Analysis of Stereoscopic PIV Measurements
using Synthetic PIV Images
A. Petracci1, C.W.H. van Doorne1, J. Westerweel1 and B. Lecordier2
1
Delft University of Technology, Laboratory for Aero and Hydrodynamics,
Leeghwaterstraat 21, 2628 CA Delft, The Netherlands.
2
CORIA – LTH, UMR6614, CNRS, Université and INSA de Rouen, 76801 Saint
Etienne du Rouvray, France.
Abstract
This paper describes the use of a synthetic image generator (SIG) for the assessment of the precision of a stereoscopic PIV system. The geometry implemented
with the SIG closely matches that of an existing stereo-PIV measurement in laminar pipe flow. The calibration procedure is simulated, which demonstrates the necessity of a careful alignment between the calibration target and the light-sheet
plane. This demonstrates the possibilities for determining the tolerances for
alignment and optical configuration prior to the actual measurement, which can
save substantial costs during measurement campaigns in wind tunnel facilities.
1 Introduction
Synthetic images are becoming an essential tool in the PIV technique. They provide validation for new image analysis algorithms and for the reliability of the experimental results. Such an a priori estimate of the data quality leads to the most
effective setup configuration and saves time during the measurement session.
Synthetic PIV images for optimizing PIV performance were used extensively in
the past by Keane and Adrian (1990, 1991, 1992), Willert (1996) and Okamoto et
al. (2000), and were used for the assessment of PIV interrogation performance for
different PIV algorithms during the ‘PIV challenges’ in 2001 and 2003 (see:
http://www.pivchallenge.org).
A new Synthetic Image Generator - SIG – was developed within the EuroPIV-2
project (contract G4RD-CT-2000-00190), with the aim to provide a single standardized and portable code for the generation of synthetic PIV images. A detailed
description of the SIG is given elsewhere in this book by Lecordier et al. (2003).
One of the new features implemented in the SIG is the full support of angularstereoscopic 3D-PIV systems, allowing the simulation of complex acquisition
geometries. Moreover, the SIG can be used to simulate the calibration phase with
synthetic calibration targets, and to determine the optimal parameter settings be-
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fore starting the measurement session itself. The calibration of the 3D-PIV set-up
is one of the most critical steps during a measurement campaign, especially in the
case of the 3D-reconstruction method described by Soloff et al. (1997) and Prasad
(2000).
The aim of the present paper is to describe the implementation and use of the
SIG for stereoscopic PIV. Therefore, an existing stereoscopic PIV measurement in
laminar pipe flow was recreated with the SIG. The details of the measurement are
given by Van Doorne et al. (2003) in this book.1 Subsequently, the SIG was used
to test the sensitivity to misalignment errors between the light-sheet plane and the
calibration target. It has been demonstrated by Coudert and Schon (2001) and Van
Doorne et al. (2003) that such a misalignment can be a significant source of error
in PIV measurements. In the case of the pipe flow measurements by Van Doorne
et al. (2003) it was necessary to create an entry to the pipe for the insertion of the
calibration target, and to maintain optical access from both sides of the target and
to minimize optical distortions. It was found that the procedure is highly susceptible to misalignment, orientation and deformation of the calibration target. Therefore, it can be very time consuming to determine the maximum allowable tolerances for misalignment, orientation and deformation during an experiment. The
demand for a standardized tool that can predict the performance of a PIV measurement initiated the development of the SIG program.
The sections below describe how the stereoscopic configuration is implemented
in the SIG, the procedure for the generation of the calibration targets, and the generation of particle fields. This is followed by sections that contain the results of the
analysis and the comparison with the experimental results. The main conclusions
are summarized in the final section.
2 Geometry
This section contains a brief description of the stereoscopic PIV set-up that was
used for the actual measurements in laminar and turbulent pipe flow; for a detailed
description we refer to the paper by Van Doorne et al. (2003).
The measurements are carried out in a 28-meter long circular pipe, with a
40 mm inner diameter. The light sheet is obtained from a twin-cavity pulsed
Nd:YAG laser, and has a thickness of 1 mm. The light-sheet plane is perpendicular to the main flow direction; see Fig. 1. This makes it possible to observe the full
pipe cross flow, although it reduces the measured dynamic range as the motion of
the tracer particles is perpendicular to the light-sheet plane. As a matter of fact, to
avoid lost of correlation, the particle displacement has to be kept within about onequarter of the laser sheet thickness (Keane and Adrian 1992).
1
This is a reprint of: Van Doorne, C.W.H., Westerweel, J., Nieuwstadt, F.T.M. (2002),
‘Stereoscopic PIV measurements of transition in pipe flows, measurement uncertainty in
th
laminar and turbulent flow.’ In: Proc. 11 Int.Symp. Application of Laser Techniques to
Fluid Mechanics, July 8-11, 2002 (Lisbon, Portugal).
PIV Accuracy 201
The two CCD cameras are placed at angles of +45 and –45 degrees with respect
to the light sheet normal, observing the illuminated area from opposite sides. The
optical configuration satisfies the Scheimpflug condition (Prasad 2000), so that the
full viewing area is in focus. The test section of the pipe consists in a rectangular
glass enclosure filled with water. The optical access is achieved through two water
prisms placed on the wall of the enclosure in order to minimize the optical aberrations; see Fig. 2. Therefore, it is permitted to disregard any correction for the image distortion due to changes in the refractive index.
mirror
lenses
Nd:YAG laser
test section
y
z
+45o
-45o
x
CCD camera on
Scheimpflugmount
laser sheet
Fig. 1. schematic of the simulated setup; the main flow direction is from right to
left.
a)
b)
Fig. 2. a) the real test section of the pipe with the water prisms and the two Kodak CCD
cameras on Scheimpflug mounts; b) the test section as observed by left camera, through the
water prism.
Following the scheme in Fig. 3 and keeping in mind that every unit used in the
SIG configuration file is related to pixels and to millimeters according to this relation:
1 SIG unit ≡ 4 pixels ≡ 0.16 mm,
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one obtains the detailed geometry for the stereoscopic PIV setup, i.e. the image
dimensions, the particle space domain, the light sheet characteristics, the optical
path, the projection angles and the CCD characteristics, as given in Table 1. It
should be noted that in the SIG the x-coordinate is always aligned with the lightsheet plane (see Fig. 3), whereas in the pipe flow measurements it would be natural to associate the x-coordinate with the main flow direction (viz., pipe axis).
Fig. 3. schematic with all the conventions used by SIG to recreate a stereoscopic angular
PIV system with cameras in opposite views and laser sheet perpendicular to the main flow
direction.
Table 1. overview of the relevant parameters for the SIG configuration files to simulate the
experimental conditions.
Image size
Particle space dimension
Particle displacement
Light sheet position
Light sheet thickness
Camera angles
Scheimpflug angle
CCD fill ratio
CCD saturation level
CCD pixel pitch
Object distance do1 = do2
Image distance di1 = di2
Aperture
Magnification
Real units
1008 x 1008 pixels
40 x 40 x 1.8 mm
10 pixels
0 mm
1 mm
θ1 = +45°; θ2 = -45°
α1 = +12.8°; α2 = -12.8°
0.75
1.0
110.77 mm-1
260 mm
59.15 mm
f# 4
0.228
SIG units
1008 x 1008
250 x 250 x 11.25
2.5
0
6.25
θ1 = 45°; θ2 = 135°
α1 = 12.8°; α2 = 347.2°
0.75
1.0
17.72
1625
370
4
0.228
PIV Accuracy 203
Two different configuration files are needed, one for each camera, because of
their different angle of view. Examples of the parameter declaration in the SIG can
be found in the CD enclosed with this book.
3 Generation of Calibration Sets
With the geometry specified in Table. 1, it is necessary to first generate a set of
images for a ‘synthetic’ calibration target at different positions with respect to a
reference location (viz., the location of the light-sheet plane).
Fig. 4. crossed pattern to be used as input for the SIG; the distance between the marks is 3.9
mm (98 pixels) and their thickness is 0.24 mm (6 pixels).
With the aid of a simple MATLAB script a calibration image that consists of
white + marks on a black background is generated; see Fig. 4. By means of another MATLAB script this image is transformed into a file, referred to as a ‘grid
file’, containing a particle field; this script transforms each pixel with a non-zero
gray value in a particle within the 3-dimensional object domain with a diameter
that is proportional to the square root of the pixel gray value. (This script can be
used for transforming any arbitrary gray value image.) By changing the z-position
values results in displacing the calibration target along the z-axis with respect to
the object plane. The SIG will then generate TIFF images of the calibration target
in several positions in space along the z-axis, as each camera in the real set-up
would acquire it (see Fig. 5), and as is needed in order to set up the stereoscopic
reconstruction in the PIV analysis software.
4 Generation of Particle Images
This section describes the procedure for generating the particles fields that correspond to the laminar pipe flow in the measurements by Van Doorne et al. (2003).
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A set of particles, randomly distributed within the object domain defined for the
SIG, was created by means of a FORTRAN program that calls the standard
drand48 uniform random number generator. Another FORTRAN program reads
the particle file, and displaced it along the axial direction (viz., z-coordinate direction for the SIG) according to a parabolic displacement field to emulate a laminar
pipe flow.
Fig. 5. TIFF images generated by the SIG of the calibration target simulating left and right
camera acquisition.
In order to determine the required number of particles that needs to be produced, several particle fields were generated with an increasing number density Ni
(expressed in particles per mm3). In this way we could plot a graph (see Fig. 6) for
the fraction of valid data as a function of the seeding density, similar to those that
appear in the papers by Keane and Adrian (1990, 1991, 1992). Also, in this way it
was possible to match as closely as possible to the seeding density in the actual
measurements. It was decided to produce particle fields that would correspond
with a number density of 40 particles/mm3. At this seeding density the fraction of
spurious vectors is effectively zero, so any loss of correlation due to insufficient
seeding is avoided.
Fig. 6. percentage of validated vectors in the PIV results as a function of the
seeding density (Ni).
PIV Accuracy 205
The synthetic PIV images, generated by the SIG in TIFF format, were processed with a commercial PIV code (LaVision DaVis v6.3), identically to the processing of the image data in the measurements by Van Doorne et al. (2003). The
settings for the PIV analysis are listed in Table 2.
5 Results: Error Prediction
As mentioned by Prasad and Adrian (1993), Willert (1997), Prasad (2000) and
Coudert and Schon (2001), and as investigated by Van Doorne (2002), the registration error occurs when, during the calibration phase, the center of the light sheet
does not exactly coincide with the position of the grid. This leads to a reconstruction error during the analysis of the 3D vector field adding 2D in-plane displacements not present in reality.
The laminar pipe flow studied by Van Doorne et al. (2003) is an excellent test
case to demonstrate this effect. This effect is due to the back projection from an
image plane to another one that does not coincide with the true location of the
light-sheet plane. The effect becomes more pronounced when the gradient of the
displacement field becomes larger. In the case of the laminar pipe flow this means
that the error becomes larger with increasing distance from the pipe center, resulting in poor accuracy especially for near-wall measurements, as illustrated in
Fig. 7.
Table 2. the seeding density value of the synthetic images for the laminar flow mimic and
an overview of the values chosen for the PIV analysis.
Seeding density
Interrogation
Window size
Iteration #
Windows overlap
Initial window shift
Correlation function
Post processing
40 particles/mm3
Multipass, with constant window size
32 x 32 (pixels)
2
50 %
0
Normalized: (I1-I1avg)*(I2-I2avg)/rms
Median filter
In the measurements, Van Doorne et al. (2003) traversed the light-sheet plane
with respect to the reference position of the calibration target, and then determined
the optimum position of the light-sheet plane for which the registration error vanishes. This same procedure was recreated with the SIG, by means of generating
different sets of calibration targets, centered in slightly different positions with respect to the (fixed) position of the light-sheet plane. Initially, the first grid image is
generated at a position of 0 mm, i.e. aligned with the light-sheet plane, and then
misaligned in steps of ±0.16 mm. The displacement between the two grid images
is kept constant and equal to +0.32 mm. The whole series of calibration sets can
be found in Table 3. In this way it was possible recreate the effects of the registration error for the case of a laminar pipe flow, and to demonstrate that only a cali-
206 Session 3
bration target that is perfectly aligned with the light-sheet plane can give optimal
results.
Fig. 7. laminar pipe flow; zoomed in plane vector field with no registration error (left) and
with registration error (right).
Table 3. calibration sets used to investigate the prediction capability for the registration error with the SIG; the second and the third column show the initial position of the target and
its position after the displacement.
Calibration sets
-0.8 / -0.48
-0.64 / -0.32
-0.48 / -0.16
-0.32 / 0
-0.16 / 0.16
0 / 0.32
0.16 / 0.48
0.32 / 0.64
0.48 / 0.8
First grid image
(mm)
-0.8
-0.64
-0.48
-0.32
-0.16
0
0.16
0.32
0.48
Second grid image
(mm)
-0.48
-0.32
-0.16
0
0.16
0.32
0.48
0.64
0.8
Displacement
(mm)
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
The results are shown in Fig. 8, and compared against the results obtained by
Van Doorne et al. (2003). The plot shows that the results from the synthetic images and from the experiment are behaving in the same way, i.e. the registration
error ε is directly proportional to the misalignment γ of the calibration target. It
should be noted that the registration error result from the synthetic images does
not vanish for a perfectly aligned configuration. This is a still open question, but
the problem seems to be related to the accuracy in the de-warping process or to the
SIG’s simulation of the Gaussian shape of the laser sheet. Anyway, this error is on
the order of a hundredth of a pixel while the resolution of the real system is on the
order of a tenth of a pixel, as has been pointed out by Van Doorne et al. (2003).
PIV Accuracy 207
Fig. 8. registration error (ε) along x as a function of the misalignment of the calibration target with the laser sheet (γ).
Table 4. calibration sets used to investigate the capability of prediction of errors due to the
increase of the displacement between the targets; the second and the third column show the
position of the first target and the position of the second one.
Calibration sets
0 / 0.16
0 / -0.16
0 / 0.32
0 / -0.32
0 / 0.48
0 / -0.48
0 / 0.64
0 / -0.64
0 / 0.8
0 / -0.8
-0.16 / 0.16
-0.32 / 0.32
-0.48 / 0.48
-0.64 / 0.64
First grid image
(mm)
0
0
0
0
0
0
0
0
0
0
-0.16
-0.32
-0.48
-0.64
Second grid image
(mm)
0.16
-0.16
0.32
-0.32
0.48
-0.48
0.64
-0.64
0.8
-0.8
0.16
0.32
0.48
0.64
Displacement
(mm)
0.16
-0.16
0.32
-0.32
0.48
-0.48
0.64
-0.64
0.8
-0.8
0.32
0.64
0.96
1.28
The use of the SIG can be extended to predict under which conditions the software for the stereoscopic PIV analysis is providing the most reliable results in
terms of the calibration configuration. With the SIG it is possible to generate many
calibration sets, every one aligned with the laser sheet, but with a different value
208 Session 3
for the target displacement, or with a target displacement that is upstream rather
then downstream, or even with different kinds of targets (dotted, crossed), creating
any kind of combination the experimentalist would like to explore prior to setting
up the actual measurements.
For this purpose, we synthesized several targets at different locations, upstream
and downstream with respect to the light-sheet plane. Then these targets were
combined into different calibration sets, as shown in Table 4. These were subsequently applied to the analysis of the same synthetically generated image data of a
laminar pipe flow.
Fig. 9. Error on the horizontal velocity component (ε) as function of the gap between the
targets (∆); first grid image aligned with the center of the laser sheet (squares) and symmetrically misaligned (circles).
The graph in Fig. 9 shows that the increase of the displacement between the
targets does not imply a significant change in the reliability of the stereoscopic
PIV analysis. As expected, the error is consistent for equal displacement, either
positive or negative. Only using a displacement value with an absolute value
larger than 0.4 mm (i.e., 40% of the light sheet thickness) can cause a higher
fluctuation level, although error maintains within about one-tenth of the registration error.
When the target displacement is increased in concurrence with a misalignment,
so that targets are found at symmetrical locations with respect to the light-sheet
plane, it is found that the error becomes large, which is mainly due to registration
error discussed above. This can be clearly seen in Fig. 10: here the error due to the
symmetrical misalignment is perfectly superimposed onto the registration error
curve in Fig. 8, where the gap between the targets was maintained constant.
PIV Accuracy 209
Fig. 10. comparison between error on the horizontal velocity component (ε) due to
symmetrical misalignment (γ) of the grids and registration error.
6 Conclusions
The SIG was created with the aim to provide an experimentalist the ability of
simulating different kinds of experimental configurations for PIV, including complex imaging configurations such as encountered in stereoscopic PIV. It can be
utilized in the preparatory phase of an experiment, and allows to test for artifacts
that arise due to imperfections in the implementation of the set-up, and to detect
critical dependencies for certain experimental parameters, as was demonstrated in
the present paper for the registration error as a function of a misalignment between
the calibration target and light-sheet plane.
It is thus possible to determine the tolerances for alignment and optical configuration before the actual measurement. The SIG provides an excellent tool to assess
these tolerances prior to the measurement session, and therefore can save substantial costs during measurement campaigns in wind tunnel facilities.
References
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210 Session 3
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