Experiments in Fluids

, Volume 49, Issue 6, pp 1307–1324 | Cite as

Tomographic particle tracking velocimetry using telecentric imaging

Research Article


The goal of this article is to discuss 3D Particle Tracking Velocimetry (PTV) in a tomographic reconstructed voxel space with at least doubling the spatial resolution compared to classical 3D PTV. For this purpose, a new tomographic reconstruction technique based on telecentric imaging in combination with the epipolar geometry is presented. The method overcomes the need for memory intensive weighting matrices or cost intensive iterations, which are necessary in iterative algebraic reconstruction techniques. A characteristic of tomographic reconstruction is the reconstruction of ghost particles. As the aim of PTV is the reconstruction of true particle paths, this article focuses on the removal of ghost particles and ghost trajectories. The method is validated via a synthetic turbulent flow field and via the benchmark experiment of a vortex ring.

List of symbols


Aspect ratio (I/K)


Focal point


Control point


Fundamental matrix


Size of the voxel space in i-direction (in the image plane)


Intensity profile of a particle

Ix, Iy

Image size [pix]

IxM, IyM

Object size [mm]


Size of the voxel space in k-direction (normal to the image plane)


Size of the epipolar row


Size of the voxel row


Magnification (IM/I), number reconstructed trajectories


Number of voxel occupied by a particle; number of time steps

OP = (x, y)T

Image coordinate system [pix]

OC = (xC, yC, zC)T

Focal point coordinate system [mm]

OW = (xW, yW, zW)T

Global coordinate system [mm]

OI = (i, j, k)T

Voxel space coordinate system [vox]


Quality of reconstruction


Transformation matrix


Intensity of a pixel element


Intensity of a voxel row element


Intensity of a voxel element


Object point (xW, yW, zW)T [mm]


Candidate for a trajectory


Diameter of a particle [pix], [mm]


Epipoles (x, y)T [pix], difficulty in tracking


Number of particles being part of the trajectory


Epipolar line (x, y)T [pix]


Focal length [mm]


Epipolar row [pix]


Voxel row [vox]


Index along the epipolar row


Index along the voxel row


Particle links from one frame to the next frame; velocity of polynomial fit


Particles per pixel


Centroid position of a particle in object space with sub-voxel accuracy


Scaling factor [mm/pix] or [mm/vox]


Spread parameter


Time [s], time steps [–]


Velocity [mm/s]


Median particle distance [mm] [pix] [vox]


Separation time [s]


Tilting angle between the master camera and a second camera [°]


Rotational angle between the master camera and a second camera [°]


Angular displacement between the master camera and a second camera [°]


Accuracy, standard deviation


Quality function


Epipolar plane



Parts of the experimental study have been funded by the Deutsche Forschungsgemeinschaft (DFG) within the focus program SPP 1147 under grant #BR1494.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institut für Mechanik und Fluiddynamik, Professur für Strömungsmechanik und StrömungsmaschinenTU Bergakademie FreibergFreibergGermany

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