Abstract

Depth-of-field extension and accurate 3D position location are two important issues in digital holography for particle characterization and motion tracking. We propose a method of locating the axial positions of both opaque and transparent objects in the reconstructed 3D field in the wavelet domain. The spatial–frequency property of the reconstructed image is analyzed from the viewpoint of the point spread function of the digital inline holography. The reconstructed image is decomposed into high- and low-frequency subimages. By using the variance of the image gradient in the subimages as focus metrics, the depth-of-field of the synthesis image can be extended with all the particles focalized, and the focal plane of the object can be accurately determined. The method is validated by both simulated and experimental holograms of transparent spherical water droplets and opaque nonspherical coal particles. The extended-focus image is applied to the particle pairing in a digital holographic particle tracking velocimetry to obtain the 3D vector field.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  43. D. Moreno-Hernandez, J. Andrés Bueno-García, J. Ascención Guerrero-Viramontes, and F. Mendoza-Santoyo, “3D particle positioning by using the Fraunhofer criterion,” Opt. Lasers Eng. 49, 729–735 (2011).
    [CrossRef]
  44. J. Widjaja and P. Chuamchaitrakool, “Holographic particle tracking using Wigner–Ville distribution,” Opt. Lasers Eng. 51, 311–316 (2013).
    [CrossRef]
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  46. J. T. Huang, C. H. Shen, S. M. Phoong, and H. Chen, “Robust measure of image focus in the wavelet domain,” in Intelligent Signal Processing and Communication Systems (ISPACS) (IEEE, 2005), pp. 157–160.
  47. J. Kautsky, J. Flusser, B. Zitov, and S. Simberov, “A new wavelet-based measure of image focus,” Pattern Recogn. Lett. 23, 1785–1794 (2002).
  48. X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
    [CrossRef]
  49. Y. Wu, X. Wu, S. Saengkaew, S. Meunier-Guttin-Cluzel, L. Chen, K. Qiu, X. Gao, G. Grhan, and K. Cen, “Digital Gabor and off-axis particle holography by shaped beams: a numerical investigation with GLMT,” Opt. Commun. 305, 247–254 (2013).
    [CrossRef]
  50. S. Baek and S. Lee, “A new two-frame particle tracking algorithm using match probability,” Exp. Fluids 22, 23–32 (1996).
    [CrossRef]

2013 (6)

C. Deng, J. Huang, G. Li, and Y. Yang, “Application of constrained least squares filtering technique to focal plane detection in digital holography,” Opt. Commun. 291, 52–60 (2013).
[CrossRef]

J. Widjaja and P. Chuamchaitrakool, “Holographic particle tracking using Wigner–Ville distribution,” Opt. Lasers Eng. 51, 311–316 (2013).
[CrossRef]

Y. Wu, X. Wu, S. Saengkaew, S. Meunier-Guttin-Cluzel, L. Chen, K. Qiu, X. Gao, G. Grhan, and K. Cen, “Digital Gabor and off-axis particle holography by shaped beams: a numerical investigation with GLMT,” Opt. Commun. 305, 247–254 (2013).
[CrossRef]

D. Allano, M. Malek, F. Walle, F. Corbin, G. Godard, S. Coëtmellec, B. Lecordier, J.-M. Foucaut, and D. Lebrun, “Three-dimensional velocity near-wall measurements by digital in-line holography: calibration and results,” Appl. Opt. 52, A9–A17 (2013).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, “Improved depth resolution by single-exposure in-line compressive holography,” Appl. Opt. 52, A223–A231 (2013).
[CrossRef]

J. K. Abrantes, M. Stanislas, S. Coudert, and L. F. A. Azevedo, “Digital microscopic holography for micrometer particles in air,” Appl. Opt. 52, A397–A409 (2013).
[CrossRef]

2012 (3)

2011 (2)

D. Moreno-Hernandez, J. Andrés Bueno-García, J. Ascención Guerrero-Viramontes, and F. Mendoza-Santoyo, “3D particle positioning by using the Fraunhofer criterion,” Opt. Lasers Eng. 49, 729–735 (2011).
[CrossRef]

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]

2010 (3)

L. Tian, N. Loomis, J. A. Domnguez-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]

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42, 531–555 (2010).
[CrossRef]

S. Coëtmellec, N. Verrier, M. Brunel, and D. Lebrun, “General formulation of digital in-line holography from correlation with a chirplet function,” J. Eur. Opt. Soc. 5, 10027 (2010).
[CrossRef]

2009 (6)

S. Kim and S. J. Lee, “Measurement of dean flow in a curved micro-tube using micro digital holographic particle tracking velocimetry,” Exp. Fluids 46, 255–264 (2009).
[CrossRef]

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

I. Bergoënd, T. Colomb, N. Pavillon, Y. Emery, and C. Depeursinge, “Depth-of-field extension and 3D reconstruction in digital holographic microscopy,” Proc. SPIE 7390, 73901C (2009).
[CrossRef]

J. Weng, J. Zhong, and C. Hu, “Phase reconstruction of digital holography with the peak of the two-dimensional Gabor wavelet transform,” Appl. Opt. 48, 3308–3316 (2009).
[CrossRef]

M. Paturzo and P. Ferraro, “Creating an extended focus image of a tilted object in Fourier digital holography,” Opt. Express 17, 20546–20552 (2009).
[CrossRef]

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

2008 (11)

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]

J. Sheng, E. Malkeil, 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.-i. Satake, A. Takafumi, K. Hiroyuki, K. Tomoaki, S. Kazuho, and I. Tomoyoshi, “Measurements of three-dimensional flow in microchannel with complex shape by micro-digital-holographic particle-tracking velocimetry,” J. Heat Transfer 130, 042413 (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]

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).

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]

S. J. Jeong and C. K. Hong, “Pixel-size-maintained image reconstruction of digital holograms on arbitrarily tilted planes by the angular spectrum method,” Appl. Opt. 47, 3064–3071 (2008).
[CrossRef]

P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A 25, 1744–1761 (2008).
[CrossRef]

M. Antkowiak, N. Callens, C. Yourassowsky, and F. Dubois, “Extended focused imaging of a microparticle field with digital holographic microscopy,” Opt. Lett. 33, 1626–1628 (2008).
[CrossRef]

L. Cao, G. Pan, J. de Jong, S. Woodward, and H. Meng, “Hybrid digital holographic imaging system for three-dimensional dense particle field measurement,” Appl. Opt. 47, 4501–4508 (2008).
[CrossRef]

Y. Yang and B.-s. Kang, “Experimental validation for the determination of particle positions by the correlation coefficient method in digital particle holography,” Appl. Opt. 47, 5953–5960 (2008).
[CrossRef]

2007 (2)

A. Marian, F. Charriere, T. Colomb, F. Montfort, J. Kuehn, P. Marquet, and C. Depeursinge, “On the complex three-dimensional amplitude point spread function of lenses and microscope objectives: theoretical aspects, simulations and measurements by digital holography,” J. Microsc. 225, 156–169 (2007).
[CrossRef]

F. Soulez, L. Denis, C. Fournier, É. 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 (1)

2005 (2)

2004 (2)

G. Pajares and J. Manuel de la Cruz, “A wavelet-based image fusion tutorial,” Pattern Recogn. 37, 1855–1872 (2004).

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]

2003 (2)

D. Lebrun, A. M. Benkouider, and S. Cotmellec, “Particle field digital holographic reconstruction in arbitrary tilted planes,” Opt. Express 11, 224–229 (2003).
[CrossRef]

M. Malek, S. Coetmellec, D. Allano, and D. Lebrun, “Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter,” Opt. Commun. 223, 263–271 (2003).
[CrossRef]

2002 (3)

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

K. D. Hinsch, “Holographic particle image velocimetry,” Meas. Sci. Technol. 13, R61–R72 (2002).
[CrossRef]

J. Kautsky, J. Flusser, B. Zitov, and S. Simberov, “A new wavelet-based measure of image focus,” Pattern Recogn. Lett. 23, 1785–1794 (2002).

2000 (1)

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]

1997 (1)

M. Adams, T. M. Kreis, and W. P. O. Jueptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234–240 (1997).
[CrossRef]

1996 (1)

S. Baek and S. Lee, “A new two-frame particle tracking algorithm using match probability,” Exp. Fluids 22, 23–32 (1996).
[CrossRef]

1989 (1)

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recogn. Lett. 9, 19–25 (1989).

1976 (1)

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

Abrantes, J. K.

Adams, M.

M. Adams, T. M. Kreis, and W. P. O. Jueptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234–240 (1997).
[CrossRef]

Alfieri, D.

Allano, D.

D. Allano, M. Malek, F. Walle, F. Corbin, G. Godard, S. Coëtmellec, B. Lecordier, J.-M. Foucaut, and D. Lebrun, “Three-dimensional velocity near-wall measurements by digital in-line holography: calibration and results,” Appl. Opt. 52, A9–A17 (2013).
[CrossRef]

M. Malek, S. Coetmellec, D. Allano, and D. Lebrun, “Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter,” Opt. Commun. 223, 263–271 (2003).
[CrossRef]

Andrés Bueno-García, J.

D. Moreno-Hernandez, J. Andrés Bueno-García, J. Ascención Guerrero-Viramontes, and F. Mendoza-Santoyo, “3D particle positioning by using the Fraunhofer criterion,” Opt. Lasers Eng. 49, 729–735 (2011).
[CrossRef]

Antkowiak, M.

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]

Ascención Guerrero-Viramontes, J.

D. Moreno-Hernandez, J. Andrés Bueno-García, J. Ascención Guerrero-Viramontes, and F. Mendoza-Santoyo, “3D particle positioning by using the Fraunhofer criterion,” Opt. Lasers Eng. 49, 729–735 (2011).
[CrossRef]

Azevedo, L. F. A.

Baek, S.

S. Baek and S. Lee, “A new two-frame particle tracking algorithm using match probability,” Exp. Fluids 22, 23–32 (1996).
[CrossRef]

Barbastathis, G.

Benkouider, A. M.

Bergoënd, I.

I. Bergoënd, T. Colomb, N. Pavillon, Y. Emery, and C. Depeursinge, “Depth-of-field extension and 3D reconstruction in digital holographic microscopy,” Proc. SPIE 7390, 73901C (2009).
[CrossRef]

I. Bergoënd, T. Colomb, N. Pavillon, Y. Emery, and C. Depeursinge, “Extended depth-of-field and 3D information extraction in digital holographic microscopy,” in Advances in Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWB5.

Brunel, M.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

S. Coëtmellec, N. Verrier, M. Brunel, and D. Lebrun, “General formulation of digital in-line holography from correlation with a chirplet function,” J. Eur. Opt. Soc. 5, 10027 (2010).
[CrossRef]

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.

Cao, L.

Cen, K.

Y. Wu, X. Wu, S. Saengkaew, S. Meunier-Guttin-Cluzel, L. Chen, K. Qiu, X. Gao, G. Grhan, and K. Cen, “Digital Gabor and off-axis particle holography by shaped beams: a numerical investigation with GLMT,” Opt. Commun. 305, 247–254 (2013).
[CrossRef]

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

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]

Chamberlin-Long, D.

Charriere, F.

A. Marian, F. Charriere, T. Colomb, F. Montfort, J. Kuehn, P. Marquet, and C. Depeursinge, “On the complex three-dimensional amplitude point spread function of lenses and microscope objectives: theoretical aspects, simulations and measurements by digital holography,” J. Microsc. 225, 156–169 (2007).
[CrossRef]

Chen, H.

J. T. Huang, C. H. Shen, S. M. Phoong, and H. Chen, “Robust measure of image focus in the wavelet domain,” in Intelligent Signal Processing and Communication Systems (ISPACS) (IEEE, 2005), pp. 157–160.

Chen, L.

Y. Wu, X. Wu, S. Saengkaew, S. Meunier-Guttin-Cluzel, L. Chen, K. Qiu, X. Gao, G. Grhan, and K. Cen, “Digital Gabor and off-axis particle holography by shaped beams: a numerical investigation with GLMT,” Opt. Commun. 305, 247–254 (2013).
[CrossRef]

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

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]

Chen, W.

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

Choo, Y.

Chuamchaitrakool, P.

J. Widjaja and P. Chuamchaitrakool, “Holographic particle tracking using Wigner–Ville distribution,” Opt. Lasers Eng. 51, 311–316 (2013).
[CrossRef]

Coetmellec, S.

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Appl. Phys. Lett. (1)

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

Exp. Fluids (3)

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Figures (11)

Fig. 1.
Fig. 1.

Experimental setup of digital inline particle holography.

Fig. 2.
Fig. 2.

(a) Experimental coal particle hologram and (b) the reconstructed plane image at a depth position of 12.3 cm.

Fig. 3.
Fig. 3.

(a) The depth-of-field extended image and (b) the decision map of the wavelet coefficient of the low-frequency band.

Fig. 4.
Fig. 4.

Local spatial–frequency analysis of the in-focus and out-of-focus images. (a) In-focus particle image, (b) out-of-focus particle image, (c) wavelet decomposition of (a), with the upper right, upper left, lower right and lower left subimages corresponding to the LL, HL, LH and HH, respectively, and (d) wavelet decomposition of (b).

Fig. 5.
Fig. 5.

Focal plane measurement curve in the high-frequency subimages of (a) an opaque coal particle and (b) the transparent water droplet.

Fig. 6.
Fig. 6.

3D positions of the reconstructed coal particles.

Fig. 7.
Fig. 7.

Comparison of focus plane measurement between the proposed method and the point intensity, the intensity variance, and the entropy methods for (a) nonspherical opaque coal particles and (b) spherical transparent water droplets.

Fig. 8.
Fig. 8.

Depth error of simulated particles from near- to far-field. (a) Absolute depth errors of opaque particles and droplets and (b) relative depth errors.

Fig. 9.
Fig. 9.

Extended-focus image used for particle pairing in DHPTV. The gray background is the extended-focus image of frame 1. The red plus signs denote the centroids of the detected particle in frame 1, the closed curves are the boundaries of the detected particle in frame 2, and the green arrows denote the motion between the paired particles.

Fig. 10.
Fig. 10.

Comparison of particle size distribution between frame 1 and frame 2.

Fig. 11.
Fig. 11.

3D vectors of the hologram pair with the vector color and length proportional to vector magnitude and the spheres proportional to the particle size.

Equations (5)

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

I(x,y,z)=1Iholo(x,y)ψz(x,y),
G(x,h)=HLSx+HHSx,G(y,h)=LHSx+HHSx,G(x,l)=LLSx,G(y,l)=LLSx,
Sx=(101202101)
Gh=G(x,h)2+G(y,h)2,Gl=G(x,l)2+G(y,l)2.
εH,z=nm[Gh(n,m)Gh(n,m)¯]2,εL,z=nm[Gl(n,m)Gl(n,m)¯]2,

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