8TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY - PIV09
Melbourne, Victoria, Australia, August 25-28, 2009

Tomo PTV using 3D Scanning Illumination and Telecentric Imaging
J. Kitzhofer1, C. Brücker1 and O. Pust2
1

Institut für Mechanik und Fluiddynamik, Professur für Strömungsmechanik und Strömungsmaschinen,
TU Bergakademie Freiberg, 09596, GERMANY
Jens.Kitzhofer@imfd.tu-freiberg.de2

Dantec Dynamics A/S, DK-2740 Skovlunde, DENMARKABSTRACT
The article discusses the tomographic reconstruction ofparticles for the flow visualisation technique PTV (ParticleTracking Velocimetry) and its application on the real flow of avortex ring using 3D scanning illumination and telecentric
imaging. In standard 3D PTV an increasing number density ofparticles increases the problem of stereo-matching andoverlapping particle images limiting the resolution for a threecamera set-up to 0.005 ppp (particles per pixel)[5]. Therefore,in classical 3D PTV the maximum number of observabletrajectories is limited to the order of 10³ in a typical cubic
volume. This number can be increased by developments like
Scanning PTV [5,7]. However, the mentioned limitations stillexist. Tomo PTV in combination with a scanning illumination
overcomes these limitations within at least a doubling of thespatial resolution of every single scanned volume. The model
flow to determine the measurement method of Tomo PTV
described herein is a vortex ring.

1. INTRODUCTION
The investigation of flow fields is usually performed within an
Eulerian framework. For the analysis of turbulent flows theLagrangian frame gives additional important information
about turbulent mixing, dispersion etc. This requires thereconstruction of long Lagrangian trajectories with a highspatial resolution. In standard 3D PTV methods the epipolargeometry is used to detect corresponding particle images
between different camera views after the localisation of the 2D
centroid positions. The tracking of the particles is done either
in 2D or in 3D or as a combination of both. The problem ofstereo-matching and overlapping particle images limit themaximum number of linkable particles from one frame to theother frame to a number of 0.005 ppp (particles per pixel)[5].
In Tomo PTV the tracking is done in 3D space after thedetermination of the 3D centroid positions of the particles inspace. The tomographic reconstruction of the particles isperformed as a combination of the epipolar geometry and amultiplication of gray-values of corresponding pixels in thedifferent camera views [4]. This is possible due to thetelecentric imaging resulting in a parallel projection for theobserved volume. Each pixel value in one camera occupied bya particle is multiplied with all pixel values along thecorresponding epipolar line in the other camera. Thus grayvalue-weighted particles are reconstructed at defined voxelpositions. The by-product of tomographic reconstructions is
the reconstruction of ghost particles [1]. In particle tracking
methods it is sufficient to detect and to delete ghost particles
for not building false particle paths. Different detection criteria
are necessary to decrease the number of ghost particles [4].
The strongest decrease is achieved by the use of a multicamera-setup. Furthermore ghost particles can be detected bya size based criterion, because ghost particles often appear as aparticle artefact [7]. Beside the fact that a scanning
illumination can increase the spatial resolution of standard
PTV [2], the scanning illumination helps to detect ghostparticles. Reconstructed particles appearing in a region
without illumination are identified to be ghost particles. The
ghost particles appearing within the illuminated sheet aredetected by the particle tracking method itself. The tracking isdone with the 4-frame method after performing the 3D particle
reconstruction and the following 3D centroid localization inthe object space. A condition for the detection of ghost
trajectories is the smoothness of a trajectory. Ghost trajectories
are blinking or are too short to build up the true path of atrajectory.

2. TOMOGRAPHIC RECONSTRUCTION
2.1 Principle
A mathematical model for a stereoscopic camera setup is
given by the epipolar geometry. It describes, that a point,
which is found in one camera, has to be along a line in thesecond camera. Mathematically the relation between bothcameras is described by the fundamental matrix F. The
relation of a 2D image position in camera one to the positionin camera two is called epipolar equation resulting in a line incamera two called epipolar line. In the context of calibration,
the fundamental matrix has to be evaluated for eachcombination of the cameras.
Once the fundamental matrix is determined, gray value
weighted particles can be reconstructed at defined voxel
positions. The epipolar line for each pixel in one camera
occupied by a gray value larger than zero is determined. The
position of the voxel element is defined by the pixel positionin camera one and by the position along the epipolar line. The
gray value of the voxel element is calculated by amultiplication of gray values of corresponding pixels in both
image views (fig.1).

Figure 1: Tomographic reconstruction
If more than two cameras are used to reconstruct the particles
in the measured volume, the reconstructed volumes for eachcombination of cameras have to be multiplied [4].

The investigations in this article are performed for a threecamera set-up with scanning illumination. Ten cinematic lightsheets with a thickness of 10 mm illuminate the measured
volume. The light sheets have an overlap of 1 mm. The
tomographic reconstruction of the particles is performed foreach light sheet. After the 3D centroid determination, thereconstructed light sheet volumes are combined. In theoverlapping regions the same particles are reconstructed twice.
The accuracy of the twice reconstructed particles is 1/10 pixel,
resulting in a simple nearest neighbour comparison to findtwice reconstructed particles.
2.2 Detection of Ghost Particles
The first detection criterion is the combination ofreconstructed volumes due to a multi-camera set-up. Figure 2shows the number of reconstructed particles as a function of
the real number of particles for a two camera set-up and athree camera set-up. The dataset is generated with syntheticparticles in a defined voxel space. The particle size ishomogenous (7 voxel). The red line shows the results for a
two camera set-up. With increasing number of real particles
the number of reconstructed particles increases rapidly. A
three camera set-up (green line) can strongly decrease thenumber of ghost particles. 20 % of the reconstructed particles
are ghost particles for 0.01 ppp.

randomly distributed in voxel space and parallel projected
onto the synthetic image planes. Afterwards the particles arereconstructed as described in section 2. By comparison withthe known 3D particle position the accuracy of thedetermination of the particle positions can be evaluated. The
accuracy σ is defined as the difference between the estimatedposition and the true position of a particle. The accuracy σi indirection i is 0.12 pix, σj in direction j is 0.02 pix and σk indirection along the epipolar line is 0.15 pix for the 3-camera
set-up.
3.2 Tracking Algorithm
Ouellette et al. [6] tested the quality of several 3D tracking
algorithms. The quality of the 4-frame method (Minimum
Change in Acceleration) outperformed the other tested
algorithms like Nearest Neighbour or 3 frame algorithm. An
upgrade for the 4-frame method is achieved herein due to thetomographic reconstruction. As the size of the particles isknown in 3D space, ambiguities can be decreased. The quality
function for possible linked particles from one frame to thenext frame reads:

Φ tij , size = Ν tij+1 − Ν tij(1)

Nt indicates the number of occupied voxel of a particle atframe t and Nt+1 the number of occupied voxel of a particle atframe t+1. The particle with the smallest change in size ischosen for the trajectory.
If this criterion provides no solution, the 3D intensity
distribution of the possible candidates (t+1) is compared withthe 3D intensity distribution of the particle already being partof the trajectory (t). The one with the best fit is chosen.

⎛ ∑ I N ,ij ⎞⎜⎟tΦ ij ,int = ⎜ N⎟⎜ max( I N ) ⎟⎝⎠Figure 2: Reconstructed particles as a function of real
particles for a 2-camera setup (red line), a 3-camera
setup (green line) and the 3-camera setup with size
based criterion (black line)
The second detection criterion is called size based criterion.
Ghost particles appear as a kind of artefact of particles [7].
This means that ghost particles don’t have the same size asreconstructed real particles. A simple threshold is chosen todelete the particles, which are too small to be real particles. Inthe present synthetic dataset the threshold is set to 4 voxel
resulting in a reduction of 14 % for 0.01 ppp in comparison
with the 3-camera setup.
The third implemented criterion is the detection of ghost
particles due to the light sheet thickness. If a particle isreconstructed at a position in space, where has been noillumination, the reconstructed particle is deleted as will bedescribed in section 4.

t +1⎛ ∑ I N ,ij ⎞⎜⎟−⎜ N⎟⎜ max( I N ) ⎟⎝⎠t

3.3 Detection of Ghost Trajectories
The following two criteria are grouped in the detection ofshort and long ghost trajectories. Figure 3 shows a typicalresult for a tomographic reconstructed trajectory and its
surroundings in case of the experimental setup that will be
described in section 4.

short ghost trajectories
long ghost
trajectories

3. PARTICLE TRACKING
3.1 Determination of Centroid Positions
Ouellette et al. [6] compared several algorithms fordetermining the centers of particles. The Gaussian fitting
delivered best results due to sub-pixel accuracy, speed androbustness to noise. The accuracy for determining the centers
is estimated with a synthetic dataset. Particles (7 voxel) are(2)Figure 3: Reconstructed trajectory and environment

The criteria for short ghost trajectories can be interpreted as akind of save threshold. Most of the ghost trajectories are ofsmall lengths up to three frames. Particle paths existing for
only three frames don’t yield much information for a fluid
mechanical interpretation. Thus a cut off is made, which has tobe chosen carefully not to delete true particle paths.
For the detection of long ghost trajectories, a first guess tests
the similarities of trajectories in 3D space. This checks frame
identity, speed, direction and change in direction. Trajectories
fitting these conditions are compared. Long parallel ghost
trajectories have a characteristic blinking. The particle pathhas breaks. Moreover, characteristic for this kind of ghost
trajectory is the size of the particle building a trajectory. The
particle size in true trajectories is nearly constant. The particle
size of ghost trajectories building a path changes whilemoving along the particle path [4]. Usually the particle
appears small sized in the beginning, grows up to a maximum
size and shrinks until appearing no more in space. If thesecriteria fit a selected trajectory, the trajectory is a ghost
trajectory and is deleted.

The data presented is evaluated with the 3-camera setup andthe size based criterion. The shape of the vortex ring is clearlyrecognizable. Figure 5b shows the vortex ring in the top view.
The outer borders of the scanning light sheet are illustrated
with red lines. Moreover the particles appearing outside theilluminated light sheet are marked red. These particles are
identified to be ghost particles and can be deleted for further
investigations.

4. EXPERIMENTThe connection of the ten scanning light sheets for one total
scan is shown in figure 6. Every different coloured light sheetmeans a successive scan. The circled shape of the vortex ringis recognizable.
The overlapping area between the fifth and the sixth lightsheet is marked with blue lines. Inside the overlapping area
particles are marked with yellow dots. These particles arereconstructed in both light sheets, found by the nearest
neighbour comparison. As described above, the accuracy is1/10 pixel.

4.1 Experimental Set-up
The experimental set-up is shown in figure 4. The laser beamof a continuous Argon-Ion laser (a) Coherent Innova 70 (2 W)
passes an optical lens system (b) to adjust the desired
thickness of the light sheets. The rotating mirror drum (c)reflects the laser beam into the direction of the observed
volume and generates successively 10 parallel light sheet
planes with a thickness of 10 mm (f) [3]. The studied flow is avortex ring travelling in an octagonal glass tank (e) filled withwater. The vortex is generated at the exit of a piston tube witha diameter of 50 mm (g). The neutrally buoyant seeding
particles (100 microns) are injected into the center of thevortex generator. The particle images are recorded with a threecamera system consisting of digital high speed cameras
Photron APX RS with a resolution of 1024 x 1024 Pixel² andan angular displacement of 45°, -45° and 90°. The cameras areequipped with telecentric lenses at f-number 16 resulting in aparallel projection for the observed volume. The side of theoctagon opposite to the entrance side for the laser is coveredwith a light absorbing mat that reduces stray reflections. Thisis also valid for the faces opposite the cameras, thus giving aperfectly black background. The experiments are performed
with a recording rate of 1000 frames/s. Using 10 scanningplanes results in a separation time of 10 ms for eachsubsequent illumination of one scan plane. The image size ofthe cameras and the light sheet thickness define the measured
volume, resulting in about 90 x 90 x 90 mm³.
dgbaedfc

Figure 4: Experimental Set-up (a Ar-Ion-laser, b lenssystem, c rotating mirror drum, d high speed camera, eoctagon, f light sheets, g vortex generator)
4.2 Results
4.2.1 Tomographic Reconstruction
The tomographic reconstruction of one scanning light sheet in
the middle of the vortex ring for one single frame is shown infigure 5. Figure 5a shows an isometric view of the vortex ring.

Figure 5: a) Isometric view b) Top view of one lightsheet in the middle of the vortex ring

Overlap

Figure 6: Top view of the connection of the scanninglight sheets for one total scan
4.2.2 Particle TrackingThe result for the 3D trajectories of one scanning light sheet in
the middle of the vortex is shown in figure 7. The cut off ofthe trajectories on the right side of the vortex ring results fromthe viewing field of the third camera. This part of the vortex
could not be observed by the third camera. Nevertheless, theshape is clearly recognizable. The reason for the highmagnitude in absolute velocity in the inner part of the axis ofrotation is that the induced velocity of the vortex ring issuperimposed with the translational velocity of the vortex ring.
This is in well agreement with the fluid mechanicalcharacteristics of a vortex ring.
At the end of the width of the light sheet appear trajectories,
which have a sudden cut off. These trajectories continue in thenext light sheet. Figure 8 shows the connection of the ten
scanning planes for a moving observer as a function ofabsolute velocity. A cut between the light sheets is notrecognisable.

factor of number light sheets. Nevertheless, the number oflinkable particles is no more defined by the problem of stereo
matching or overlapping particles, but by the detection of
ghost particles and the ratio of distance between particles andmedian particle displacement.
The telecentric imaging simplifies the reconstruction
algorithms and increases the size of the measured volume
about the depth of focus of the telecentric lenses. As well as
commonly used reconstruction algorithms like for example
MART [1], the processing time of the reconstruction
algorithm is long. Further developments have to optimize theprocessing time.
Observed Volume
Seeded Volume
Light Sheets
Light Sheet thickness
Light Sheet Overlap
Median particle displacement
Median Number of Links (Light Sheet in the middle)
Median Number of Links (All Light Sheets)
Calculated Number of Links (Observed Volume)
Total Number of Trajectories (All Light Sheets)

Figure 7: Reconstructed trajectories for one scanninglight sheet as a function of velocity [mm/s] a) top view b)
isometric view

700 cm³
320 cm³
101 cm0,1 cm
5 pixel
1050
3000
6500
18000

Table 1: Statistics of Scanning Tomo PTV in applicationof the vortex ring

ACKNOWLEDGMENTS
The authors thank Prof. Maas for the discussions and thebrainstorming about the calibration procedure and the particle
tracking. Moreover, the authors thank Dantec Dynamics forthe support of the hardware equipment.

REFERENCES[1] Elsinga G.E. (2008) Tomographic Particle Image
Velocimetry, Ph.D. Thesis, Department of Aerospace
Engineering, Delft University of Technology

Figure 8: Iso view of the vortex ring for all ten scanningplanes as a function of absolute velocity [mm/s]
The accuracy of the calculated velocity is estimated by thestandard deviation. Assuming that the vortex ring is in thelaminar phase, the total standard deviation of all reconstructedtrajectories σvx in x-direction is 2.42 mm/s, σvy in y-directionis 1.66 mm/s, σvz in z-direction is 2.32 mm/s and σvabs for themagnitude in velocity is 2.16mm/s.
Table 1 describes the statistics of Tomo PTV with a scanning
illumination for the vortex ring experiment. About the half ofthe observed volume was seeded with particles. In all scanningplanes the median number of links, meaning a particle
observable and linkable for two time steps, is 3000. If thewhole volume is seeded with particles, the links can beincreased and then calculates to 6500. The efficiency of Tomo
PTV with a scanning illumination becomes clear by the 18000
trajectories, which could be reconstructed for more than 10time steps.

5. CONCLUSION
Tomographic Particle Tracking Velocimetry can increase thespatial resolution of determined trajectories about a factor two
in comparison with standard PTV. Moreover the scanning
illumination increases the number of trajectories about the[2] Hoyer, K., Holzner, M., Lüthi, B., Guala, M., Liberzon,M., Kinzelbach, W. (2005) 3D Scanning Particle Tracking
Velocimetry, Experiments in Fluids 39, 923-934[3] Kitzhofer, J., Kirmse, C., Brücker, Ch. (2009) 3D
Scanning Particle Tracking Velocimetry by using High
Speed Digital Cameras and Telecentric Lenses, Notes onNumerical Fluid Mechanics, Springer Verlag[4] Kitzhofer, J., Brücker, Ch. (2009) Tomographic Particle
Tracking Velocimetry, submitted to Experiments in Fluids[5] Maas H.G. (1992) Digitale Photogrammetrie in derdreidimensionalen Strömungsmesstechnik, Ph.D. Thesis,
ETH Zürich
[6] Ouelette, N.T., Xu, H., Bodenschatz, E., (2006) A
quantitative study of three-dimensional Lagrangianparticle tracking algorithms, Experiments in Fluids 40,
301-313[7] Putze, T. (2008) Geometrische und stochastische Modelle
zur Optimierung der Leistungsfähigkeit des 3D PTV,
Ph.D. Thesis, Fakultät Forst-, Geo- und Hydrowissenschaften, Dresden University of Technology