Abstract

In-line digital holography is an imaging technique that is being increasingly used for studying three-dimensional flows. It has been previously shown that very accurate reconstructions of objects could be achieved with the use of an inverse problem framework. Such approaches, however, suffer from higher computational times compared to less accurate conventional reconstructions based on hologram backpropagation. To overcome this computational issue, we propose a coarse-to-fine multiscale approach to strongly reduce the algorithm complexity. We illustrate that an accuracy comparable to that of state-of-the-art methods can be reached while accelerating parameter-space scanning.

© 2012 Optical Society of America

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2012 (1)

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Mees, “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 (2)

S. Lim, D. L. Marks, and D. J. Brady, “Sampling and processing for compressive holography [Invited],” Appl. Opt. 50, H75–H86 (2011).
[CrossRef]

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, and M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” Proc. SPIE 8043, 80430S (2011).
[CrossRef]

2010 (7)

2009 (6)

L. Denis, D. A. Lorenz, and D. Trede, “Greedy solution of ill-posed problems: error bounds and exact inversion,” Inverse Probl. 25, 115017 (2009).
[CrossRef]

D. Needell and J. Tropp, “Cosamp: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (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]

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009).
[CrossRef]

F. Toschi and E. Bodenschatz, “Lagrangian properties of particles in turbulence,” Ann. Rev. Fluid Mech. 41, 375–404 (2009).
[CrossRef]

J. Sheng, E. Malkiel, and J. Katz, “Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer,” J. Fluid Mech. 633, 17–60 (2009).
[CrossRef]

2008 (1)

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the a ‘inverse problem’ approach,” Meas. Sci. Technol. 19, 074005 (2008).
[CrossRef]

2007 (4)

2006 (1)

2005 (1)

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9(2005).
[CrossRef]

2004 (3)

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional–two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699–705 (2004).
[CrossRef]

L. Huang, K. Kumar, and A. S. Mujumdar, “Simulation of a spray dryer fitted with a rotary disk atomizer using a three-dimensional computional fluid dynamic model,” Dry. Technol. 22, 1489–1515 (2004).
[CrossRef]

S. Sotthivirat and J. Fessler, “Penalized-likelihood image reconstruction for digital holography,” J. Opt. Soc. Am. A 21, 737–750 (2004).
[CrossRef]

2003 (3)

E. Malkiel, J. Sheng, J. Katz, and J. R. Strickler, “The three-dimensional flow field generated by a feeding calanoid copepod measured using digital holography,” J. Exp. Biol. 206, 3657–3666 (2003).
[CrossRef]

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

M. Liebling, T. Blu, and M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

2002 (1)

M. Ellero, M. Kröger, and S. Hess, “Viscoelastic flows studied by smoothed particle dynamics,” J. Non-Newton. Fluid Mech. 105, 35–51 (2002).
[CrossRef]

2000 (2)

Murata, “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. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

1993 (3)

M. Unser, A. Aldroubi, and M. Eden, “The L2 polynomial spline pyramid,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 364–379 (1993).
[CrossRef]

L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett. 18, 846–848 (1993).
[CrossRef]

S. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process. 41, 3397–3415 (1993).
[CrossRef]

1992 (1)

T. J. Pedley and J. O. Kessler, “Hydrodynamic phenomena in suspensions of swimming microorganisms,” Ann. Rev. Fluid Mech. 24, 313–358 (1992).
[CrossRef]

1976 (1)

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

1974 (2)

J. A. Högbom, “Aperture synthesis with a non-regular distribution of interferometer baselines,” Astron. Astrophys. Suppl. Series 15, 417–426 (1974).

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Aldroubi, A.

M. Unser, A. Aldroubi, and M. Eden, “The L2 polynomial spline pyramid,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 364–379 (1993).
[CrossRef]

Allano, D.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9(2005).
[CrossRef]

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional–two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699–705 (2004).
[CrossRef]

Angelini, E.

Atlan, M.

Blu, T.

M. Liebling, T. Blu, and M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

Bodenschatz, E.

F. Toschi and E. Bodenschatz, “Lagrangian properties of particles in turbulence,” Ann. Rev. Fluid Mech. 41, 375–404 (2009).
[CrossRef]

Brady, D. J.

Buraga-Lefebvre, C.

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

Callens, N.

Cen, K. F.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9(2005).
[CrossRef]

Chareyron, D.

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Mees, “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]

Cheong, F. CH.

Choi, K.

Choi, Y.

Y. Choi and S. Lee, “Holographic analysis of three-dimensional inertial migration of spherical particles in micro-scale pipe flow,” Microfluid. Nanofluid. 9, 819–829 (2010).
[CrossRef]

Coëtmellec, S.

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional–two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699–705 (2004).
[CrossRef]

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

Demoulin, F.

J. Reveillon and F. Demoulin, “Effects of the preferential segregation of droplets on evaporation and turbulent mixing,” J. Fluid Mech. 583, 273–302 (2007).
[CrossRef]

Denis, L.

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Mees, “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]

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, and M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” Proc. SPIE 8043, 80430S (2011).
[CrossRef]

C. Fournier, L. Denis, and T. Fournel, “On the single point resolution of on-axis digital holography,” J. Opt. Soc. Am. A 27, 1856–1862 (2010).
[CrossRef]

L. Denis, D. A. Lorenz, and D. Trede, “Greedy solution of ill-posed problems: error bounds and exact inversion,” Inverse Probl. 25, 115017 (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]

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the a ‘inverse problem’ approach,” Meas. Sci. Technol. 19, 074005 (2008).
[CrossRef]

F. Soulez, L. Denis, E. Thiébaut, C. Fournier, and C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” J. Opt. Soc. Am. A 24, 3708–3716 (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]

Dubois, F.

Ducottet, C.

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the a ‘inverse problem’ approach,” Meas. Sci. Technol. 19, 074005 (2008).
[CrossRef]

Eden, M.

M. Unser, A. Aldroubi, and M. Eden, “The L2 polynomial spline pyramid,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 364–379 (1993).
[CrossRef]

Ellero, M.

M. Ellero, M. Kröger, and S. Hess, “Viscoelastic flows studied by smoothed particle dynamics,” J. Non-Newton. Fluid Mech. 105, 35–51 (2002).
[CrossRef]

Fessler, J.

Fournel, T.

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, and M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” Proc. SPIE 8043, 80430S (2011).
[CrossRef]

C. Fournier, L. Denis, and T. Fournel, “On the single point resolution of on-axis digital holography,” J. Opt. Soc. Am. A 27, 1856–1862 (2010).
[CrossRef]

Fournier, C.

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Mees, “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]

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, and M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” Proc. SPIE 8043, 80430S (2011).
[CrossRef]

C. Fournier, L. Denis, and T. Fournel, “On the single point resolution of on-axis digital holography,” J. Opt. Soc. Am. A 27, 1856–1862 (2010).
[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]

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the a ‘inverse problem’ approach,” Meas. Sci. Technol. 19, 074005 (2008).
[CrossRef]

F. Soulez, L. Denis, E. Thiébaut, C. Fournier, and C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” J. Opt. Soc. Am. A 24, 3708–3716 (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]

Gire, J.

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Mees, “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]

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the a ‘inverse problem’ approach,” Meas. Sci. Technol. 19, 074005 (2008).
[CrossRef]

Goepfert, C.

Grier, D. G.

Grosjean, N.

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Mees, “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]

Hess, S.

M. Ellero, M. Kröger, and S. Hess, “Viscoelastic flows studied by smoothed particle dynamics,” J. Non-Newton. Fluid Mech. 105, 35–51 (2002).
[CrossRef]

Högbom, J. A.

J. A. Högbom, “Aperture synthesis with a non-regular distribution of interferometer baselines,” Astron. Astrophys. Suppl. Series 15, 417–426 (1974).

Horisaki, R.

Huang, L.

L. Huang, K. Kumar, and A. S. Mujumdar, “Simulation of a spray dryer fitted with a rotary disk atomizer using a three-dimensional computional fluid dynamic model,” Dry. Technol. 22, 1489–1515 (2004).
[CrossRef]

Javidi, B.

Katz, J.

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

J. Sheng, E. Malkiel, and J. Katz, “Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer,” J. Fluid Mech. 633, 17–60 (2009).
[CrossRef]

E. Malkiel, J. Sheng, J. Katz, and J. R. Strickler, “The three-dimensional flow field generated by a feeding calanoid copepod measured using digital holography,” J. Exp. Biol. 206, 3657–3666 (2003).
[CrossRef]

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, 1st ed. (Prentice Hall, 1993).

Kessler, J. O.

T. J. Pedley and J. O. Kessler, “Hydrodynamic phenomena in suspensions of swimming microorganisms,” Ann. Rev. Fluid Mech. 24, 313–358 (1992).
[CrossRef]

Kim, S.-H.

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods, 1st ed. (Wiley-VCH, 2005).

Krishnatreya, B. J.

Kröger, M.

M. Ellero, M. Kröger, and S. Hess, “Viscoelastic flows studied by smoothed particle dynamics,” J. Non-Newton. Fluid Mech. 105, 35–51 (2002).
[CrossRef]

Kumar, K.

L. Huang, K. Kumar, and A. S. Mujumdar, “Simulation of a spray dryer fitted with a rotary disk atomizer using a three-dimensional computional fluid dynamic model,” Dry. Technol. 22, 1489–1515 (2004).
[CrossRef]

Lam, E. Y.

Lance, M.

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Mees, “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]

Lebrun, D.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9(2005).
[CrossRef]

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional–two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699–705 (2004).
[CrossRef]

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

Lee, S.

Y. Choi and S. Lee, “Holographic analysis of three-dimensional inertial migration of spherical particles in micro-scale pipe flow,” Microfluid. Nanofluid. 9, 819–829 (2010).
[CrossRef]

Lee, S.-H.

Liebling, M.

M. Liebling, T. Blu, and M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

Lim, S.

Lorenz, D.

Lorenz, D. A.

L. Denis, D. A. Lorenz, and D. Trede, “Greedy solution of ill-posed problems: error bounds and exact inversion,” Inverse Probl. 25, 115017 (2009).
[CrossRef]

Malek, M.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9(2005).
[CrossRef]

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional–two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699–705 (2004).
[CrossRef]

Malkiel, E.

J. Sheng, E. Malkiel, and J. Katz, “Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer,” J. Fluid Mech. 633, 17–60 (2009).
[CrossRef]

E. Malkiel, J. Sheng, J. Katz, and J. R. Strickler, “The three-dimensional flow field generated by a feeding calanoid copepod measured using digital holography,” J. Exp. Biol. 206, 3657–3666 (2003).
[CrossRef]

Mallat, S.

S. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process. 41, 3397–3415 (1993).
[CrossRef]

Marié, J. L.

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Mees, “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]

Marim, M.

Marks, D. L.

Mees, L.

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Mees, “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]

Meng, H.

Mujumdar, A. S.

L. Huang, K. Kumar, and A. S. Mujumdar, “Simulation of a spray dryer fitted with a rotary disk atomizer using a three-dimensional computional fluid dynamic model,” Dry. Technol. 22, 1489–1515 (2004).
[CrossRef]

Murata,

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

Needell, D.

D. Needell and J. Tropp, “Cosamp: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

Olivo-Marin, J.

Onural, L.

Özkul, C.

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional–two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699–705 (2004).
[CrossRef]

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

Pan, G.

Patte-Rouland, B.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9(2005).
[CrossRef]

Pedley, T. J.

T. J. Pedley and J. O. Kessler, “Hydrodynamic phenomena in suspensions of swimming microorganisms,” Ann. Rev. Fluid Mech. 24, 313–358 (1992).
[CrossRef]

Pu, S. L.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9(2005).
[CrossRef]

Reveillon, J.

J. Reveillon and F. Demoulin, “Effects of the preferential segregation of droplets on evaporation and turbulent mixing,” J. Fluid Mech. 583, 273–302 (2007).
[CrossRef]

Rivenson, Y.

Roichman, Y.

Royer, H.

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Schockaert, C.

Seifi, M.

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, and M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” Proc. SPIE 8043, 80430S (2011).
[CrossRef]

Sheng, J.

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

J. Sheng, E. Malkiel, and J. Katz, “Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer,” J. Fluid Mech. 633, 17–60 (2009).
[CrossRef]

E. Malkiel, J. Sheng, J. Katz, and J. R. Strickler, “The three-dimensional flow field generated by a feeding calanoid copepod measured using digital holography,” J. Exp. Biol. 206, 3657–3666 (2003).
[CrossRef]

Sotthivirat, S.

Soulez, F.

Stern, A.

Strickler, J. R.

E. Malkiel, J. Sheng, J. Katz, and J. R. Strickler, “The three-dimensional flow field generated by a feeding calanoid copepod measured using digital holography,” J. Exp. Biol. 206, 3657–3666 (2003).
[CrossRef]

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C. Fournier, L. Denis, E. Thiebaut, T. Fournel, and M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” Proc. SPIE 8043, 80430S (2011).
[CrossRef]

Thiébaut, E.

Thiébaut, É.

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

Toschi, F.

F. Toschi and E. Bodenschatz, “Lagrangian properties of particles in turbulence,” Ann. Rev. Fluid Mech. 41, 375–404 (2009).
[CrossRef]

Trede, D.

L. Denis, D. A. Lorenz, and D. Trede, “Greedy solution of ill-posed problems: error bounds and exact inversion,” Inverse Probl. 25, 115017 (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]

Tropp, J.

D. Needell and J. Tropp, “Cosamp: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

Tyler, G. A.

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

Unser, M.

M. Liebling, T. Blu, and M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

M. Unser, A. Aldroubi, and M. Eden, “The L2 polynomial spline pyramid,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 364–379 (1993).
[CrossRef]

van Blaaderen, A.

van Oostrum, P.

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Yi, G.-R.

Yourassowsky, C.

Zhang, X.

Zhang, Z.

S. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process. 41, 3397–3415 (1993).
[CrossRef]

Ann. Rev. Fluid Mech. (3)

T. J. Pedley and J. O. Kessler, “Hydrodynamic phenomena in suspensions of swimming microorganisms,” Ann. Rev. Fluid Mech. 24, 313–358 (1992).
[CrossRef]

F. Toschi and E. Bodenschatz, “Lagrangian properties of particles in turbulence,” Ann. Rev. Fluid Mech. 41, 375–404 (2009).
[CrossRef]

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

Appl. Comput. Harmon. Anal. (1)

D. Needell and J. Tropp, “Cosamp: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

Appl. Opt. (2)

Astron. Astrophys. Suppl. Series (1)

J. A. Högbom, “Aperture synthesis with a non-regular distribution of interferometer baselines,” Astron. Astrophys. Suppl. Series 15, 417–426 (1974).

Dry. Technol. (1)

L. Huang, K. Kumar, and A. S. Mujumdar, “Simulation of a spray dryer fitted with a rotary disk atomizer using a three-dimensional computional fluid dynamic model,” Dry. Technol. 22, 1489–1515 (2004).
[CrossRef]

Exp. Fluids (1)

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9(2005).
[CrossRef]

IEEE Trans. Image Process. (1)

M. Liebling, T. Blu, and M. Unser, “Fresnelets: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

M. Unser, A. Aldroubi, and M. Eden, “The L2 polynomial spline pyramid,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 364–379 (1993).
[CrossRef]

IEEE Trans. Signal Process. (1)

S. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process. 41, 3397–3415 (1993).
[CrossRef]

Inverse Probl. (1)

L. Denis, D. A. Lorenz, and D. Trede, “Greedy solution of ill-posed problems: error bounds and exact inversion,” Inverse Probl. 25, 115017 (2009).
[CrossRef]

J. Display Technol. (1)

J. Exp. Biol. (1)

E. Malkiel, J. Sheng, J. Katz, and J. R. Strickler, “The three-dimensional flow field generated by a feeding calanoid copepod measured using digital holography,” J. Exp. Biol. 206, 3657–3666 (2003).
[CrossRef]

J. Fluid Mech. (2)

J. Sheng, E. Malkiel, and J. Katz, “Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer,” J. Fluid Mech. 633, 17–60 (2009).
[CrossRef]

J. Reveillon and F. Demoulin, “Effects of the preferential segregation of droplets on evaporation and turbulent mixing,” J. Fluid Mech. 583, 273–302 (2007).
[CrossRef]

J. Mod. Opt. (1)

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

J. Non-Newton. Fluid Mech. (1)

M. Ellero, M. Kröger, and S. Hess, “Viscoelastic flows studied by smoothed particle dynamics,” J. Non-Newton. Fluid Mech. 105, 35–51 (2002).
[CrossRef]

J. Opt. Soc. Am. A (5)

Meas. Sci. Technol. (2)

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional–two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699–705 (2004).
[CrossRef]

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the a ‘inverse problem’ approach,” Meas. Sci. Technol. 19, 074005 (2008).
[CrossRef]

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Y. Choi and S. Lee, “Holographic analysis of three-dimensional inertial migration of spherical particles in micro-scale pipe flow,” Microfluid. Nanofluid. 9, 819–829 (2010).
[CrossRef]

New J. Phys. (1)

D. Chareyron, J. L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, and L. Mees, “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]

Nouv. Rev. Opt. (1)

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Opt. Express (4)

Opt. Laser Technol. (1)

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

Opt. Lasers Eng. (1)

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

Opt. Lett. (3)

Proc. SPIE (1)

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, and M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” Proc. SPIE 8043, 80430S (2011).
[CrossRef]

Other (3)

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods, 1st ed. (Wiley-VCH, 2005).

S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, 1st ed. (Prentice Hall, 1993).

http://www.fftw.org/ (visited on 10 July 2012).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Hologram of a spherical microparticle, (b) sampled four-dimensional (4D) search space for exhaustive search step, (c) a one-dimensional (1D) profile of the cost function of the particle for visualization purposes. This cost function is jointly optimized in practice over the four parameters (x, y, z, r) during the local optimization step. The result of the exhaustive search is used as the initial point for this optimization. The parameters used in this example are the following: laser wavelength λ=0.532μm, pixel size 7 μm, signal-to-noise ratio 50, size of the hologram 2048×2048 pixels, distance between particle and sensor 0.3 m, and radius 33 μm.

Fig. 2.
Fig. 2.

Proposed multiscale algorithm for particle detection and sizing from a digital hologram.

Fig. 3.
Fig. 3.

(a) Schema of the proposed multiscale algorithm, (b) 1D profile of the cost function computed on the original hologram. Black crosses show the results of estimation after each step of the pyramidal multiscale algorithm on the profile of the cost function; black solid circle shows an example of coarse estimation from exhaustive search of FAST (Fig. 2) with kmax=0 (single-scale approach). As shown here, this coarse detection should be found inside the main basin of the cost function, whereas the coarse estimation using the pyramidal multiscale algorithm could be outside the basin.

Fig. 4.
Fig. 4.

(a) Zoomed-in captured hologram containing two spherical microparticles, (b) zoomed-in downsampled hologram considering both Eqs. (9) and (11) as the criteria (Tkmax=min(Tkmax(i),Tkmax(ii))=4), (c) zoomed-in downsampled hologram using only Eq. (11) for the downsampling factor (Tkmax=9). Most of the high frequencies are filtered out, which makes it impossible for an exhaustive search to find a relevant coarse estimation of parameters.

Fig. 5.
Fig. 5.

(a) Experimental hologram of six spherical microparticles in the field of view of the sensor, (b) cleaned hologram with FAST (Fig. 2) for kmax=2, (c) cleaned hologram with FAST (Fig. 2) for kmax=0 (single-scale approach). In the captured holograms, the magnitude of the signal remains high after cleaning of the in-the-field particles. This is due to the signature of the out-of-field particles, which are close to the borders.

Tables (1)

Tables Icon

Table 1. Accuracy and Computational Time When Going from a Single Scale to a Pyramid with Three Scalesa

Equations (29)

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

di=1Npartαimi,
DW2(d,m)=(dm)tW(dm),
u,vW=utWv1tW1(=kwkukvkkwkfor a diagonalW:W=diag(w)),
uW2=u,uW=utWu1tW1(=kwkuk2kwkfor a diagonalW:W=diag(w)).
argminα01iKαmidW2.
argmaxi[d,miW]+2miW2,
mi()=πri2λzi·sin(πρ2λzi)·J1c(2πriρλzi)·sinc(πsΔxλzi)·sinc(πsΔyλzi),
ď=F(k)d,
Tkmax(i)=1κλzmin2q+1/2,kmax(i)=log2(Tkmax(i)),
i()=mi()·f(),
Tkmax(ii)=2(L10rmaxκ),kmax(ii)=log2(Tkmax(ii)).
var(θ^a)[I1]a,a,
[I]a,b=12(m(θ)θa)tW(m(θ)θb).
[I]a,b(k)=Tk22σ2((θ)θa)t((θ)θb).
{θ0B(θ(kmax))θ(kmax)B(θ(kmax1))θ(1)B(θ).
πρq2λz=q2π+π/2.
πx0Tkκλz=π,
(2q+1/2)λz<λzTk.
Tkmax=1κλzmin2q+1/2,kmax=log2(Tkmax),
[hz*f](x,y)=1iλzf(ξ,η)hz(xξ,yη)dξdη,
hz(x,y)=1iλzexp(iπ(x2+y2)λz).
[hz*f](x,y)=1iλzf(ξ,η)exp(iπλz[x2+ξ2+y2+η22xξ2yη])dξdη.
πξ2+η2maxλzπ,
[hz*f](x,y)1iλzexp(iπλz[x2+y2])f(ξ,η)exp(2πi[xλzξ+yλzη])dξdη,
[hz*f](x,y)hz(x,y)·Fxλz,yλz{f},
10π(rmax+Tκ/2)2λzmin<π.
zmin=zNyquist=Lκ2λ,
T<2(L10rmaxκ).
Tkmax=2(L10rmaxκ),kmax=log2(T),

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