The EUROPIV Synthetic Image Generator (S.I.G.)
B. Lecordier1, J. Westerweel2
1
UMR 6614 CNRS CORIA - Université and INSA de Rouen, BP12, F-76801
Saint Etienne du Rouvray Cedex, (France), Bertrand.Lecordier@coria.fr,
http://www.coria.fr.
2
Delft University of Technology Laboratory for Aero and Hydrodynamics,
Leeghwaterstraat 21, 2628 CA Delft (Netherlands),
j.westerweel@wbmt.tudelft.nl, http://www.ahd.tudelft.nl
Abstract
The aim of this paper is to present the main features of the PIV Synthetic Image
Generator (SIG) which was developed in the frame of the EUROPIV 2 project.
The aim of developing this generator was to have a standardised tool, which allows the generation of identical synthetic PIV images in different teams and to
simplify the performance evaluation of PIV processing algorithms. A second objective was to have a flexible tool that can be used to prepare a PIV experiment by
optimizing the recording parameters on realistic synthetic images. This was quite
useful and successful in the EUROPIV 2 project. Consequently, it was decided to
make this tool available to the scientific community. The basic version of the SIG
is provided on the CD-ROM going with the present book. It will be available and
updated on the PIVnet website: pivnet.sm.go.dlr.de.
1 Introduction
Interrogation algorithms for PIV images are becoming more complex and diverse.
Perhaps not more than five years ago, most algorithms were practically identical,
using a linear approach to the computation of the image spatial correlation and a
simple peak-detection and interpolation scheme. Nowadays, there exists a whole
spectrum of (non-linear) methods for computing the spatial correlation that include continuous, sub-pixel interpolation in the image domain, and advanced
techniques for the estimation of the displacement. Several questions arise in relation to these advanced algorithms. First of all, every developer of such new algorithms wishes to validate that the algorithm performs as expected and that the implemented algorithm is free of programming errors (viz., bug testing). At a more
academic level, one may be interested which of these methods and algorithms performs optimally as a function of various experimental parameters, like seeding
density, particle-image diameter, in-plane and out-of-plane loss-of-pairs, and the
magnitude of spatial velocity gradient. Also, at a very practical level, one would
like to evaluate whether a particular advanced algorithm yields advantages over
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simplified algorithms taking into account the increased computational costs. A
well-proven method for such investigations is the use of synthetic input data (for
which the true signal is known), and compare the results of the method against the
actual signal input. This approach was extensively used by Keane and Adrian
(1990, 1991, 1993) who used synthetic PIV images to determine optimal design
rules for the image density, in-plane and out-of-plane particle image displacement,
and maximal variation of the velocity field over the interrogation domain. Later,
Willert (1996) used synthetic PIV images to determine the precision as a function
of the dimensions of the interrogation domain and the particle-image diameter.
More recently, the Japanese Society for Visualization has provided a web-based
facility to generate standardized PIV images1.
One of the objectives of the EUROPIV-2 program was to investigate the optimal performance of PIV under various circumstances. For this purpose it was decided to develop a standard program for the generation of synthetic PIV images.
Previous work where synthetic PIV images were generated have in common that
they are typically designed for generating images from a planar (viz., 2D) object
domain. Hence, effects due to the finite thickness of the light sheet, and nonnormal observation angles (as encountered in stereoscopic PIV systems) were
generally not included in earlier work. In particular the extension towards synthetic PIV images for stereoscopic systems seems appropriate, as this configuration is more or less a standard one for commercial PIV systems.
This paper contains a description of the EUROPIV-2 Synthetic Image Generator, or SIG. It has been based on a collection of programs developed at the Laboratory for Aero and Hydrodynamics at the Delft University of Technology. These
programs have been integrated into a single standardized code (by using a standardized programming language and standardized image and data formats) and
extended to include stereoscopic imaging within this project. Elsewhere in this
publication can be found several publications where the SIG program was used for
evaluation, optimisation and testing of PIV algorithms (Lecordier et al. 2004,
Miliat et al. 2004, Petracci et al. 2004).
2 General Features
The main goal the SIG package is to provide to end-users a common tool to generate synthetic images of particles. The SIG program includes realistic physical
models with numerous adjustable parameters. The main features of the generator
are: (i) a fully customisable environment, being able to simulate 2D or 3D optical
set-up in details as laser sheet positioning in the test section, laser sheet thickness
and shape (rectangle and gaussian), optical path, object plane, image plane, CCD
parameters (pitch, noise…), and (ii) a full support for orthogonal and angularstereoscopic PIV configurations (see Figure 1). Thanks to the 3D optical model
and the finite thickness of the laser sheet crossing the virtual test section being
taken into account, the effect of out-of-plane motion and particle displacement
1
http://www.vsj.or.jp/piv/
PIV Accuracy 147
perpendicular to the light-sheet plane can be investigated as a function of the optical parameters (e.g., image magnification). The 3D optical model can also be used
to generate a stereoscopic calibration grid in order to validate different calibration
algorithms. The details of all the SIG models will be given in the subsequent sections.
2.1 Input files
To generate a single image, the SIG program needs two input files:
•
one file that contains the 2D or 3D coordinates of each particle in the
virtual test section;
•
a second file that contains all the parameters that control the image
generation.
From these two files, the SIG program generates two output files: the synthetic
image in either TIFF or RAW file format, and a log file with all the relevant information about the process. It should be mentioned that for reasons of flexibility,
the SIG program does not include the generation of the particle field itself; this
task has to be performed externally by means of another program of any kind,
which can generate successive particle fields with known particle displacement
(e.g., a simple translation, solid-body rotation, or a turbulent displacement field
computed by means of direct numerical simulation, or DNS).
The input particle file in ASCII format is row arranged (i.e., one particle per
line) and has four different formats:
• x y
(2D particle field without particle diameters)
(2D particle field with particle diameters)
• x y dp
• x y z
(3D particle field without particle diameters)
• x y z dp (3D particle field with particle diameters
where (x,y) and (x,y,z,) correspond to the 2D and 3D coordinates respectively of
particles in the virtual test section, and dp is the particle diameter. This last parameter is used to attribute different intensity levels I (i.e., I ∝ d p ) to each parti2
cle in the image, which can be useful when the program that produces the particle
fields takes into account the drag force on particle motion.
For the configuration file, the netcdf file format has been adopted (see:
http://www.unidata.ucar.edu/packages/netcdf/) in order facilitate file sharing between users without risk of file conversion problem. This format has already been
adopted in the previous EUROPIV project (Stanislas et al. 2000) and a version to
store PIV data is proposed in the present book (Willert 2004). A couple of details
on the configuration file parameters will be presented in the subsequent sections.
2.2 The sig package
The SIG program is part of the sig package. The complete sig package is divided
into four parts:
• A library (called libsig) containing all the useful functions to create
and manipulate images, particle fields, and I/O file manipulation;
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•
A main program (called sig), which is the user interface to generate
synthetic images from a configuration file and a particle file.
• A documentation file in HTML format;
• Examples of 2D and 3D particle field and associated configuration
files to generate examples of synthetic images.
The SIG package programs are mainly written in the ANSI C language which
can be compiled with any ANSI C compiler. The sig program makes use of typical
UNIX features, like input file and output file redirection and command-line arguments. (These features are also common for the MS-DOS operating system.) As a
consequence, the simplest way to run the sig program is to use any UNIX-like operating system, such as Linux. Without any modification to the source code, an
alternative way to use it within a Windows operating system is to install
a Unix layer providing substantial UNIX API functionalities on a Win32 operating
system (see: http://www.cygwin.com/). In such a case, Unix and Windows programs can be run simultaneously, and data (images and particle fields) can be
shared between operating systems.
The remainder of this paper will describe the different models used in the SIG
program, the details being presented in the SIG documentation provided in the
SIG package. The last part of the paper will shortly present two applications of the
SIG program.
Fig. 1 Orthogonal and stereoscopic projection model of the synthetic image generator.
PIV Accuracy 149
3 Geometrical and Optical Configurations
The SIG package simulates orthogonal and angular stereoscopic configurations
(see Figure 1). The parameter file contains all the geometric information about the
image (di) and object (do) distances, the CCD dimensions, the volume of the virtual test section, and the angles of projection. All the dimensions are specified in
the same unit, called “real unit”, and they must have the same ratio between them
then in a real optical configuration. The light sheet location and thickness are defined with the same unit, and crosses the test section in the object plane. All the
particles included in the light sheet are imaged on the image plane where the CCD
is located. The (x,y) and (X,Y) coordinates correspond to the coordinates in the
image and object domains respectively. The z and Z coordinates correspond to the
coordinate perpendicular to the image and object planes respectively (see Figure
1).
z
Lens 2
Light sheet
Z
X
di2
d02
Light sheet
α2 < 0
Y
Z
X
α1 > 0
d01
Lens
θ1 > 0
di
y
di1
Y
Light sheet
Z
X
d01
α1 < 0
d02
θ1 < 0
α2 > 0
θ2 > 0
x
CCD 1
z
y
di2
di1
Lens 1
x CCD 1
z
y
Lens 1
x
z
z
CCD 2
θ2 > 0
d0
CCD
x
Y
y
Lens 2
y
x
z CCD 2
Fig. 2 Example of different optical configuration simulated by the SIG.
The SIG program can simulate three different optical configurations (see Fig. 2):
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•
•
•
Simple orthogonal projection without effect of the Z particle displacement on the particle image;
Orthogonal projection which takes into account depth effects to include
the influence of the Z particle motion on the in-plane velocity measurement;
Angular stereoscopic projection;
The full description of the projection model will be done in a subsequent section.
4 The Configuration File
The configuration file is one of the two input files that are required to generate
synthetic images. It contains all the parameters used for the control of the SIG
physical models (e.g., for the CCD, the laser sheet, and the dimensions of the virtual test section). As mentioned before, this file complies with the netcdf format,
which makes file sharing between researchers and different computer platforms
easier. The file is divided in 6 parts, and each part contains several editable fields
(see Table 1). The description of each editable field is given in the documentation
of the SIG package. The last column of the configuration file gives a short description of the field data and also the unit in which the data is represented (e.g.,
real, unit, real/unit, etc.), and in some cases the range of the data.
Table 1. Main parameters of the configuration files of the SIG program
Image dimension and dimension of particle field
p_dimX
= 512
p_dimY
= 512
r_xmin
= 0.0
r_xmax
= 1.0
r_ymin
= 0.0
r_ymax
= 1.0
r_zmin
= 0.0
r_zmax
= 1.0
light sheet information
lsheet_type
= "uniform"
lsheet_rpos_z
lsheet_rthickness
Particle information
part_distribution
part_min_diam
part_max_diam
part_mean_diam
part_std_diam
Pattern_type
Pattern_meanx
Pattern_meany
= 0.5
= 0.02
=
=
=
=
=
=
=
=
"uniform"
0.1
4.0
1.0
0.2
"gaussian"
2.0
2.0
Image width (pixel)
Image height (pixel)
r_xmin (real)
r_xmax (real)
r_ymin (real)
r_ymax (real)
r_zmin (real)
r_zmax (real)
uniform, gaussian, triangle,
cosine and squarecosine
light sheet position (unit:real)
light sheet thickness (unit:real)
uniform, gaussian
gaussian, circle rectangle
Pixel
Pixel
PIV Accuracy 151
Projection information and optic information
Projection_type
= "normal"
Projection_angle
= 45
Projection_tilt_angle
= 16.699
optic_object_distance
= 1000
optic_image_distance
= 100
optic_magnification
= 0.1
CCD Information
ccd_fill_ratio_x
= 0.75
ccd_fill_ratio_y
= 0.75
ccd_saturation_level
= 1.00
ccd_background_type
= “uniform”
ccd_background_mean_level
= 0.0
ccd_background_std_noise
= 0.0
ccd_pixel_horizontal_pitch
= 156250.0
ccd_pixel_vertical_pitch
= 156250.0
seed for the random generator
Seed_number1
= 1
Seed_number2
= 100
Seed_number3
= 10000
normal, angular
angle of view
tilt angle
Object Distance d0 (real)
Image Distance di (real)
di/d0
[0.0;1.0]
[0.0;1.0]
[0.0;1.0]
uniform, gaussian
grey level
grey level
(pixel/real)
(pixel/real)
5 Internal Models in the SIG Package
5.1 Laser sheet model
The shape of the light sheet can be chosen from 5 different types: "uniform",
"gaussian", "triangle", "cosine" and "squarecosine". Only the
first two types are of interest for practical purposes; the other types can be used for
theoretical purposes only to investigate the relation between the in-plane loss-ofpairs FO and the shape of the light-sheet profile. The position of the light sheet in
the test section is specified by: lsheet_rpos_z, in real units. In many situations the light sheets can be considered to be (nearly) homogeneous in the in-plane
coordinates (i.e., x and y), and therefore only the z coordinate needs to be specified. A variation of the z coordinate of the light sheet can be useful in simulating
multi-plane PIV images (Raffel et al. 1996). The thickness of the light sheet in the
simulation domain is defined by the parameter lsheet_rthickness in real
units. For a Gaussian profile the thickness is defined as the e-2 width of the profile.
5.2 Optical projection model
In the SIG program is implemented a simple pinhole projection model which links
the particle coordinates (X,Y,Z) in the object domain to the particle-image coordinates (x,y) in the image (viz., CCD) plane. Thus, the optical projection model is
aberration-free, but it will be quite simple to add any aberration model in the pro-
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jection module. The projection model in the case of an angular stereoscopic configuration is given by:
pi cos(α)−ri sin(α)−d i sin(α)

 x =di sin(α)+ pi sin(α)+ri cos(α)+d i cos(α)

qidi cos(α)
 y=
sin(
)
+
p
α
ri cos(α)+d i cos(α)

i
(1)
 pi = X cos(θ)−Z sin(θ)
qi =Y
ri = X sin(θ)+ Z cos(θ)−(d0 +di)
(2)
with:
where the angles θ and α are the optical angle of the camera axis and the tilt angle
of the CCD, respectively. The sign convention for the angles is shown in Figure 2.
In the case of orthogonal projection: θ = 0 and α = 0, and the projection equations are simplified to:
 x = Xd i
 Z −d 0

Yd i
 y = Z −d 0
(3)
From this model, the Z coordinate of the particle is still involved, and so it is
possible to study the influence of the particle displacement along Z on the in-plane
velocity components. In Figure 3, the effect of a uniform Z particle displacement
of –100 µm (top fields) and 100 µm (bottom fields) on the in-plane velocity measurement is simulated for different optical magnifications. As observed under real
experimental conditions, for high magnification factor, the Z particle displacements have significant effect on the (u,v) velocity measurement (Lourenço 1988).
For an image magnification factor close to unity, a uniform Z particle displacement of 100 µm induces in-plane displacements larger than 0.5 pixel. On the other
hand, when the image magnification is close to 0.1 (as in numerous PIV experiments) the effect of Z particle displacement becomes negligible compared to other
bias sources.
The last projection model of the SIG program is based on the previous orthogonal projection model (3), but it does not include any effects due to motion in
the direction of the Z coordinate. This model considers all the particles of the test
section as if they would be located in the median plane of the laser light sheet (Z =
0). This simple orthogonal projection model is then given by:
PIV Accuracy 153
M0=1
di=100 mm
d0=100 mm
M0=0.5
di=100 mm
d0=500 mm
M0=0.1
di=50 mm
d0=500 mm
M0=0.1
di=100 mm
d0=1000 mm
u’=0.3 pixel
|u|max=0.54 pixel
u’=0.15 pixel
|u|max=0.29 pixel
u’=0.06 pixel
|u|max=0.15 pixel
u’=0.03 pixel
|u|max=0.10 pixel
Fig. 3 Effect of uniform Z particle displacement of –100 µm (top) and 100 µm (bottom) on
the in-plane velocity measurement for different optical magnification factors.
 x = − Xd i

 −dYd0 i
 y = d 0
(4)
5.3 Intensity distribution of particle image and CCD model
The optical model is used to locate the particle coordinates on the image plane
(CCD), which also corresponds to the maximum of the intensity distribution of
each particle. In the SIG package, we have adopted a 2D Gaussian curve to simulate the intensity distribution. This approximation of first order is close to the Airy
function given by the Fraunhofer diffraction theory of a monochromatic spot
through a circular lens. This approximation is accurate as long as the dimension of
the particle in the test section is small compared to the impulse response of the
optical system as is generally the case. (A typical diameter for tracer particles in
air, e.g. oil droplets, is 1-2 µm, and in water, e.g. hollow-glass spheres, is 8-20 µm;
at 0.1 magnification, 500 nm wavelength and an f# = 4 aperture stop the diffraction-limit spot diameter is larger than the geometric particle-image diameter in
both cases.) For each particle in the test section, a 2D intensity distribution is projected onto the CCD plane (see Figure 4). The width of the 2D gaussian intensity
distribution is defined by two parameters in the configuration file: σpx (pattern_meanx) and σpy (pattern_meany), which are constant over the whole image
154 Session 3
plane. This implicitly assumes a high-quality aberration-free lens. Most high-end
optical lens systems for 35 mm photography meet these requirements over the
typical area of a CCD sensor near the optical axis. The use of two parameters in
orthogonal directions makes it possible to consider non-square (viz., rectangular)
pixel geometries. It should also be mentioned that this model does not include a
motion blur of the particle image. This condition is usually met for contemporary
PIV systems where the illumination source is a twin pulsed Nd:YAG laser with a
less than 10-ns pulse duration.
The CCD is composed of pixels regularly distributed over the surface and it is
located in the image plane. In the SIG, the CCD resolution can reach up to 4k×4k
pixels with different pitch values along the x and y directions. In addition, to
simulate the effect of the limited fill ratio of a CCD, two numbers frx
(ccd_fill_ratio_x) and fry (ccd_fill_ratio_y), varying in a range between 0.0 and 1.0,
indicate the ratio of the sensitive area of 1 pixel to the pixel pitch. The intensity
level of each pixel is then obtained by a 2D integration of the Gaussian intensity
distribution over the sensitive part of the CCD (see Figure 4):
frx
2
frx
xi −
2
I(xi; yi)∝d p2∫
xi +
2
2

 yi + fry 
y− y p  
dy
exp − 1  x− xp  dx∫ fr2y exp − 1 
2 σ py  
 2  σ px   yi− 2
 

(5)
This expression can be re-written in terms of error functions, which are standard
functions in the C math library :
I ( xi ; y i ) ∝
π
8
d p2σ pxσ py ×

 x − x p + 12 frx 
 x − x p − 12 frx
 − erf 
 σ px 2

 σ px 2




 ×


 y − y p + 12 fr y 
 y − y p − 12 fr y
 − erf 


 σ py 2
σ py 2







×  erf 


×  erf 

(6)
Hence, the determination of the intensity grey values does not require integration. It should be mentioned that up to now, the CCD model considers the particles
as independent scattering sites, and the final intensity level of a single pixel results
from the superposition (viz., summation) of all the contributions of particles. This
principally assumes that the scattered light is incoherent. Because the light source
in most PIV systems is a (pulsed) laser (viz., coherent light source), a more realistic model would be based on the complex amplitude of the scattered light in order
to perform the summation in the spectral domain, and so take into account interference phenomena. This would only be required when the density of the particle
images becomes so high that the source density, defined as the number density
of particle images per unit area multiplied by the area of a single particle image,
PIV Accuracy 155
becomes close to unity (Adrian and Yao 1985). Without this advanced scattering
model, the SIG program is not adapted to speckle phenomena investigations, but
in most practical applications the speckle limit is never reached. However, one
must be careful not to increase the number of tracer particles in the virtual measurement volume without validating that one is still operating the program below
the speckle limit. For example, a synthetic PIV image of 1k×1k-pixels that contains 105 particle images with a 2-pixel diameter, has a source density of 0.3; this
value is already very close to the speckle limit (i.e., 30% of the particle images
overlap), and interference effects start to become significant. The user can find the
number of particle-images actually generated to determine the source density in
the log file generated by the SIG program.
Fig. 4 Integration model of the particle intensity distribution over a limited sensitive area
of the CCD sensor.
One important parameter when synthetic images of particles are produced is to
estimate the effective size of the particle image. This is an important parameter in
relation to the occurrence of so-called “peak-locking”. Eq. 5 clearly shows that the
final size of the particle on the images results from the combined effects of the
width of the intensity distribution (σpx and σpy) and the fill ratio value (frx and fry) of
the CCD. Figure 5 gives the theoretical variation of particle image width (defined
as the Imax/2 width of the intensity of a particle image) for different CCD fill ratios
and intensity distribution widths. For large values of the intensity distribution (σpx
and σpy), the fill ratio parameter becomes negligible, and the image particle width
depends only of the σp parameter and tends toward: 2 ln 2σ p , i.e. the width of a
Gaussian distribution. A similar behaviour is observed for very small values of the
fill ratio. This behaviour can be generalized for a ratio σ p f r larger than 2. For
smaller values, the width depends both on the σp and fr parameters.
Other additional features have been added to the CCD model. For instance, a
CCD background noise can be added either with a uniform level or random levels
with Gaussian distribution. A saturation level parameter in the configuration file
can also be adjusted to set the gain of the CCD.
156 Session 3
Fig. 5 Theoretical image particle diameter defined as Imax/2 width of the intensity of particle
image versus the CCD fill ratio (fr) and the width of the intensity distribution of particle
(σx).
5.4 Particle distribution
As shown in the previous section, the size of the particle image results from the
combined effects of CCD fill ratio and particle pattern width. This model is still
valid as long as the particle diameter is smaller than the dimensions of the impulse
response of the optical system. In many applications, especially for PIV measurements in gas (viz., air) flows, these experimental conditions are generally met.
Nevertheless, the maximum intensity level of the particle is roughly proportional
to the square of the diameter dp (Adrian and Yao 1985), so a slight variation of the
particle diameter can affect the maximum intensity level even if the particle image
size is constant. In order to simulate this effect, within the limits of the previous
model, a “pseudo particle diameter” can be attributed to each particle. The standard particle diameter is equal to unity and in this case the intensity level only depends on the particle positioning in the laser sheet. In the configuration file, the
particle diameter distribution can be chosen from 2 different types: “uniform”,
“gaussian”.
For uniform distribution, all the particles have the same diameter equal to
“part_mean_diam” (default 1.0). The “part_std_diam” parameter in the configuration allows to adjust the width of the particle diameter distribution for the
“gaussian” model. In addition, to avoid particle diameters that become impractically small or large, the particle diameter distribution can be bounded by two fixed
PIV Accuracy 157
values. The particle diameter can also be indicated in the third (2D file) and fourth
(3D file) row of the particle coordinate file. In this case, the particle diameter distribution is defined externally to the SIG program. This feature is very useful in
the case of a particle field produced by means of a simulation taking into account
the particle drag forces. In such a case, the biggest particles have higher intensity
levels than the smaller particles, but also tend to have a larger lag with respect to
the fluid velocity; this introduces a bias on the PIV measurements. With this feature the contribution to the velocity measurement can be investigated in terms of
particle size.
Fig. 6 Synthetic Images of particle generated from the same particle field with different
particle information (σpx and σpy).
5.5 Additional and useful features
For each generated image, an output file (log file) containing relevant statistical
information about the image is saved. In Table 2, an example of output file is presented. The first part of the file contains information about the particle field and
the particle image density. The second part gives statistical information about grey
level distribution in image. They are useful to check for instance the fraction of
saturated pixel. The third part of the file deals with statistical information linked to
the particles used to generate the image: mean light sheet level, mean particle diameter…
This file contains very useful information to accurately adjust the SIG parameter
(ex: CCD saturation level). In addition, at the end of the output file, the configuration file is copied to always keep track of the image generation process.
The particle coordinates in the image can also be saved in order to know their exact location. This feature is very useful to validate and compare different particle
tracking techniques. In addition to particle locations in the image and object
planes (in pixel and real unit respectively), the file contains different local information for each particle such as light sheet intensity and particle image size.
158 Session 3
Table 2. Main information of the SIG output file
Information about particle file
3200000
Number of particles read
25557
Number of particles used to create image
7.99e-01
Percentage of particles used to create image
2.44e-02
Particle density in the image (part/pixel^2)
6.24
Number of particles in a window of 16x16 pixels
24.96
Number of particles in a window of 32x32 pixels
99.83
Number of particles in a window of 64x64 pixels
0
Maximum X particle location in pixel
1023
Maximum X particle location in pixel
0
Minimum Y particle location in pixel
1023
Maximum Y particle location in pixel
2.007e-07
Minimum X particle location in real space
1.000e-01
Maximum X particle location in real space
3.477e-07
Minimum Y particle location in real space
1.000e-01
Maximum Y particle location in real space
4.960e-02
Maximum Z particle location in real space
5.040e-02
Maximum Z particle location in real space
8.000e-06
Volume of the particle in the real space (real^3)
Image Information
1
Minimum grey level in the image
255
Maximum grey level in the image
26.1
Mean grey level of the image
25.9
Std grey level of the image
12
Number of saturated pixels
1.14e-03
Percentage of saturated pixels
1.00
Minimum value of the background noise
5.00
Maximum value of the background noise
3.00
Mean value of the background noise
0.57
Std of the background noise
951501
Number of modified pixels during particle addition
90.742
Percentage of modified pixels during particle addition
Light sheet and particle information
0.1353
Minimum sheet level for the particles
1.0000
Maximum sheet level for the particles
0.5984
Mean sheet level for the particles
0.2885
Std sheet level for the particles
0.1312
Minimum particle diameter
1.9371
Maximum particle diameter
1.0004
Mean particle diameter
0.2003
Std particle diameter
0.13
Minimum particle level
222.46
Maximum particle level
35.44
Mean particle level
23.74
Std particle level
For different features, such as background noise addition, the SIG program
calls a random number generator. In the standard use of the SIG, the random generator is initialised with 3 integers deduced from the internal clock of the computer, and so the same particle field can produce slightly different images. To dis-
PIV Accuracy 159
able this feature, 3 numbers, different from zero and used to seed the random generator, can be set in the configuration file. In such a case, successive calls to the
SIG program with the same particle fields and configuration file produce identical
images, and that whatever the computer used. This feature is very convenient
when an analysis by means of the SIG is performed by different partners.
6 Application of SIG Program
In the framework of the EUROPIV II project, the S.I.G has been extensively used
to evaluate the individual effect of various experimental parameters (seeding concentration, size of particle…) on the accuracy of PIV evaluation techniques. For
instance, Fig. 6 shows two examples of synthetic images generated from the same
particle fields but with different σpx and σpy parameters. From these images, the effect of the ‘peak-locking” on the accuracy of the PIV evaluation was studied
(Miliat et al. 2004, Lecordier et al. 2004). The SIG program has also been used to
evaluate and compare the potential and intrinsic limitations of different PIV
evaluation algorithms to measure turbulence statistics and properties (like the
mean velocity field, the mean turbulent fluctuation level, and the turbulent power
spectrum) from PIV records (Lecordier et al. 2004). Another original application
of the SIG is presented by Petracci et al. (2004). In this case the SIG was implemented to mimic the angular stereoscopic PIV set-up for a turbulent pipe flow
used by Van Doorne et al. (2004). The SIG was used to validate the errors that occur as a result of a misalignment between the light sheet and the stereoscopic calibration target, as was found in the actual experimental situation. This demonstrates the usefulness of the SIG to identify and evaluate potential sources of error
prior to the actual experiment.
7 Conclusions
In this paper the main features of a new synthetic image generator, or SIG, are described. The main purpose was to have a common and standardized manner of
generating synthetic PIV images for investigating the performance of PIV as a
function of various optical and experimental parameters (e.g., particle image density and particle image diameter). Great care was dedicated to generate the particle
images in a proper manner, and to provide feedback to the user with regard to the
image properties (viz., image density and source density). The SIG can be used to
compare the performance of different PIV interrogation algorithms. The main advantage of the standardization is that different researchers can use it independently, but can still generate identical synthetic image fields in large numbers. This
implies that different algorithms used by different users can be easily tested using
identical input images. In addition, the PIV performance can be tested in a statistical fashion. The SIG also has the capability of generating synthetic image sets for
various stereoscopic PIV configurations. We expect this is a very useful addition,
as stereoscopic PIV has become a default commercial configuration. The SIG can
be a useful tool for estimating the error levels that can be expected in a given con-
160 Session 3
figuration as a function of the experimental parameters, as is demonstrated in a
couple of accompanying papers elsewhere in this book. It is relatively easy to extend the capabilities of the SIG program, for example by adding codes for the particle displacements. This can be a simple translation, but one can also use a direct
numerical simulation (DNS) to obtain realistic velocity fields and particle dynamics. This can be used to investigate effects that are often neglected, like two-phase
flow effects in PIV measurements. In the current SIG program a relatively simple
optical model is used; future releases might include coherent illumination (viz.,
speckle effects) and an imaging model that also includes out-of-focus imaging.
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Acknowledgements
We acknowlege the participation of José Nogueira, from Madrid University, at the beginning of this work during a nice workshop in Delft.
This work has been performed under the EUROPIV2 project. EUROPIV2 (A joint program
to improve PIV performance for industry and research) is a collaboration between LML
URA CNRS 1441, DASSAULT AVIATION, DASA, ITAP, CIRA, DLR, ISL, NLR,
ONERA and the universities of Delft, Madrid, Oldenburg, Rome, Rouen (CORIA URA
CNRS 230), St Etienne (TSI URA CNRS 842), Zaragoza. The project is managed by LML
URA CNRS 1441 and is funded by the European Union within the 5th framework (Contract N°: G4RD-CT-2000-00190).