Abstract

By using the Hilbert–Huang transform, a novel method is proposed to perform the task of particle sizing and axial locating directly from in-line digital holograms rather than reconstructing the optical field. The intensity distribution of the particle hologram is decomposed into intrinsic mode functions (IMFs) by the empirical mode decomposition. From the Hilbert spectrum of these IMFs, the axial location of the particle can be calculated by fitting the spectrum to a straight line, and the particle size can be derived from the singularities of the spectrum. Our method does not need to predefine any basis function; thus the whole process is fast and efficient. The validity and accuracy of the method are demonstrated by the numerical simulations and experiments. It is expected that this method can be used in on-line particle sizing and 3D tracking.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. R. Guildenbecher, P. L. Reu, H. L. Stuaffacher, and T. Grasser, “Accurate measurement of out-of-plane particle displacement from the cross correlation of sequential digital in-line holograms,” Opt. Lett. 38, 4015–4018 (2013).
    [CrossRef]
  2. F. Verpillat, F. Joud, P. Desbiolles, and M. Gross, “Dark-field digital holographic microscopy for 3D-tracking of gold nanoparticles,” Opt. Express 19, 26044–26055 (2011).
    [CrossRef]
  3. Y. Wu, X. Wu, Z. Wang, L. Chen, and K. Cen, “Coal powder measurement by digital holography with expanded measurement area,” Appl. Opt. 50, H22–H29 (2011).
    [CrossRef]
  4. D. Lebrun, L. Méès, D. Fréchou, S. Coëtmellec, M. Brunel, and D. Allano, “Long time exposure digital in-line holography for 3-D particle trajectography,” Opt. Express 21, 23522–23530 (2013).
    [CrossRef]
  5. Y. Yang, G. Li, L. Tang, and L. Huang, “Integrated gray-level gradient method applied for the extraction of three-dimensional velocity fields of sprays in in-line digital holography,” Appl. Opt. 51, 255–267 (2012).
    [CrossRef]
  6. L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
    [CrossRef]
  7. W. Chen, C. J. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
    [CrossRef]
  8. L. Tian, N. Loomis, J. A. Dominguez-Caballero, and G. Barbastathis, “Quantitative measurement of size and three-dimensional position of fast-moving bubbles in air-water mixture flows using digital holography,” Appl. Opt. 49, 1549–1554 (2010).
    [CrossRef]
  9. L. Denis, D. Lorenz, E. Thiébaut, C. Fourier, and D. Trede, “Inline hologram reconstruction with sparsity constraints,” Opt. Lett. 34, 3475–3477 (2009).
    [CrossRef]
  10. W. Yang, A. B. Kostinski, and R. A. Shaw, “Depth-of-focus reduction for digital in-line holography of particle fields,” Opt. Lett. 30, 1303–1305 (2005).
    [CrossRef]
  11. W. Yingchun, W. Xuecheng, Y. Jing, W. Zhihua, G. Xiang, Z. Binwu, C. Linghong, Q. Kunzan, G. Gréhan, and C. Kefa, “Wavelet-based depth-of-field extension, accurate autofocusing, and particle pairing for digital inline particle holography,” Appl. Opt. 53, 556–564 (2014).
    [CrossRef]
  12. M. Antkowiak, N. Callens, C. Yourassowsky, and F. Dubois, “Extended focused imaging of a micro particle field with digital holographic microscopy,” Opt. Lett. 33, 1626–1628 (2008).
    [CrossRef]
  13. C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47, D71–D79 (2008).
    [CrossRef]
  14. C. Buraga-Lefebvre, S. Coetmellec, D. Lebrun, and C. Ozkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
    [CrossRef]
  15. Y. Yang, B. Kang, and Y. Choo, “Application of the correlation coefficient method for determination of the focal plane to digital particle holography,” Appl. Opt. 47, 817–824 (2008).
    [CrossRef]
  16. M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424–2430 (2004).
    [CrossRef]
  17. P. Langehanenberg, B. Kemper, D. Dirksen, and G. von Bally, “Autofocusing in digital holographic phase contrast microscopy on pure phase objects for live cell imaging,” Appl. Opt. 47, D176–D182 (2008).
    [CrossRef]
  18. D. Kapfenberger, A. Sonn-Segev, and Y. Roichman, “Accurate holographic imaging of colloidal particle pairs by Rayleigh-Sommerfeld reconstruction,” Opt. Express 21, 12228–12237 (2013).
    [CrossRef]
  19. G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” Opt. Acta 23, 685–700 (1976).
    [CrossRef]
  20. K. Nishihara, S. Hatano, and K. Nagayama, “New method of obtaining particle diameter by the fast Fourier transform pattern of the in-line hologram,” Opt. Eng. 36, 2429–2439 (1997).
    [CrossRef]
  21. L. Denis, C. Fournier, T. Fournel, C. Ducottet, and D. Jeulin, “Direct extraction of the mean particle size from a digital hologram,” Appl. Opt. 45, 944–952 (2006).
    [CrossRef]
  22. L. Onural and M. T. Özgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A 9, 252–260 (1992).
    [CrossRef]
  23. J. Widjaja and S. Soontaranon, “All wavelet analysis of in-line particle holograms,” Opt. Lasers Eng. 47, 1325–1333 (2009).
    [CrossRef]
  24. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
    [CrossRef]
  25. N. E. Huang, “New method for nonlinear and nonstationary time series analysis: empirical mode decomposition and Hilbert spectral analysis,” Proc. SPIE 4056, 197–209 (2000).
    [CrossRef]
  26. N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. A 459, 2317–2345 (2003).
    [CrossRef]
  27. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford University, 1948).

2014

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

W. Yingchun, W. Xuecheng, Y. Jing, W. Zhihua, G. Xiang, Z. Binwu, C. Linghong, Q. Kunzan, G. Gréhan, and C. Kefa, “Wavelet-based depth-of-field extension, accurate autofocusing, and particle pairing for digital inline particle holography,” Appl. Opt. 53, 556–564 (2014).
[CrossRef]

2013

2012

2011

2010

2009

L. Denis, D. Lorenz, E. Thiébaut, C. Fourier, and D. Trede, “Inline hologram reconstruction with sparsity constraints,” Opt. Lett. 34, 3475–3477 (2009).
[CrossRef]

W. Chen, C. J. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

J. Widjaja and S. Soontaranon, “All wavelet analysis of in-line particle holograms,” Opt. Lasers Eng. 47, 1325–1333 (2009).
[CrossRef]

2008

2006

2005

2004

2003

N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. A 459, 2317–2345 (2003).
[CrossRef]

2000

N. E. Huang, “New method for nonlinear and nonstationary time series analysis: empirical mode decomposition and Hilbert spectral analysis,” Proc. SPIE 4056, 197–209 (2000).
[CrossRef]

C. Buraga-Lefebvre, S. Coetmellec, D. Lebrun, and C. Ozkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

1998

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

1997

K. Nishihara, S. Hatano, and K. Nagayama, “New method of obtaining particle diameter by the fast Fourier transform pattern of the in-line hologram,” Opt. Eng. 36, 2429–2439 (1997).
[CrossRef]

1992

1976

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” Opt. Acta 23, 685–700 (1976).
[CrossRef]

Allano, D.

Antkowiak, M.

Barbastathis, G.

Binwu, Z.

Brunel, M.

Buraga-Lefebvre, C.

C. Buraga-Lefebvre, S. Coetmellec, D. Lebrun, and C. Ozkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

Callens, N.

Cen, K.

Chen, L.

Chen, W.

W. Chen, C. J. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

Choo, Y.

Coetmellec, S.

C. Buraga-Lefebvre, S. Coetmellec, D. Lebrun, and C. Ozkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

Coëtmellec, S.

Denis, L.

Desbiolles, P.

Dirksen, D.

Dominguez-Caballero, J. A.

Dubois, F.

Ducottet, C.

Embrione, V.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

Fan, K. L.

N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. A 459, 2317–2345 (2003).
[CrossRef]

Ferraro, P.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

Fourier, C.

Fournel, T.

Fournier, C.

Fréchou, D.

Fusco, S.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

Gloersen, P.

N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. A 459, 2317–2345 (2003).
[CrossRef]

Grasser, T.

Gréhan, G.

Gross, M.

Guildenbecher, D. R.

Hatano, S.

K. Nishihara, S. Hatano, and K. Nagayama, “New method of obtaining particle diameter by the fast Fourier transform pattern of the in-line hologram,” Opt. Eng. 36, 2429–2439 (1997).
[CrossRef]

Hennelly, B. M.

Huang, L.

Huang, N. E.

N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. A 459, 2317–2345 (2003).
[CrossRef]

N. E. Huang, “New method for nonlinear and nonstationary time series analysis: empirical mode decomposition and Hilbert spectral analysis,” Proc. SPIE 4056, 197–209 (2000).
[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

Jeulin, D.

Jing, Y.

Joud, F.

Kang, B.

Kapfenberger, D.

Kefa, C.

Kemper, B.

Kostinski, A. B.

Kunzan, Q.

Langehanenberg, P.

Lebrun, D.

D. Lebrun, L. Méès, D. Fréchou, S. Coëtmellec, M. Brunel, and D. Allano, “Long time exposure digital in-line holography for 3-D particle trajectography,” Opt. Express 21, 23522–23530 (2013).
[CrossRef]

C. Buraga-Lefebvre, S. Coetmellec, D. Lebrun, and C. Ozkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

Li, G.

Liebling, M.

Linghong, C.

Liu, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

Long, S. R.

N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. A 459, 2317–2345 (2003).
[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

Loomis, N.

Lorenz, D.

McElhinney, C. P.

Méès, L.

Memmolo, P.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

Merola, F.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

Miccio, L.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

Nagayama, K.

K. Nishihara, S. Hatano, and K. Nagayama, “New method of obtaining particle diameter by the fast Fourier transform pattern of the in-line hologram,” Opt. Eng. 36, 2429–2439 (1997).
[CrossRef]

Naughton, T. J.

Netti, P. A.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

Nishihara, K.

K. Nishihara, S. Hatano, and K. Nagayama, “New method of obtaining particle diameter by the fast Fourier transform pattern of the in-line hologram,” Opt. Eng. 36, 2429–2439 (1997).
[CrossRef]

Onural, L.

Özgen, M. T.

Ozkul, C.

C. Buraga-Lefebvre, S. Coetmellec, D. Lebrun, and C. Ozkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

Paciello, A.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

Qu, W.

N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. A 459, 2317–2345 (2003).
[CrossRef]

Quan, C. J.

W. Chen, C. J. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

Reu, P. L.

Roichman, Y.

Shaw, R. A.

Shen, S. S. P.

N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. A 459, 2317–2345 (2003).
[CrossRef]

Shen, Z.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

Shih, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

Sonn-Segev, A.

Soontaranon, S.

J. Widjaja and S. Soontaranon, “All wavelet analysis of in-line particle holograms,” Opt. Lasers Eng. 47, 1325–1333 (2009).
[CrossRef]

Stuaffacher, H. L.

Tang, L.

Tay, C. J.

W. Chen, C. J. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

Thiébaut, E.

Thompson, B. J.

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” Opt. Acta 23, 685–700 (1976).
[CrossRef]

Tian, L.

Titchmarsh, E. C.

E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford University, 1948).

Trede, D.

Tung, C. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

Tyler, G. A.

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” Opt. Acta 23, 685–700 (1976).
[CrossRef]

Unser, M.

Ventre, M.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

Verpillat, F.

von Bally, G.

Wang, Z.

Widjaja, J.

J. Widjaja and S. Soontaranon, “All wavelet analysis of in-line particle holograms,” Opt. Lasers Eng. 47, 1325–1333 (2009).
[CrossRef]

Wu, M. C.

N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. A 459, 2317–2345 (2003).
[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

Wu, X.

Wu, Y.

Xiang, G.

Xuecheng, W.

Yang, W.

Yang, Y.

Yen, N. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

Yingchun, W.

Yourassowsky, C.

Zheng, Q.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

Zhihua, W.

Appl. Opt.

Y. Wu, X. Wu, Z. Wang, L. Chen, and K. Cen, “Coal powder measurement by digital holography with expanded measurement area,” Appl. Opt. 50, H22–H29 (2011).
[CrossRef]

Y. Yang, G. Li, L. Tang, and L. Huang, “Integrated gray-level gradient method applied for the extraction of three-dimensional velocity fields of sprays in in-line digital holography,” Appl. Opt. 51, 255–267 (2012).
[CrossRef]

L. Tian, N. Loomis, J. A. Dominguez-Caballero, and G. Barbastathis, “Quantitative measurement of size and three-dimensional position of fast-moving bubbles in air-water mixture flows using digital holography,” Appl. Opt. 49, 1549–1554 (2010).
[CrossRef]

W. Yingchun, W. Xuecheng, Y. Jing, W. Zhihua, G. Xiang, Z. Binwu, C. Linghong, Q. Kunzan, G. Gréhan, and C. Kefa, “Wavelet-based depth-of-field extension, accurate autofocusing, and particle pairing for digital inline particle holography,” Appl. Opt. 53, 556–564 (2014).
[CrossRef]

C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47, D71–D79 (2008).
[CrossRef]

Y. Yang, B. Kang, and Y. Choo, “Application of the correlation coefficient method for determination of the focal plane to digital particle holography,” Appl. Opt. 47, 817–824 (2008).
[CrossRef]

P. Langehanenberg, B. Kemper, D. Dirksen, and G. von Bally, “Autofocusing in digital holographic phase contrast microscopy on pure phase objects for live cell imaging,” Appl. Opt. 47, D176–D182 (2008).
[CrossRef]

L. Denis, C. Fournier, T. Fournel, C. Ducottet, and D. Jeulin, “Direct extraction of the mean particle size from a digital hologram,” Appl. Opt. 45, 944–952 (2006).
[CrossRef]

Appl. Phys. Lett.

W. Chen, C. J. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Lab Chip

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, “Particle tracking by full-field complex wavefront subtraction in digital holography microscopy,” Lab Chip 14, 1129–1134 (2014).
[CrossRef]

Opt. Acta

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” Opt. Acta 23, 685–700 (1976).
[CrossRef]

Opt. Eng.

K. Nishihara, S. Hatano, and K. Nagayama, “New method of obtaining particle diameter by the fast Fourier transform pattern of the in-line hologram,” Opt. Eng. 36, 2429–2439 (1997).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

C. Buraga-Lefebvre, S. Coetmellec, D. Lebrun, and C. Ozkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

J. Widjaja and S. Soontaranon, “All wavelet analysis of in-line particle holograms,” Opt. Lasers Eng. 47, 1325–1333 (2009).
[CrossRef]

Opt. Lett.

Proc. R. Soc. A

N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. A 459, 2317–2345 (2003).
[CrossRef]

Proc. R. Soc. Lond. A

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454, 903–995 (1998).
[CrossRef]

Proc. SPIE

N. E. Huang, “New method for nonlinear and nonstationary time series analysis: empirical mode decomposition and Hilbert spectral analysis,” Proc. SPIE 4056, 197–209 (2000).
[CrossRef]

Other

E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford University, 1948).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Simulated in-line particle holograms and their radial intensity distribution: (a) rod-like particle hologram, (b) radial intensity distribution of hologram (a), (c) spherical particle hologram, and (d) radial intensity distribution of hologram (c).

Fig. 2.
Fig. 2.

Hilbert–Huang transform flow chart.

Fig. 3.
Fig. 3.

IMFs and Hilbert spectrum of IMF1: (a) original signal, (b)–(f) five IMFs, (g) a radius, (h) Hilbert spectrum of IMF1, and (i) Hilbert spectrum of original signal. The red line in (h) is a fitting line of the data.

Fig. 4.
Fig. 4.

(a) Schematic of in-line digital holography experimental setup. (b) Recorded hologram.

Fig. 5.
Fig. 5.

(a) 1D cross section of the original hologram using just one horizonal line. (b) Superposition of all lines along the rod. (c) First IMF of (b). (d) Hilbert spectrum of IMF1.

Fig. 6.
Fig. 6.

(a) Schematic of the two-particle in-line digital holography experimental setup. (b) Recorded hologram.

Fig. 7.
Fig. 7.

Experimental results of spherical particle [blue star, error of recording distance (z); red point, error of particle size (α)].

Tables (4)

Tables Icon

Table 1. Calculated Recording Distance z (α=50μm)

Tables Icon

Table 2. Calculated Particle Radius α (z=20cm)

Tables Icon

Table 3. Calculated z and α in the Experiment

Tables Icon

Table 4. Calculated Distance Δd between Two Particles

Equations (8)

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

I(r)=14αλzcos(πr2λzπ4)sinc(2αrλz)+(2αλz)2[sinc(2αrλz)]2,
I(r)=12πα2λzsin(πr2λz)[2J1(2παr/λz)2παr/λz]+(πα2λz)2[2J1(2παr/λz)2παr/λz]2,
ddr(πr2λzπ4)=2πrλz=2πf,
f=r/λz.
x(t)=i=1nci+rn.
c¯i(t)=1π+ci(τ)tτdτ.
αi(t)=ci2(t)+c¯i2(t);Φi(t)=arctanc¯i(t)ci(t).
fi(t)=12πdΦi(t)dt.

Metrics