Uncertainty characterization of particle depth measurement using digital in-line holography and the hybrid method

Jian Gao; Daniel R. Guildenbecher; Phillip L. Reu; Jun Chen

doi:10.1364/OE.21.026432

Uncertainty characterization of particle depth measurement using digital in-line holography and the hybrid method

Jian Gao, Daniel R. Guildenbecher, Phillip L. Reu, and Jun Chen

Optics Express
Vol. 21,
Issue 22,
pp. 26432-26449
(2013)
•https://doi.org/10.1364/OE.21.026432

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Jian Gao, Daniel R. Guildenbecher, Phillip L. Reu, and Jun Chen, "Uncertainty characterization of particle depth measurement using digital in-line holography and the hybrid method," Opt. Express 21, 26432-26449 (2013)

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Related Topics
Table of Contents Category
- Holography
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Digital holography (090.1995)
- Three-dimensional image processing (100.6890)
- Instrumentation, measurement, and metrology (120.0120)
- Particles (350.4990)

About this Article
History
- Original Manuscript: July 23, 2013
- Revised Manuscript: October 6, 2013
- Manuscript Accepted: October 11, 2013
- Published: October 28, 2013

Accessible

Open Access

Abstract

In the detection of particles using digital in-line holography, measurement accuracy is substantially influenced by the hologram processing method. In particular, a number of methods have been proposed to determine the out-of-plane particle depth (z location). However, due to the lack of consistent uncertainty characterization, it has been unclear which method is best suited to a given measurement problem. In this work, depth determination accuracies of seven particle detection methods, including a recently proposed hybrid method, are systematically investigated in terms of relative depth measurement errors and uncertainties. Both synthetic and experimental holograms of particle fields are considered at conditions relevant to particle sizing and tracking. While all methods display a range of particle conditions where they are most accurate, in general the hybrid method is shown to be the most robust with depth uncertainty less than twice the particle diameter over a wide range of particle field conditions.

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References

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Publication

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673 (2004).
[Crossref]
J. Sheng, E. Malkiel, and J. Katz, “Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer,” Exp. Fluids 45, 1023–1035 (2008).
[Crossref]
D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Méès, “Testing an in-line digital holography inverse method for the Lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New J. Phys. 14, 043039 (2012).
[Crossref]
N. A. Buchmann, C. Atkinson, and J. Soria, “Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows,” Meas. Sci. Technol. 24, 024005 (2013).
[Crossref]
J. Lee, K. A. Sallam, K. C. Lin, and C. D. Carter, “Spray structure in near-injector region of aerated jet in subsonic crossflow,” J. Propul. Power 25, 258–266 (2009).
[Crossref]
Q. Lü, Y. Chen, R. Yuan, B. Ge, Y. Gao, and Y. Zhang, “Trajectory and velocity measurement of a particle in spray by digital holography,” Appl. Opt. 48, 7000–7007 (2009).
[Crossref] [PubMed]
Y. Yang and B. seon Kang, “Digital particle holographic system for measurements of spray field characteristics,” Opt. Laser Eng. 49, 1254–1263 (2011).
[Crossref]
J. Gao, D. R. Guildenbecher, P. L. Reu, V. Kulkarni, P. E. Sojka, and J. Chen, “Quantitative, three-dimensional diagnostics of multiphase drop fragmentation via digital in-line holography,” Opt. Lett. 38, 1893–1895 (2013).
[Crossref] [PubMed]
J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, and A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Nat. Acad. Sci. USA 104, 17512–17517 (2007).
[Crossref] [PubMed]
S. J. Lee, K. W. Seo, Y. S. Choi, and M. H. Sohn, “Three-dimensional motion measurements of free-swimming microorganisms using digital holographic microscopy,” Meas. Sci. Technol. 22, 064004 (2011).
[Crossref]
L. Tian, N. Loomis, J. A. Domínguez-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] [PubMed]
D. Lebrun, D. Allano, L. Méès, F. Walle, F. Corbin, R. Boucheron, and D. Fréchou, “Size measurement of bubbles in a cavitation tunnel by digital in-line holography,” Appl. Opt. 50, H1–H9 (2011).
[Crossref] [PubMed]
J. P. Fugal, R. A. Shaw, E. W. Saw, and A. V. Sergeyev, “Airborne digital holographic system for cloud particle measurements,” Appl. Opt. 43, 5987–5995 (2004).
[Crossref] [PubMed]
Y.-S. Choi and S.-J. Lee, “Three-dimensional volumetric measurement of red blood cell motion using digital holographic microscopy,” Appl. Opt. 48, 2983–2990 (2009).
[Crossref] [PubMed]
T. Khanam, M. N. Rahman, A. Rajendran, V. Kariwala, and A. K. Asundi, “Accurate size measurement of needle-shaped particles using digital holography,” Chem. Eng. Sci. 66, 2699–2706 (2011).
[Crossref]
S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[Crossref]
J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45, 3893–3901 (2006).
[Crossref] [PubMed]
V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123–128 (2005).
[Crossref]
J. P. Fugal, T. J. Schulz, and R. A. Shaw, “Practical methods for automated reconstruction and characterization of particles in digital in-line holograms,” Meas. Sci. Technol. 20, 075501 (2009).
[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] [PubMed]
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] [PubMed]
D. R. Guildenbecher, J. Gao, P. L. Reu, and J. Chen, “Digital holography simulations and experiments to quantify the accuracy of 3D particle location and 2D sizing using a proposed hybrid method,” Appl. Opt. 52, 3790–3801 (2013).
[Crossref] [PubMed]
V. Palero, M. Arroyo, and J. Soria, “Digital holography for micro-droplet diagnostics,” Exp. Fluids 43, 185–195 (2007).
[Crossref]
E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[Crossref]
Y. Yang, B. seon Kang, and Y. jun Choo, “Application of the correlation coefficient method for determination of the focal plane to digital particle holography,” Appl. Opt. 47, 817–824 (2008).
[Crossref] [PubMed]
G. Pan and H. Meng, “Digital holography of particle fields: Reconstruction by use of complex amplitude,” Appl. Opt. 42, 827–833 (2003).
[Crossref] [PubMed]
W. Yang, A. B. Kostinski, and R. A. Shaw, “Phase signature for particle detection with digital in-line holography,” Opt. Lett. 31, 1399–1401 (2006).
[Crossref] [PubMed]
F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 5895–5908 (2006).
[Crossref] [PubMed]
C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul”, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Laser Eng. 33, 409–421 (2000).
[Crossref]
S. Soontaranon, J. Widjaja, and T. Asakura, “Extraction of object position from in-line holograms by using single wavelet coefficient,” Opt. Commun. 281, 1461–1467 (2008).
[Crossref]
F. Soulez, L. Denis, C. Fournier, Éric Thiébaut, and C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” J. Opt. Soc. Am. A 24, 1164–1171 (2007).
[Crossref]
J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz-Mie theory and its application to micro-holography,” Appl. Opt. 23, 4140–4148 (1984).
[Crossref]
D. K. Singh and P. K. Panigrahi, “Improved digital holographic reconstruction algorithm for depth error reduction and elimination of out-of-focus particles,” Opt. Express 18, 2426–2448 (2010).
[Crossref] [PubMed]

2013 (3)

N. A. Buchmann, C. Atkinson, and J. Soria, “Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows,” Meas. Sci. Technol. 24, 024005 (2013).
[Crossref]

J. Gao, D. R. Guildenbecher, P. L. Reu, V. Kulkarni, P. E. Sojka, and J. Chen, “Quantitative, three-dimensional diagnostics of multiphase drop fragmentation via digital in-line holography,” Opt. Lett. 38, 1893–1895 (2013).
[Crossref] [PubMed]

D. R. Guildenbecher, J. Gao, P. L. Reu, and J. Chen, “Digital holography simulations and experiments to quantify the accuracy of 3D particle location and 2D sizing using a proposed hybrid method,” Appl. Opt. 52, 3790–3801 (2013).
[Crossref] [PubMed]

2012 (2)

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] [PubMed]

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Méès, “Testing an in-line digital holography inverse method for the Lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New J. Phys. 14, 043039 (2012).
[Crossref]

2011 (5)

S. J. Lee, K. W. Seo, Y. S. Choi, and M. H. Sohn, “Three-dimensional motion measurements of free-swimming microorganisms using digital holographic microscopy,” Meas. Sci. Technol. 22, 064004 (2011).
[Crossref]

Y. Yang and B. seon Kang, “Digital particle holographic system for measurements of spray field characteristics,” Opt. Laser Eng. 49, 1254–1263 (2011).
[Crossref]

T. Khanam, M. N. Rahman, A. Rajendran, V. Kariwala, and A. K. Asundi, “Accurate size measurement of needle-shaped particles using digital holography,” Chem. Eng. Sci. 66, 2699–2706 (2011).
[Crossref]

D. Lebrun, D. Allano, L. Méès, F. Walle, F. Corbin, R. Boucheron, and D. Fréchou, “Size measurement of bubbles in a cavitation tunnel by digital in-line holography,” Appl. Opt. 50, H1–H9 (2011).
[Crossref] [PubMed]

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] [PubMed]

2010 (3)

D. K. Singh and P. K. Panigrahi, “Improved digital holographic reconstruction algorithm for depth error reduction and elimination of out-of-focus particles,” Opt. Express 18, 2426–2448 (2010).
[Crossref] [PubMed]

L. Tian, N. Loomis, J. A. Domínguez-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] [PubMed]

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[Crossref]

2009 (4)

J. P. Fugal, T. J. Schulz, and R. A. Shaw, “Practical methods for automated reconstruction and characterization of particles in digital in-line holograms,” Meas. Sci. Technol. 20, 075501 (2009).
[Crossref]

J. Lee, K. A. Sallam, K. C. Lin, and C. D. Carter, “Spray structure in near-injector region of aerated jet in subsonic crossflow,” J. Propul. Power 25, 258–266 (2009).
[Crossref]

Y.-S. Choi and S.-J. Lee, “Three-dimensional volumetric measurement of red blood cell motion using digital holographic microscopy,” Appl. Opt. 48, 2983–2990 (2009).
[Crossref] [PubMed]

Q. Lü, Y. Chen, R. Yuan, B. Ge, Y. Gao, and Y. Zhang, “Trajectory and velocity measurement of a particle in spray by digital holography,” Appl. Opt. 48, 7000–7007 (2009).
[Crossref] [PubMed]

2008 (3)

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

J. Sheng, E. Malkiel, and J. Katz, “Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer,” Exp. Fluids 45, 1023–1035 (2008).
[Crossref]

S. Soontaranon, J. Widjaja, and T. Asakura, “Extraction of object position from in-line holograms by using single wavelet coefficient,” Opt. Commun. 281, 1461–1467 (2008).
[Crossref]

2007 (3)

V. Palero, M. Arroyo, and J. Soria, “Digital holography for micro-droplet diagnostics,” Exp. Fluids 43, 185–195 (2007).
[Crossref]

J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, and A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Nat. Acad. Sci. USA 104, 17512–17517 (2007).
[Crossref] [PubMed]

F. Soulez, L. Denis, C. Fournier, Éric Thiébaut, and C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” J. Opt. Soc. Am. A 24, 1164–1171 (2007).
[Crossref]

2006 (3)

W. Yang, A. B. Kostinski, and R. A. Shaw, “Phase signature for particle detection with digital in-line holography,” Opt. Lett. 31, 1399–1401 (2006).
[Crossref] [PubMed]

J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45, 3893–3901 (2006).
[Crossref] [PubMed]

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 5895–5908 (2006).
[Crossref] [PubMed]

2005 (1)

V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123–128 (2005).
[Crossref]

2004 (2)

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673 (2004).
[Crossref]

J. P. Fugal, R. A. Shaw, E. W. Saw, and A. V. Sergeyev, “Airborne digital holographic system for cloud particle measurements,” Appl. Opt. 43, 5987–5995 (2004).
[Crossref] [PubMed]

2003 (1)

G. Pan and H. Meng, “Digital holography of particle fields: Reconstruction by use of complex amplitude,” Appl. Opt. 42, 827–833 (2003).
[Crossref] [PubMed]

2000 (2)

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[Crossref]

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

1984 (1)

F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz-Mie theory and its application to micro-holography,” Appl. Opt. 23, 4140–4148 (1984).
[Crossref]

Adolf, J.

Allano, D.

F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz-Mie theory and its application to micro-holography,” Appl. Opt. 23, 4140–4148 (1984).
[Crossref]

Arroyo, M.

V. Palero, M. Arroyo, and J. Soria, “Digital holography for micro-droplet diagnostics,” Exp. Fluids 43, 185–195 (2007).
[Crossref]

Asakura, T.

S. Soontaranon, J. Widjaja, and T. Asakura, “Extraction of object position from in-line holograms by using single wavelet coefficient,” Opt. Commun. 281, 1461–1467 (2008).
[Crossref]

Asundi, A. K.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[Crossref]

Atkinson, C.

N. A. Buchmann, C. Atkinson, and J. Soria, “Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows,” Meas. Sci. Technol. 24, 024005 (2013).
[Crossref]

Barbastathis, G.

Belas, R.

Boucheron, R.

Buchmann, N. A.

N. A. Buchmann, C. Atkinson, and J. Soria, “Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows,” Meas. Sci. Technol. 24, 024005 (2013).
[Crossref]

Buraga-Lefebvre, C.

Callens, N.

Carter, C. D.

J. Lee, K. A. Sallam, K. C. Lin, and C. D. Carter, “Spray structure in near-injector region of aerated jet in subsonic crossflow,” J. Propul. Power 25, 258–266 (2009).
[Crossref]

Cen, K.

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] [PubMed]

Chareyron, D.

Chen, J.

Chen, L.

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] [PubMed]

Chen, Y.

Q. Lü, Y. Chen, R. Yuan, B. Ge, Y. Gao, and Y. Zhang, “Trajectory and velocity measurement of a particle in spray by digital holography,” Appl. Opt. 48, 7000–7007 (2009).
[Crossref] [PubMed]

Choi, Y. S.

Choi, Y.-S.

Y.-S. Choi and S.-J. Lee, “Three-dimensional volumetric measurement of red blood cell motion using digital holographic microscopy,” Appl. Opt. 48, 2983–2990 (2009).
[Crossref] [PubMed]

Coëtmellec, S.

Corbin, F.

Darakis, E.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[Crossref]

Denis, L.

Domínguez-Caballero, J. A.

Dubois, F.

Fournier, C.

Fréchou, D.

Fugal, J. P.

J. P. Fugal, R. A. Shaw, E. W. Saw, and A. V. Sergeyev, “Airborne digital holographic system for cloud particle measurements,” Appl. Opt. 43, 5987–5995 (2004).
[Crossref] [PubMed]

Gao, J.

Gao, Y.

Q. Lü, Y. Chen, R. Yuan, B. Ge, Y. Gao, and Y. Zhang, “Trajectory and velocity measurement of a particle in spray by digital holography,” Appl. Opt. 48, 7000–7007 (2009).
[Crossref] [PubMed]

Ge, B.

Q. Lü, Y. Chen, R. Yuan, B. Ge, Y. Gao, and Y. Zhang, “Trajectory and velocity measurement of a particle in spray by digital holography,” Appl. Opt. 48, 7000–7007 (2009).
[Crossref] [PubMed]

Gire, J.

Goepfert, C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Gouesbet, G.

F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz-Mie theory and its application to micro-holography,” Appl. Opt. 23, 4140–4148 (1984).
[Crossref]

Grehan, G.

F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz-Mie theory and its application to micro-holography,” Appl. Opt. 23, 4140–4148 (1984).
[Crossref]

Grosjean, N.

Guildenbecher, D. R.

Huang, L.

Ilchenko, V.

V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123–128 (2005).
[Crossref]

jun Choo, Y.

Kariwala, V.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[Crossref]

Katz, J.

J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45, 3893–3901 (2006).
[Crossref] [PubMed]

Khanam, T.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[Crossref]

Kostinski, A. B.

W. Yang, A. B. Kostinski, and R. A. Shaw, “Phase signature for particle detection with digital in-line holography,” Opt. Lett. 31, 1399–1401 (2006).
[Crossref] [PubMed]

Kulkarni, V.

Lance, M.

Lebrun, D.

Lee, J.

J. Lee, K. A. Sallam, K. C. Lin, and C. D. Carter, “Spray structure in near-injector region of aerated jet in subsonic crossflow,” J. Propul. Power 25, 258–266 (2009).
[Crossref]

Lee, S. J.

Lee, S.-J.

Y.-S. Choi and S.-J. Lee, “Three-dimensional volumetric measurement of red blood cell motion using digital holographic microscopy,” Appl. Opt. 48, 2983–2990 (2009).
[Crossref] [PubMed]

Lex, T.

V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123–128 (2005).
[Crossref]

Li, G.

Lin, K. C.

J. Lee, K. A. Sallam, K. C. Lin, and C. D. Carter, “Spray structure in near-injector region of aerated jet in subsonic crossflow,” J. Propul. Power 25, 258–266 (2009).
[Crossref]

Loomis, N.

Lü, Q.

Q. Lü, Y. Chen, R. Yuan, B. Ge, Y. Gao, and Y. Zhang, “Trajectory and velocity measurement of a particle in spray by digital holography,” Appl. Opt. 48, 7000–7007 (2009).
[Crossref] [PubMed]

Malkiel, E.

J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45, 3893–3901 (2006).
[Crossref] [PubMed]

Marié, J. L.

Méès, L.

Meng, H.

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673 (2004).
[Crossref]

G. Pan and H. Meng, “Digital holography of particle fields: Reconstruction by use of complex amplitude,” Appl. Opt. 42, 827–833 (2003).
[Crossref] [PubMed]

Murata, S.

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[Crossref]

Naughton, T. J.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[Crossref]

Özkul”, C.

Palero, V.

V. Palero, M. Arroyo, and J. Soria, “Digital holography for micro-droplet diagnostics,” Exp. Fluids 43, 185–195 (2007).
[Crossref]

Pan, G.

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673 (2004).
[Crossref]

G. Pan and H. Meng, “Digital holography of particle fields: Reconstruction by use of complex amplitude,” Appl. Opt. 42, 827–833 (2003).
[Crossref] [PubMed]

Panigrahi, P. K.

Place, A. R.

Pu, Y.

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S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
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Appl. Opt. (12)

F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz-Mie theory and its application to micro-holography,” Appl. Opt. 23, 4140–4148 (1984).
[Crossref]

G. Pan and H. Meng, “Digital holography of particle fields: Reconstruction by use of complex amplitude,” Appl. Opt. 42, 827–833 (2003).
[Crossref] [PubMed]

J. P. Fugal, R. A. Shaw, E. W. Saw, and A. V. Sergeyev, “Airborne digital holographic system for cloud particle measurements,” Appl. Opt. 43, 5987–5995 (2004).
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Y.-S. Choi and S.-J. Lee, “Three-dimensional volumetric measurement of red blood cell motion using digital holographic microscopy,” Appl. Opt. 48, 2983–2990 (2009).
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Q. Lü, Y. Chen, R. Yuan, B. Ge, Y. Gao, and Y. Zhang, “Trajectory and velocity measurement of a particle in spray by digital holography,” Appl. Opt. 48, 7000–7007 (2009).
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Chem. Eng. Sci. (2)

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[Crossref]

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V. Palero, M. Arroyo, and J. Soria, “Digital holography for micro-droplet diagnostics,” Exp. Fluids 43, 185–195 (2007).
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J. Opt. Soc. Am. A (1)

J. Propul. Power (1)

J. Lee, K. A. Sallam, K. C. Lin, and C. D. Carter, “Spray structure in near-injector region of aerated jet in subsonic crossflow,” J. Propul. Power 25, 258–266 (2009).
[Crossref]

Meas. Sci. Technol. (4)

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673 (2004).
[Crossref]

N. A. Buchmann, C. Atkinson, and J. Soria, “Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows,” Meas. Sci. Technol. 24, 024005 (2013).
[Crossref]

New J. Phys. (1)

Opt. Commun. (1)

S. Soontaranon, J. Widjaja, and T. Asakura, “Extraction of object position from in-line holograms by using single wavelet coefficient,” Opt. Commun. 281, 1461–1467 (2008).
[Crossref]

Opt. Express (2)

Opt. Laser Eng. (2)

Y. Yang and B. seon Kang, “Digital particle holographic system for measurements of spray field characteristics,” Opt. Laser Eng. 49, 1254–1263 (2011).
[Crossref]

Opt. Laser Technol. (1)

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[Crossref]

Opt. Lett. (2)

W. Yang, A. B. Kostinski, and R. A. Shaw, “Phase signature for particle detection with digital in-line holography,” Opt. Lett. 31, 1399–1401 (2006).
[Crossref] [PubMed]

Proc. Nat. Acad. Sci. USA (1)

Proc. SPIE (1)

V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123–128 (2005).
[Crossref]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Supplementary Material (1)

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Fig. 1 DIH for particle field detection: (a) recording and (b) reconstruction.

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Fig. 2 Illustration of the HYBRID method. (a) synthetic in-line hologram. (b) I_min(k, l). (c) T_max(k, l). (d) D_T (k, l). (e) global sharpness profile. (f) ��_{t_o}{I_min}. (g) ℰ {��_{t_o}{I_min}}. (h) refined particle binary images. Inset: Local intensity I_r(k, l, z′_d)

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Fig. 3 Relative depth error and relative depth uncertainty for detection of single circular (a) and square (b) particles ( Media 1).

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Fig. 4 Illustration of the influence of Fresnel number on particle detection. (a) Hologram simulated at F = 0.063, D₀ = 200 μm, z₀ = 0.3 m. Inset: particle image obtained by reconstruction of the hologram at z_r = 0.3 m. (b) Intensity profile along the red dotted line in (a). (c) Intensity profile obtained by reconstruction of the hologram in (a) at z_r = z₀, z₀ ± 10D₀. (d) Hologram simulated at F = 0.004, D₀ = 40 μm, z₀ = 0.2 m. Inset: particle image obtained by reconstruction of the hologram at z_r = 0.2 m. (e) Intensity profile along the red dotted line in (d). (f) Intensity profile obtained by reconstruction of the hologram in (d) at z_r = z₀, z₀ ± 10D₀. The visibility of the holograms in (a) and (d) is enhanced for clarity. The hologram dimension is 1024 × 7.4 μm. No random noise is included in the simulation.

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Fig. 5 Relative error of in-plane position and size measurement (a) and relative uncertainty of in-plane position and size measurement (b) for the HYBRID method. W: width; H: height.

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Fig. 6 (a) Example synthetic hologram at F̄ = 0.013, ρ_n = 6 mm⁻². (b) Example synthetic hologram at F̄ = 0.032, ρ_n = 6 mm⁻². (c) Reconstruction of the hologram in (b) at the depth of the particle enclosed by the window. (d) Zoomed-in image of the particle enclosed in (c).

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Fig. 7 Illustration of the processing of experimental holograms. (a) sample hologram. (b) reconstructed intensity at the average particle depth. (c) particle binary image extracted by the HYBRID method. (d) depth distribution of detected particles along the x (horizontal) direction. Image contrast is adjusted for better visibility.

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Fig. 8 A photo of the cuvette filled with silicone oil and particles (a), Sample hologram (b) and the corresponding binary image extracted (c). The hologram contrast is adjusted for better visibility.

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Tables (4)

Table 1 Error of measured mean displacement, mean relative depth error and relative depth uncertainty for detection of synthetic particle fields.

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Table 2 Detection effectiveness and mean size measurement error of the HYBRID method in detection of synthetic particle fields.

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Table 3 Error of measured mean displacement and relative depth uncertainty for measurement of a planar experimental particle field.

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Table 4 Error of measured mean displacement and relative depth uncertainty for measurement of a 3D experimental particle field after removal of the overlapping particles such as those circled in Fig. 8(c).

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Equations (20)

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E_{r} (k, l, z_{r}) = ℱ^{- 1} {ℱ {h (m, n)} G (m^{'}, n^{'}, z_{r})} .

G (m^{'}, n^{'}, z_{r}) = exp (j \frac{2 π}{λ} z_{r} \sqrt{1 - {(\frac{λ m^{'}}{M Δ ξ})}^{2} - {(\frac{λ n^{'}}{N Δ η})}^{2}}) circ (\sqrt{{(\frac{λ m^{'}}{M Δ ξ})}^{2} + {(\frac{λ n^{'}}{N Δ η})}^{2}})

I_{\min} (k, l) = min_{z_{r}} I_{r} (k, l, z_{r})

T_{\max} (k, l) = max_{z_{r}} T (k, l, z_{r})

D_{T} (k, l) = arg max_{z_{r}} T (k, l, z_{r}) .

T (k, l, z_{r}) = {[A_{r} (k, l, z_{r}) \otimes S_{x}]}^{2} + {[A_{r} (k, l, z_{r}) \otimes S_{y}]}^{2},

S (t) = \frac{\sum_{k, l} (ℰ {𝒯_{t} {I_{\min}}} \cdot T_{\max})}{\sum_{k, l} ℰ {𝒯_{t} {I_{\min}}}},

S_{W} (t) = \frac{\sum_{k, l \in W} (ℰ {𝒯_{t} {I_{\min}}} \cdot T_{\max})}{\sum_{k, l \in W} ℰ {𝒯_{t} {I_{\min}}}},

LAP (z_{r}) = \sum_{k, l \in W} {[I_{r} (k, l, z_{r}) \otimes lap]}^{2},

lap = (\begin{matrix} 0 & 1 & 0 \\ 1 & - 4 & 1 \\ 0 & 1 & 0 \end{matrix})

C C (z_{r}) = \frac{\sum_{k, l \in W} [C (k, l, z_{r} - Δ C_{z} / 2) C (k, l, z_{r} + Δ C_{z} / 2)]}{\sqrt{\sum_{k, l \in W} {[C (k, l, z_{r} - Δ C_{z} / 2)]}^{2} \sum_{k, l \in W} {[C (k, l, z_{r} + Δ C_{z} / 2)]}^{2}}},

VAR (z_{r}) = \frac{1}{N_{P}} \sum_{k, l \in P} {[I_{r} (k, l, z_{r}) - {\bar{I}}_{P} (z_{r})]}^{2},

z_{d} = arg min_{z_{r}} [\frac{1}{N_{P}} \sum_{k, l \in P} I_{r} (k, l, z_{r})] .

z_{d} = \frac{1}{N_{I E}} \sum_{k, l \in I E} D_{I} (k, l),

D_{I} (k, l) = arg min_{z_{r}} I_{r} (k, l, z_{r})

I G_{1} (z_{r}) = \frac{1}{N_{E E}} \sum_{k, l \in E E} I_{r} (k, l, z_{r}) - \frac{1}{N_{I E}} \sum_{k, l \in I E} I_{r} (k, l, z_{r}),

{IG}_{2} (z_{r}) = \frac{1}{N_{E E}} \sum_{k, l \in E E} I_{r} (k, l, z_{r}) - \frac{1}{N_{P}} \sum_{k, l \in P} I_{r} (k, l, z_{r}) .

E_{a}^{(i)} (k, l) = ℱ^{- 1} {ℱ {E_{a}^{(i - 1)} (k, l)} G (k^{'}, l^{'}, z_{0, i - 1} - z_{0, i})} p_{i} (k, l) .

p_{i} (k, l) = {\begin{matrix} 0, \sqrt{{(k Δ ξ - x_{0, i})}^{2} + {(l Δ η - y_{0, i})}^{2}} \leq D_{0, i} / 2 \\ 1, \sqrt{{(k Δ ξ - x_{0, i})}^{2} + {(l Δ η - y_{0, i})}^{2}} > D_{0, i} / 2 \end{matrix}

h (m, n) = {| ℱ^{- 1} {ℱ {E_{a}^{(K)} (k, l)} G (k^{'}, l^{'}, L)} |}^{2},

	F̄ = 0.008		0.013		0.032		0.054
	ρ_n = 3 (mm⁻²)	6	3	6	3	6	3	6
	Error of Mean Displacement $\| \bar{Δ z_{d}} - Δ z_{0} \|$ (mm)
HYBRID	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
LAP	0.00	0.01	0.02	0.00	0.00	0.04	0.01	0.03
CC	0.00	0.09	0.00	0.00	0.06	0.14	0.11	0.18
VAR	0.02	0.35	0.22	0.11	0.05	0.01	0.00	0.01
MINI	0.00	0.00	0.00	0.00	0.00	0.01	0.00	0.00
MINEI	0.00	0.00	0.00	0.00	0.01	0.00	0.02	0.02
IG	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
	Mean Relative Depth Error $\bar{\| z_{d} - z_{0} \| / D_{0}}$
HYBRID	0.94	1.20	0.61	0.80	0.75	0.94	0.71	0.79
LAP	9.95	9.80	10.68	11.08	7.23	9.47	8.73	9.29
CC	2.44	5.56	1.41	3.44	22.74	98.47	23.97	63.88
VAR	252.35	117.31	79.90	29.15	5.79	4.05	0.40	2.37
MINI	0.44	0.55	0.34	0.41	0.42	0.65	0.39	0.39
MINEI	2.08	3.18	1.42	2.11	9.26	20.96	5.57	16.80
IG	0.39	0.44	0.30	0.37	0.28	0.32	0.31	0.29
	Relative Depth Uncertainty δ_z/D̄₀
HYBRID	0.76	1.19	0.53	0.65	0.31	0.58	0.37	0.67
LAP	8.76	8.73	10.15	10.73	6.24	20.14	7.69	16.69
CC	1.88	37.49	1.28	21.17	33.01	64.63	41.59	59.57
VAR	197.82	160.91	100.36	76.68	21.78	20.41	0.15	9.65
MINI	0.28	0.33	0.25	0.26	0.15	0.18	0.11	0.14
MINEI	2.02	2.62	1.71	2.25	3.89	6.35	3.16	5.84
IG	0.28	0.30	0.22	0.25	0.15	0.16	0.12	0.13

	F̄ = 0.008		0.013		0.032		0.054
	ρ_n = 3 (mm⁻²)	6	3	6	3	6	3	6
Detection Effectiveness (%)	86.5	86.4	87.2	80.2	100.0	100.0	100.0	99.8
$\bar{\| D_{d} - D_{0} \| / D_{0}}$ (%)	5.9	6.5	4.9	4.2	1.7	2.3	0.9	1.8
$\bar{\| W_{d} - D_{0} \| / D_{0}}$ (%)	7.5	7.4	6.5	6.4	2.9	3.4	2.9	3.1
$\bar{\| H_{d} - D_{0} \| / D_{0}}$ (%)	7.0	7.5	6.4	6.4	2.8	3.5	2.6	3.2

	HYBRID	LAP	CC	VAR	MINI	MINEI	IG
	Error of Mean Displacement $\| \bar{Δ z_{d}} - Δ z_{0} \|$ (μm)
Δz₀ = 127 μm	6	20	1	49	11	11	18
Δz₀ = 635 μm	2	27	6	29	0	7	7
	Relative Depth Uncertainty δ_z/D̄_d
Δz₀ = 127 μm	1.55	10.65	0.97	16.50	2.28	2.39	3.80
Δz₀ = 635 μm	1.55	11.03	1.66	18.93	2.44	2.13	4.18

	HYBRID	LAP	CC	VAR	MINI	MINEI	IG
$\| \bar{Δ z_{d}} - Δ z_{0} \|$ (mm)	0.02	4.99	5.21	0.34	0.02	0.30	6.00
δ_z/D̄_d	1.57	14.61	19.79	3.17	1.84	2.55	14.92

	F̄ = 0.008		0.013		0.032		0.054
	ρ_n = 3 (mm⁻²)	6	3	6	3	6	3	6
	Error of Mean Displacement $\| \bar{Δ z_{d}} - Δ z_{0} \|$ (mm)
HYBRID	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
LAP	0.00	0.01	0.02	0.00	0.00	0.04	0.01	0.03
CC	0.00	0.09	0.00	0.00	0.06	0.14	0.11	0.18
VAR	0.02	0.35	0.22	0.11	0.05	0.01	0.00	0.01
MINI	0.00	0.00	0.00	0.00	0.00	0.01	0.00	0.00
MINEI	0.00	0.00	0.00	0.00	0.01	0.00	0.02	0.02
IG	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
	Mean Relative Depth Error $\bar{\| z_{d} - z_{0} \| / D_{0}}$
HYBRID	0.94	1.20	0.61	0.80	0.75	0.94	0.71	0.79
LAP	9.95	9.80	10.68	11.08	7.23	9.47	8.73	9.29
CC	2.44	5.56	1.41	3.44	22.74	98.47	23.97	63.88
VAR	252.35	117.31	79.90	29.15	5.79	4.05	0.40	2.37
MINI	0.44	0.55	0.34	0.41	0.42	0.65	0.39	0.39
MINEI	2.08	3.18	1.42	2.11	9.26	20.96	5.57	16.80
IG	0.39	0.44	0.30	0.37	0.28	0.32	0.31	0.29
	Relative Depth Uncertainty δ_z/D̄₀
HYBRID	0.76	1.19	0.53	0.65	0.31	0.58	0.37	0.67
LAP	8.76	8.73	10.15	10.73	6.24	20.14	7.69	16.69
CC	1.88	37.49	1.28	21.17	33.01	64.63	41.59	59.57
VAR	197.82	160.91	100.36	76.68	21.78	20.41	0.15	9.65
MINI	0.28	0.33	0.25	0.26	0.15	0.18	0.11	0.14
MINEI	2.02	2.62	1.71	2.25	3.89	6.35	3.16	5.84
IG	0.28	0.30	0.22	0.25	0.15	0.16	0.12	0.13