3D particle tracking velocimetry using dynamic discrete tomography

Particle tracking velocimetry in 3D is becoming an increasingly important imaging tool in the study of fluid dynamics and combustion as well as plasmas. We introduce a dynamic discrete tomography algorithm for reconstructing particle trajectories from projections. The algorithm is efficient for data from two projection directions and exact in the sense that it finds a solution consistent with the experimental data. Non-uniqueness of solutions can be detected and solutions can be tracked individually.

[1]  F. Egolfopoulos,et al.  Advances and challenges in laminar flame experiments and implications for combustion chemistry , 2014 .

[2]  R. Gurka,et al.  Effects of particle size, concentration and surface coating on turbulent flow properties obtained using PIV/PTV , 2013 .

[3]  L. Lourenço Particle Image Velocimetry , 1989 .

[4]  A. Prasad Particle image velocimetry , 2000 .

[5]  A. Heppes On the determination of probability distributions of more dimensions by their projections , 1956 .

[6]  E. Thomas,et al.  Measurement of the Kinetic Dust Temperature of a Weakly Coupled Dusty Plasma , 2005, IEEE Transactions on Plasma Science.

[7]  R. Adrian Particle-Imaging Techniques for Experimental Fluid Mechanics , 1991 .

[8]  Sara Brunetti,et al.  Stability results for the reconstruction of binary pictures from two projections , 2007, Image Vis. Comput..

[9]  R. Gandy,et al.  Initial experiments in the Idaho Dusty Plasma Device , 2001 .

[10]  W. Kinzelbach,et al.  A combined scanning PTV/LIF technique to simultaneously measure the full velocity gradient tensor and the 3D density field , 2014 .

[11]  K. Schreel,et al.  The application of a 3D PTV algorithm to a mixed convection flow , 2002 .

[12]  Measurements of microbubble generation process in microchannel using ultra high-speed micro-PTV system , 2013 .

[13]  Ronald Adrian,et al.  Two-dimensional velocity measurements in a laminar flame using particle image velocimetry , 1986 .

[14]  Dirk Michaelis,et al.  Shake The Box: A highly efficient and accurate Tomographic Particle Tracking Velocimetry (TOMO-PTV) method using prediction of particle positions , 2013 .

[15]  Haitao Xu,et al.  Tracking Lagrangian trajectories in position–velocity space , 2008 .

[16]  P. Gąsior,et al.  Dust control in tokamak environment , 2008 .

[17]  F. Richard,et al.  Physical study of a gliding arc discharge , 1996 .

[19]  S. I. Krasheninnikov,et al.  Dust in magnetic fusion devices , 2011 .

[20]  Bernhard Wieneke,et al.  Tomographic particle image velocimetry , 2006 .

[21]  L. Fuchs,et al.  Mixing in Circular and Non-circular Jets in Crossflow , 2008 .

[22]  C. Du,et al.  The application of a non-thermal plasma generated by gas–liquid gliding arc discharge in sterilization , 2012 .

[23]  G. Herman,et al.  Discrete tomography : foundations, algorithms, and applications , 1999 .

[24]  D.H.J. Goodall,et al.  High speed cine film studies of plasma behaviour and plasma surface interactions in tokamaks , 1982 .

[25]  O. Bolotina,et al.  On stability of the , 2003 .

[26]  Peter Gritzmann,et al.  On Stability, Error Correction, and Noise Compensation in Discrete Tomography , 2006, SIAM J. Discret. Math..

[27]  A. Lent,et al.  Iterative reconstruction algorithms. , 1976, Computers in biology and medicine.

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

[29]  J. Goree,et al.  Diagnostics for transport phenomena in strongly coupled dusty plasmas , 2013 .

[30]  PETER GRITZMANN,et al.  Uniqueness in Discrete Tomography: Three Remarks and a Corollary , 2011, SIAM J. Discret. Math..

[31]  Fatna Tafnout,et al.  Measurements and Numerical Simulation of the Gas-Solid Flow Generated by Machining Operation , 2013 .

[32]  A. Rényi,et al.  On projections of probability distributions , 1952 .

[33]  Birgit van Dalen Stability results for uniquely determined sets from two directions in discrete tomography , 2008, Discret. Math..

[34]  K. Cen,et al.  Fundamental research on the size and velocity measurements of coal powder by trajectory imaging , 2013 .

[35]  Ronald Adrian,et al.  Multi-point optical measurements of simultaneous vectors in unsteady flow—a review , 1986 .

[36]  Alfred Hanssen,et al.  Particle tracking from image sequences of complex plasma crystals , 2006 .

[37]  Peter Gritzmann,et al.  On the computational complexity of reconstructing lattice sets from their X-rays , 1999, Discret. Math..

[38]  Peter Gritzmann,et al.  Stability and Instability in Discrete Tomography , 2000, Digital and Image Geometry.

[39]  G. S. Lewis,et al.  An investigation of the structure of a laminar non-premixed flame in an unsteady vortical flow , 1989 .

[40]  Ideal gas behavior of a strongly coupled complex (dusty) plasma. , 2012, Physical review letters.

[41]  Peter Gritzmann,et al.  Discrete Tomography: Determination of Finite Sets by X-Rays , 1995, Universität Trier, Mathematik/Informatik, Forschungsbericht.

[42]  K. Ohmi,et al.  Novel Algorithms of 3D Particle Tracking Velocimetry Using a Tomographic Reconstruction Technique , 2012 .

[43]  Alain Daurat Determination of Q-convex sets by X-rays , 2005, Theor. Comput. Sci..

[44]  G. B. Tatterson,et al.  Application of image processing to the analysis of three-dimensional flow fields , 1984 .

[45]  D. Moseev,et al.  On bias of kinetic temperature measurements in complex plasmas , 2014 .

[46]  Nobuhide Kasagi,et al.  Simultaneous measurement of fluid and dispersed phases in a particle-laden turbulent channel flow with the aid of 3-D PTV , 2000 .

[47]  C. Goertz,et al.  Dusty plasmas in the solar system , 1989 .

[48]  A. Hyatt,et al.  Dust studies in DIII-D and TEXTOR , 2009 .

[49]  Ajay K. Prasad,et al.  Stereoscopic particle image velocimetry , 2000 .

[50]  M. Oschwald,et al.  Ignition of Cryogenic H2/LOX Sprays , 2003 .

[51]  Kim,et al.  Mapping projected potential, interfacial roughness, and composition in general crystalline solids by quantitative transmission electron microscopy. , 1993, Physical review letters.

[52]  Yann Guezennec,et al.  Algorithms for fully automated three-dimensional particle tracking velocimetry , 1994 .

[53]  Jiajian Zhu,et al.  Water-cooled non-thermal gliding arc for adhesion improvement of glass-fibre-reinforced polyester , 2013 .

[54]  N. Malik,et al.  Particle tracking velocimetry in three-dimensional flows , 1993 .

[55]  Nesa L'abbe Wu,et al.  Linear programming and extensions , 1981 .

[56]  Zhiwei Sun,et al.  Dynamics, OH distributions and UV emission of a gliding arc at various flow-rates investigated by optical measurements , 2014 .

[57]  Jeremiah D. Williams,et al.  Application of tomographic particle image velocimetry to studies of transport in complex (dusty) plasma , 2011 .

[58]  P. Shukla A survey of dusty plasma physics , 2001 .

[59]  Peter Gritzmann,et al.  Dynamic discrete tomography , 2017, ArXiv.

[60]  C. Brücker,et al.  Tomographic particle tracking velocimetry using telecentric imaging , 2010 .

[61]  F. Richard,et al.  Heat string model of bi-dimensional dc Glidarc , 2000 .

[62]  Sven de Vries,et al.  Success and failure of certain reconstruction and uniqueness algorithms in discrete tomography , 1998, Int. J. Imaging Syst. Technol..

[63]  A. Fridman,et al.  Gliding arc gas discharge , 1999 .

[64]  J. Kuerten,et al.  Lagrangian and Eulerian Statistics of Pipe Flows Measured with 3D-PTV at Moderate and High Reynolds Numbers , 2013 .

[65]  Francisco Pereira,et al.  Two-frame 3D particle tracking , 2006 .

[66]  B. Wieneke Iterative reconstruction of volumetric particle distribution , 2013 .

[67]  M. Shoji,et al.  ICRF long-pulse discharge and interaction with a chamber wall and antennas in LHD , 2007 .

[68]  Yasuhiro Ogami,et al.  Measurements of the laminar burning velocity of hydrogen–air premixed flames , 2010 .

[69]  Ravindra K. Ahuja,et al.  Network Flows , 2011 .

[70]  J. Ralph,et al.  Tracking shocked dust: State estimation for a complex plasma during a shock wave , 2011, 1112.5316.

[71]  M. Aldén,et al.  Optical diagnostics of a gliding arc. , 2013, Optics express.

[72]  Fulvio Scarano,et al.  Performances of motion tracking enhanced Tomo-PIV on turbulent shear flows , 2011, Experiments in fluids.

[73]  Lei Wang,et al.  Turbulent flow in a ribbed channel: Flow structures in the vicinity of a rib , 2010 .

[74]  G. Herman,et al.  Advances in discrete tomography and its applications , 2007 .

[75]  Jochen Willneff,et al.  A spatio-temporal matching algorithm for 3D particle tracking velocimetry , 2002 .

[76]  Hideaki Kobayashi,et al.  Laminar burning velocity of hydrogen-air premixed flames at elevated pressure , 2000 .

[77]  C. Brücker 3D scanning PIV applied to an air flow in a motored engine using digital high-speed video , 1997 .

[78]  Sven de Vries,et al.  Reconstructing Crystalline Structures from Few Images Under High Resolution Transmission Electron Microscopy , 2003 .