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

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2.3 Registration of the particle images
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Intensity
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Intensity
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FIGURE 2.10: Gaussian intensity distribution of a particle image (solid line) and its discrete representation
as a function of the fill-factor, pixel response and sampling location (upper left to lower right).
The dashed lines within the Gaussian distribution indicate the collected intensity calculated for the unbiased
signal as a function of the linear pixel dimension and the long-dashed dotted line the modified
intensity value (integration over the dotted graphs).
Gaussian intensity distribution is not symmetric relative to the interface between two adjacent
pixels, as shown in the two lower and the upper right graphs of figure 2.10, the unbiased signal
increases continously from 0.48 to 0.68, in the example, until the centre of the pixel coincides
with the maximum of the Gaussian curve (lower left graphs). Under these conditions the greyvalues
of the measured intensity is again completely symmetric with respect to the continuous
distribution so that the exact location of the original function is identical with the discrete
sample. To examine the behaviour of a small fill-ratio sensor, the intensity of the dashed and
dashed dotted graphs can be compared at a particular sub-pixel location. A comparison indicates
the minor importance of this parameter as long as the particle image size covers on
average three pixels in each spatial direction. Under these circumstances the measurement
precision may be reduced as the differences between neighbouring pixel-intensities decrease
while the influence of any superimposed noise increases, but this can be compensated by using
the appropriate components for the experiment. If the particle image size is in the range of
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