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

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2.4 Particle image analysis
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Equation (2.6) states that the amplitude of the cross-correlation peak increases with increasing
image density and decreases with increasing displacement, no matter in which
direction or if the displacement of the particle images is not constant. In order to optimise
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the performance of the experiment, the number of paired particle images is of primary = importance
as only these add to the signal strength. In addition the number of correct pairings with
respect to incorrect combinations has to be optimised for increasing the signal-to-noise ratio
and thus the detectability of the signal. This can be achieved either by changing the seeding
concentration, the magnification of the imaging system or simply by increasing the light-sheet
thickness, see equation (2.7). In-plane loss-of-pairs, caused by particles entering or leaving
the measurement volume during the illuminations, due to the motion of the fluid, can be reduced
by decreasing eliminated when the search window contains the corresponding
particle image pattern selected with the template. This can be achieved either by correlating
differently sized samples as described before or by using window-shifting in connection with
multi-pass interrogation techniques [106, 109]. Using this approach two equally sized samples,
separated by the local particle image shift are cross-correlated after the local shift has
been determined within a first evaluation. Since the correlation windows are symmetrically
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shifted with respect to each other and relative to the exact measurement position, it becomes
necessary to determine where the footprint of the vector should be located (centre or corner).
This is especially important when different evaluation methods are compared because the particle
pattern employed for the evaluation may be different for the same pixel coordinates of
the displacement vector [97]. Out-of-plane loss-of-pairs can be compensated by shifting the
light-sheet in the direction of the mean particle displacement, as proposed in [52], or by using
multi-light-sheet arrangements when the out-of-plane motion is not uniform, see chapter 4.
The effect of in-plane gradients can be reduced by increasing the magnification of the imaging
system, by decreasing the time-separation between the two illuminations or by using properly
shaped interrogation windows whose linear dimension is reduced in the direction of the
gradient.
2.4.2 Signal-peak detection and displacement determination
In order to increase the accuracy in determining the location of the displacement peak from
pixel to sub-pixel accuracy, an analytical function is fitted to the highest correlation peak
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by using the adjacent correlation values [109]. Usually two one-dimensional Gaussian fits
along the two coordinates through the highest correlation coefficient are applied. The motivation
for this particular function is based on the fact that under ideal imaging conditions the
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