Experiments in Fluids

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

Tomographic particle tracking velocimetry using telecentric imaging

Research Article

Abstract

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

AR

Aspect ratio (I/K)

C

Focal point

CP

Control point

F

Fundamental matrix

I

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

IP

Intensity profile of a particle

Ix, Iy

Image size [pix]

IxM, IyM

Object size [mm]

K

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

Lr

Size of the epipolar row

Lv

Size of the voxel row

M

Magnification (IM/I), number reconstructed trajectories

N

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]

Q

Quality of reconstruction

T

Transformation matrix

Vc

Intensity of a pixel element

Vlv

Intensity of a voxel row element

Vv

Intensity of a voxel element

XW

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

c

Candidate for a trajectory

dp

Diameter of a particle [pix], [mm]

e

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

i

Number of particles being part of the trajectory

l

Epipolar line (x, y)T [pix]

lC

Focal length [mm]

lr

Epipolar row [pix]

lv

Voxel row [vox]

m

Index along the epipolar row

ms

Index along the voxel row

p

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

ppp

Particles per pixel

rP

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

sk

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

sp

Spread parameter

t

Time [s], time steps [–]

v

Velocity [mm/s]

Δs

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

Δt

Separation time [s]

κ

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

φ

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

ω

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

σ

Accuracy, standard deviation

Φ

Quality function

π

Epipolar plane

Notes

Acknowledgments

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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