, J. L. Zhao, Q. Fan, and W. Zhang, “Application of digital hologram apodization using Tukey-Window for particle in-focus position measurement,” Chin. J. Lasers 35, 1542-1547 (2008) (in Chinese).
    [CrossRef]
  5. F. Dubois, O. Monnom, C. Yourassowsky, and J.-C. Legros, “Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies,” Appl. Opt. 41, 2621-2626 (2002).
    [CrossRef] [PubMed]
  6. M. Vlcek and R. Unbehauen, “Note the window function with nearly minimum sidelobe energy,” IEEE Trans. Circuits Syst. 37, 1323-1324 (1990).
    [CrossRef]
  7. A. H. Nuttall, “Some windows with very good sidelobe behavior,” IEEE Trans. Acoust. Speech Signal Process. 29, 84-91 (1981).
    [CrossRef]
  8. T. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829-1839 (2002).
    [CrossRef]
  9. U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
    [CrossRef]
  10. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994-7001 (1999).
    [CrossRef]
  11. Q. Fan, J. L. Zhao, Q. Xiang, Y. Xu, H. Q. Lu, and J. F. Li, “Methods of improving resolution of digital holographic microscopy,” J. Optoelectron. Laser 16, 226-230 (2005) (in Chinese).

2008 (1)

Y. C. Zhang, J. L. Zhao, Q. Fan, and W. Zhang, “Application of digital hologram apodization using Tukey-Window for particle in-focus position measurement,” Chin. J. Lasers 35, 1542-1547 (2008) (in Chinese).
[CrossRef]

2007 (1)

Y.C. Zhang, J. L. Zhao, W. Zhang, and Q. Fan, “Digital hologram apodization using Tukey-window function,” Acta Photonica Sinica 36, 2256-2260 (2007) (in Chinese).

2006 (1)

R. Jóźwicki, J. Bartold, and M. Prytulak, “Application of digital hologram apodization for surface shape measurement methods,” Proc. SPIE 6254, 625415 (2006).
[CrossRef]

2005 (1)

Q. Fan, J. L. Zhao, Q. Xiang, Y. Xu, H. Q. Lu, and J. F. Li, “Methods of improving resolution of digital holographic microscopy,” J. Optoelectron. Laser 16, 226-230 (2005) (in Chinese).

2002 (3)

T. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829-1839 (2002).
[CrossRef]

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

F. Dubois, O. Monnom, C. Yourassowsky, and J.-C. Legros, “Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies,” Appl. Opt. 41, 2621-2626 (2002).
[CrossRef] [PubMed]

2000 (1)

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation: application in digital holographic microscopy,” Opt. Commun. 182, 59-69 (2000).
[CrossRef]

1999 (1)

1990 (1)

M. Vlcek and R. Unbehauen, “Note the window function with nearly minimum sidelobe energy,” IEEE Trans. Circuits Syst. 37, 1323-1324 (1990).
[CrossRef]

1981 (1)

A. H. Nuttall, “Some windows with very good sidelobe behavior,” IEEE Trans. Acoust. Speech Signal Process. 29, 84-91 (1981).
[CrossRef]

Bartold, J.

R. Jóźwicki, J. Bartold, and M. Prytulak, “Application of digital hologram apodization for surface shape measurement methods,” Proc. SPIE 6254, 625415 (2006).
[CrossRef]

Cuche, E.

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation: application in digital holographic microscopy,” Opt. Commun. 182, 59-69 (2000).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994-7001 (1999).
[CrossRef]

Depeursinge, C.

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation: application in digital holographic microscopy,” Opt. Commun. 182, 59-69 (2000).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994-7001 (1999).
[CrossRef]

Dubois, F.

Fan, Q.

Y. C. Zhang, J. L. Zhao, Q. Fan, and W. Zhang, “Application of digital hologram apodization using Tukey-Window for particle in-focus position measurement,” Chin. J. Lasers 35, 1542-1547 (2008) (in Chinese).
[CrossRef]

Y.C. Zhang, J. L. Zhao, W. Zhang, and Q. Fan, “Digital hologram apodization using Tukey-window function,” Acta Photonica Sinica 36, 2256-2260 (2007) (in Chinese).

Q. Fan, J. L. Zhao, Q. Xiang, Y. Xu, H. Q. Lu, and J. F. Li, “Methods of improving resolution of digital holographic microscopy,” J. Optoelectron. Laser 16, 226-230 (2005) (in Chinese).

Józwicki, R.

R. Jóźwicki, J. Bartold, and M. Prytulak, “Application of digital hologram apodization for surface shape measurement methods,” Proc. SPIE 6254, 625415 (2006).
[CrossRef]

Jüptner, W.

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Kreis, T.

T. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829-1839 (2002).
[CrossRef]

Legros, J.-C.

Li, J. F.

Q. Fan, J. L. Zhao, Q. Xiang, Y. Xu, H. Q. Lu, and J. F. Li, “Methods of improving resolution of digital holographic microscopy,” J. Optoelectron. Laser 16, 226-230 (2005) (in Chinese).

Lu, H. Q.

Q. Fan, J. L. Zhao, Q. Xiang, Y. Xu, H. Q. Lu, and J. F. Li, “Methods of improving resolution of digital holographic microscopy,” J. Optoelectron. Laser 16, 226-230 (2005) (in Chinese).

Marquet, P.

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation: application in digital holographic microscopy,” Opt. Commun. 182, 59-69 (2000).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994-7001 (1999).
[CrossRef]

Monnom, O.

Nuttall, A. H.

A. H. Nuttall, “Some windows with very good sidelobe behavior,” IEEE Trans. Acoust. Speech Signal Process. 29, 84-91 (1981).
[CrossRef]

Prytulak, M.

R. Jóźwicki, J. Bartold, and M. Prytulak, “Application of digital hologram apodization for surface shape measurement methods,” Proc. SPIE 6254, 625415 (2006).
[CrossRef]

Schnars, U.

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Unbehauen, R.

M. Vlcek and R. Unbehauen, “Note the window function with nearly minimum sidelobe energy,” IEEE Trans. Circuits Syst. 37, 1323-1324 (1990).
[CrossRef]

Vlcek, M.

M. Vlcek and R. Unbehauen, “Note the window function with nearly minimum sidelobe energy,” IEEE Trans. Circuits Syst. 37, 1323-1324 (1990).
[CrossRef]

Xiang, Q.

Q. Fan, J. L. Zhao, Q. Xiang, Y. Xu, H. Q. Lu, and J. F. Li, “Methods of improving resolution of digital holographic microscopy,” J. Optoelectron. Laser 16, 226-230 (2005) (in Chinese).

Xu, Y.

Q. Fan, J. L. Zhao, Q. Xiang, Y. Xu, H. Q. Lu, and J. F. Li, “Methods of improving resolution of digital holographic microscopy,” J. Optoelectron. Laser 16, 226-230 (2005) (in Chinese).

Yourassowsky, C.

Zhang, W.

Y. C. Zhang, J. L. Zhao, Q. Fan, and W. Zhang, “Application of digital hologram apodization using Tukey-Window for particle in-focus position measurement,” Chin. J. Lasers 35, 1542-1547 (2008) (in Chinese).
[CrossRef]

Y.C. Zhang, J. L. Zhao, W. Zhang, and Q. Fan, “Digital hologram apodization using Tukey-window function,” Acta Photonica Sinica 36, 2256-2260 (2007) (in Chinese).

Zhang, Y. C.

Y. C. Zhang, J. L. Zhao, Q. Fan, and W. Zhang, “Application of digital hologram apodization using Tukey-Window for particle in-focus position measurement,” Chin. J. Lasers 35, 1542-1547 (2008) (in Chinese).
[CrossRef]

Zhang, Y.C.

Y.C. Zhang, J. L. Zhao, W. Zhang, and Q. Fan, “Digital hologram apodization using Tukey-window function,” Acta Photonica Sinica 36, 2256-2260 (2007) (in Chinese).

Zhao, J. L.

Y. C. Zhang, J. L. Zhao, Q. Fan, and W. Zhang, “Application of digital hologram apodization using Tukey-Window for particle in-focus position measurement,” Chin. J. Lasers 35, 1542-1547 (2008) (in Chinese).
[CrossRef]

Y.C. Zhang, J. L. Zhao, W. Zhang, and Q. Fan, “Digital hologram apodization using Tukey-window function,” Acta Photonica Sinica 36, 2256-2260 (2007) (in Chinese).

Q. Fan, J. L. Zhao, Q. Xiang, Y. Xu, H. Q. Lu, and J. F. Li, “Methods of improving resolution of digital holographic microscopy,” J. Optoelectron. Laser 16, 226-230 (2005) (in Chinese).

Acta Photonica Sinica (1)

Y.C. Zhang, J. L. Zhao, W. Zhang, and Q. Fan, “Digital hologram apodization using Tukey-window function,” Acta Photonica Sinica 36, 2256-2260 (2007) (in Chinese).

Appl. Opt. (2)

Chin. J. Lasers (1)

Y. C. Zhang, J. L. Zhao, Q. Fan, and W. Zhang, “Application of digital hologram apodization using Tukey-Window for particle in-focus position measurement,” Chin. J. Lasers 35, 1542-1547 (2008) (in Chinese).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

A. H. Nuttall, “Some windows with very good sidelobe behavior,” IEEE Trans. Acoust. Speech Signal Process. 29, 84-91 (1981).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

M. Vlcek and R. Unbehauen, “Note the window function with nearly minimum sidelobe energy,” IEEE Trans. Circuits Syst. 37, 1323-1324 (1990).
[CrossRef]

J. Optoelectron. Laser (1)

Q. Fan, J. L. Zhao, Q. Xiang, Y. Xu, H. Q. Lu, and J. F. Li, “Methods of improving resolution of digital holographic microscopy,” J. Optoelectron. Laser 16, 226-230 (2005) (in Chinese).

Meas. Sci. Technol. (1)

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Opt. Commun. (1)

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation: application in digital holographic microscopy,” Opt. Commun. 182, 59-69 (2000).
[CrossRef]

Opt. Eng. (1)

T. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829-1839 (2002).
[CrossRef]

Proc. SPIE (1)

R. Jóźwicki, J. Bartold, and M. Prytulak, “Application of digital hologram apodization for surface shape measurement methods,” Proc. SPIE 6254, 625415 (2006).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Comparison of the new constructed windows ( L = 768 , L 0 = 512 ) with different values of k. (a) One-dimensional transmission profiles; (b) corresponding log-magnitudes of transform.

Fig. 2
Fig. 2

Digital hologram and reconstructed image by the convolution approach. (a) Original digital hologram of particles; (b) reconstructed gray image; (c) intensity-distribution profile of the first line particles in (b).

Fig. 3
Fig. 3

Reconstruction results of the digital hologram with apodization. (a) Apodized digital hologram of particles with the constructed window; (b) reconstructed gray image; (c) intensity-distribution profile of the first line particles in (b).

Fig. 4
Fig. 4

Digital holograms of particles extended to different dimensions by filling average intensity values. (a) and (c) are extended holograms with pixels of 576 × 576 and 640 × 640 ; (b) and (d) are the corresponding reconstructed images of (a) and (c); (e) and (f) are distribution profiles of the appointed lines in (b) and (d), respectively.

Fig. 5
Fig. 5

Reconstruction results of the digital hologram with extension and apodization. (a) Apodizing the extended digital hologram with the constructed window; (b) reconstructed gray image; (c) intensity-distribution profile of the first line particles in (b).

Equations (4)

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

W ( l ) = { cos k [ a ( 2 l L L 0 1 ) ] 1 l L L 0 2 1 L L 0 2 + 1 l L + L 0 2 cos k [ b ( 2 l L + L 0 + 2 1 ) ] L + L 0 2 + 1 l L ,
a = π 2 · L L 0 L 0 + 2 L ,
b = π 2 · L + L 0 + 2 L L 0 2 .
W ( p , q ) = W ( p ) W ( q ) 1 p L h , 1 q L v ,

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