Three-dimensional reconstruction of particle holograms: a fast and accurate multiscale approach.

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.

[1]  Yong-Seok Choi,et al.  Holographic analysis of three-dimensional inertial migration of spherical particles in micro-scale pipe flow , 2010 .

[2]  Shigeru Murata,et al.  Potential of digital holography in particle measurement , 2000 .

[3]  Brian J. Thompson,et al.  Fraunhofer Holography Applied to Particle Size Analysis a Reassessment , 1976 .

[4]  B. Javidi,et al.  Compressive Fresnel Holography , 2010, Journal of Display Technology.

[5]  Thierry Blu,et al.  Fresnelets: new multiresolution wavelet bases for digital holography , 2003, IEEE Trans. Image Process..

[6]  Cafer Ozkul,et al.  Application of wavelet transform to hologram analysis: three-dimensional location of particles , 2000 .

[7]  Joseph Katz,et al.  The three-dimensional flow field generated by a feeding calanoid copepod measured using digital holography , 2003, Journal of Experimental Biology.

[8]  J. Katz,et al.  Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer , 2009, Journal of Fluid Mechanics.

[9]  Ferréol Soulez,et al.  Inverse problem approach in particle digital holography: out-of-field particle detection made possible. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[10]  F. Toschi,et al.  Lagrangian Properties of Particles in Turbulence , 2009 .

[11]  S. Kay Fundamentals of statistical signal processing: estimation theory , 1993 .

[12]  Mokrane Malek,et al.  Digital in-line holography for three-dimensional two-components particle tracking velocimetry , 2004 .

[13]  Daniel L Marks,et al.  Compressive holography. , 2009, Optics express.

[14]  Catherine Yourassowsky,et al.  Focus plane detection criteria in digital holography microscopy by amplitude analysis. , 2006, Optics express.

[15]  Fook Chiong Cheong,et al.  Strategies for three-dimensional particle tracking with holographic video microscopy. , 2010, Optics express.

[16]  J. Réveillon,et al.  Effects of the preferential segregation of droplets on evaporation and turbulent mixing , 2007, Journal of Fluid Mechanics.

[17]  Thierry Fournel,et al.  On the single point resolution of on-axis digital holography. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[18]  Jeffrey A Fessler,et al.  Penalized-likelihood image reconstruction for digital holography. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[19]  Seung-Man Yang,et al.  Characterizing and tracking single colloidal particles with video holographic microscopy. , 2007, Optics express.

[20]  D. Lorenz,et al.  Greedy solution of ill-posed problems: error bounds and exact inversion , 2009, 0904.0154.

[21]  Michael Unser,et al.  The L2-Polynomial Spline Pyramid , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Ferréol Soulez,et al.  Inverse-problem approach for particle digital holography: accurate location based on local optimization. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[23]  Loïc Denis,et al.  Testing an in-line digital holography ‘inverse method’ for the Lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence , 2012 .

[24]  Hui Meng,et al.  Digital holography of particle fields: reconstruction by use of complex amplitude. , 2003, Applied optics.

[25]  Loïc Denis,et al.  Inline hologram reconstruction with sparsity constraints. , 2009, Optics letters.

[26]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[27]  D. Lebrun,et al.  Particle field characterization by digital in-line holography: 3D location and sizing , 2005 .

[28]  T. Pedley,et al.  Hydrodynamic Phenomena in Suspensions of Swimming Microorganisms , 1992 .

[29]  Elsa D. Angelini,et al.  Compressed Sensing with off-axis frequency-shifting holography , 2010, Optics letters.

[30]  Thierry Fournel,et al.  Inverse problem approaches for digital hologram reconstruction , 2011, Defense + Commercial Sensing.

[31]  S. Hess,et al.  Viscoelastic flows studied by smoothed particle dynamics , 2002 .

[32]  Edmund Y Lam,et al.  Edge-preserving sectional image reconstruction in optical scanning holography. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[33]  J. Katz,et al.  Applications of Holography in Fluid Mechanics and Particle Dynamics , 2010 .

[34]  J. Högbom,et al.  APERTURE SYNTHESIS WITH A NON-REGULAR DISTRIBUTION OF INTERFEROMETER BASELINES. Commentary , 1974 .

[35]  H Royer,et al.  An application of high-speed microholography: the mertology of fogs , 1974 .

[36]  David J. Brady,et al.  Sampling and processing for compressive holography [Invited]. , 2011, Applied optics.

[37]  Christophe Ducottet,et al.  Digital holography of particles: benefits of the ‘inverse problem’ approach , 2008 .

[38]  L. Onural,et al.  Diffraction from a wavelet point of view. , 1993, Optics letters.

[39]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[40]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[41]  A. S. Mujumdar,et al.  Simulation of a Spray Dryer Fitted with a Rotary Disk Atomizer Using a Three-Dimensional Computional Fluid Dynamic Model , 2004 .