Relatively recent options are 3D PTV (Maas et al.
1993) and defocusing PIV (Pereira et al. 2000). These
techniques rely on the identification of individual par-
ticles in the PIV recordings. The exact position of the
particle within the volume is given by the intersection
of the lines of sight corresponding to a particle image in
the recordings from several viewing directions (typi-
cally three or four). The implementation of the particle
detection and location varies with the methods. In
comparison with the previous two methods, the 3D-
PTV approach offers the advantage of being fully
digital and fully 3D without the requirement for mov-
ing parts. The velocity distribution in the volume is
obtained from either particle tracking or by 3D-cross-
correlation of the particles pattern (Schimpf et al.
2003). However, the procedure for individual particle
identification and pairing can be complex and as it is
common for planar PTV several algorithms have been
proposed, which significantly differ due to the prob-
lem-dependent implementation. The main limitation
reported in literature is the relatively low seeding
density to which these techniques apply in order to
keep a low probability of false particle detection and of
overlapping particle images. Moreover, the precision
of the volume calibration or in the description of the
imaging optics is finite. This means the lines of sight for
a particle almost never truly intersect and an inter-
section criterion is needed. Consequently the maxi-
mum seeding density in 3D PTV is kept relatively low.
Maas et al. (1993) report a seeding density of typically
0.005 particles per pixel for a three camera system.
The development of the proposed tomographic-PIV
technique is motivated by the need to achieve a 3D
measurement system that combines the simple optical
arrangement of the photogrammetric approach with a
robust particle volume reconstruction procedure,
which does not rely on particle identification. As a
consequence the seeding density can be increased, with
respect to 3D PTV, to around 0.05 particles per pixel
(as will be shown later), which is not far from the
particle image density used in planar experiments. As a
consequence the flow field within the 3D domain can
be represented with a number of velocity vectors
comparable or slightly higher than obtained in planar
PIV. Furthermore, the proposed technique features the
instantaneous flow field measurement, as opposed to
scanning PIV, opening the possibility to perform 3D
measurements in several conditions irrespective of the
flow velocity. Finally the introduction of high-repeti-
tion rate PIV hardware is expected to further extend
the measurement technique capability to a 3D time-
resolved flow diagnostic tool as already demonstrated
in a recent study (Schro
¨
der et al. 2006).
3 Working principle of tomographic-PIV
The working principle of tomographic-PIV is sche-
matically represented in Fig. 1. Tracer particles im-
mersed in the flow are illuminated by a pulsed light
source within a 3D region of space. The scattered light
pattern is recorded simultaneously from several view-
ing directions using CCD cameras similar to stereo-
PIV, applying the Scheimpflug condition between the
image plane, lens plane and the mid-object-plane. The
particles within the entire volume need to be imaged in
focus, which is obtained by setting a proper f/#. The 3D
particle distribution (the object) is reconstructed as a
3D light intensity distribution from its projections on
the CCD arrays. The reconstruction is an inverse
problem and its solution is not straightforward since it is
in general underdetermined: a single set of projections
can result from many different 3D objects. Determining
the most likely 3D distribution is the topic of tomog-
raphy (Herman and Lent 1976), which is addressed in
Fig. 1 Principle of tomographic-PIV
Exp Fluids (2006) 41:933–947 935
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