The significance of coherent flow structures for the turbulent mixing ...

3.2 Evaluation of stereo-scopic image pairs
distortions can be hardly avoided and systematic errors appear as indicated in figure 3.7. The
so called de-sampling method yield better results, provided each pixel is subdivided in at least
four sub-pixel or the bilinear interpolation where the grey levels of the four nearest integral
neighbours of a non integral coordinate are consulted to determine the appropriate value. More
sophisticated approaches like fitting a ¬v®pâäã¡åÀã type surface through a much larger number of
neighbours (cubic convolution interpolation method) yield much smoother results but at the
cost of computational time. For this reason the bilinear approach was applied for the analysis
of the results shown in chapter 5 to 7.
3.2.3 Vector field warping
As the proper de-warping in the image space is time consuming and requires a redistribution
of the original images, which does not increase confidence 4 , the de-warping can be performed
in the vector space as soon as the conventional line-by-line interrogation procedure has been
applied. Using this approach the equally spaced grid points in the object space are transformed
into the image space according to the transformation equations (3.6) and (3.7), and the velocity
at each image grid point is calculated by means of linear interpolation. In order to minimise or
avoid the interpolation procedure, the acquired images can either be evaluated with a smaller
step-size or interrogated at the proper positions given by the grid points in the object space.
The inherent drawback of this approach is the fact that the magnification factor varies over
the field of view as well as the measurement error and the detectability [51, 52]. Furthermore,
if the camera system is symmetrical and located on one side of the light-sheet (left image
in figure 3.4), the interrogation windows from each of a pair of stereoscopic images backprojection
in the physical space may differ substantially in size, which means that in effect
different flow volumes are considered for the calculation of the third velocity component 5 .
The significance of this statement will be considered in the section 3.3. For applications in
large wind tunnels the problem is further increased due to unequal object distances or nonsymmetric
stereoscopic PIV set-ups.
3.2.4 Interrogation window warping
In order to avoid any modification of the measured grey-level distribution itself and to be
independent of interpolation algorithms in the vector space, an alternative approach can be
implemented based on a local distortion of the size and shape of the interrogation window
in such a way that the number of particle images remains constant over the field of view
and the shape varies in a way that the back-projection of the local interrogation areas into
the object space is always the best approximation to a square or other desired shapes 6 . This
can be easily done either by calculating a direct correlation, which is not restricted to radix-2
sized interrogation window dimensions with rectangular shape as the conventional FFT-based
4 An initially circular particle image for example may appear elliptically after the transformation has been performed.
This artifact can bias or lower the principal measurement accuracy.
5 In the case of a symmetrical setup with a light-sheet between the two cameras (dashed configuration in figure
3.2 and right image in figure 3.4) the fluid elements considered for the calculation of the third velocity
component are equal in size but the spatial resolution remains a function of the image location.
6 The information concerning the position, size and shape of the interrogation window is known from the calibration
grid analysis simply by substituting all desired values of the object plane into the equations and using
a nearest neighbour approach to find the appropriate position in the image plane.
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