Telecentric lenses for imaging in particle image velocimetry:
a new stereoscopic approach
R. Konrath, W. Schro
Abstract A new stereoscopic approach based on telecen-
tric lenses is introduced. The method offers in-focus
imaging at high viewing angles (highly tilted object planes)
with diminishing systematic image distortion. In single-
view particle image velocimetry (PIV) applications tele-
centric lenses can be used to eliminate projection errors.
Normal and oblique viewing are tested using a commercial
telecentric lens with particle image velocimetry.
Particle image velocimetry (PIV) is a nonintrusive mea-
surement technique for steady and unsteady ﬂows, allowing
the investigation of spatial ﬂow structures (Kompenhans
and Tropea 1997). In the simplest form PIV captures the
two-dimensional velocity vectors in a plane of the ﬂow ﬁeld.
The ﬂow is seeded with small particles following the ﬂow,
and the measurement plane is illuminated by a thin light
sheet. Perpendicular to the light sheet the scattered light
from the particles is recorded with a camera at two instances
of time. The time separation depends on the maximum ﬂow
velocity and the required spatial resolution of the mea-
surement. From the particle image displacements the in-
plane velocity vectors can be extracted using digital image-
processing algorithms. In most PIV applications it is im-
portant that the particles in the light sheet are in-focus to get
small particle images, since the particle-image diameter has
a signiﬁcant impact on the resolution and accuracy of the
measurement (Adrian 1997).
In the geometrical optics approximation, the image
formation of a conventional (entocentric) lens system is a
central projection of the object space onto the image plane.
The image magniﬁcation depends on the distance between
the object and the lens. If the out-of-plane velocity com-
ponent w is not negligible in comparison with the in-plane
velocity components u and v, a projection error occurs
since the image magniﬁcation changes between the re-
cording times (Prasad and Adrian 1992). This disadvan-
tage can be overcome when telecentric lenses are used.
They form images by parallel projection of the object space
such that no projection error occurs. The details are de-
scribed in Sect. 2.
All three velocity components can be determined by
stereoscopic reconstruction. The ﬂow ﬁeld is simulta-
neously recorded from two or more different directions.
There are two basic stereoscopic conﬁgurations using
conventional lenses providing in-focus images over the
entire image plane, the translational method and the an-
gular displacement method, as introduced by Gauthier and
Riethmuller (1988). The disadvantage of the translational
method, employed by Prasad and Adrian (1992), is the
limitation of the maximum possible viewing angle by
image aberrations and the angular aperture of the lenses,
which reduces the accuracy of the out-of-plane velocity
component. The angular displacement method, described
by Prasad and Jensen (1995) and employed by Willert
(1997), possesses the drawback that a systematic image
In this paper a new stereoscopic approach using tele-
centric lenses is presented that is not limited by the
viewing angle and shows no systematic image distortion.
Throughout the presentation the geometrical optics ap-
proximation is assumed (Hecht 1998).
Telecentric lens systems
If the entrance pupil of a lens system is at inﬁnity, the lens
is called telecentric in object space. In this case the
imaging rays between object and lens are parallel to the
optical axis. Therefore, the image is formed by the parallel
projection of the object onto the image plane, and the
image magniﬁcation does not depend on the object dis-
tance. Two different designs of telecentric lenses are pos-
sible. That is, they are either telecentric in object or image
space, or telecentric in object and image space.
Single-sided telecentric lens
In the following, a lens telecentric in object space is as-
sumed. The main difference compared to a conventional
imaging arrangement is that a small aperture stop is lo-
cated in the back focal plane of the lens (Fig. 1a). Only the
light rays that are approximately parallel to the optical axis
of the lens pass the aperture stop and form the image. Now
the central ray of all originating rays from an object point
transmitting the aperture stop passes through the back
focal point instead of the lens center point. From
geometrical optics it follows that the transversal image
magniﬁcation depends only on the image distance b and
Received: 2 November 1999 / Accepted: 21 December 2001
Published online: 23 August 2002
Ó Springer-Verlag 2002
R. Konrath (&), W. Schro
Aerodynamisches Institut, RWTH-Aachen,
52062 Aachen, Germany
Experiments in Fluids 33 (2002) 703–708