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

4 Multiplane Stereo Particle Image Velocimetry
regard to the lens than the sagittal rays and they have a shorter focal length. This results in a
significant change in symmetry as a function of the image distance. The initially circular cross
section of the beam, emerging from the lens, becomes elliptically with the major axis in the
sagittal plane and degenerates into a line (primary image) at the tangential or meridional focus.
Beyond this point the beam cross-section rapidly expands until it is again circular (circle of
least confusion). Moving further away from the lens the beam cross-section again deforms
into a line (secondary image) while the orientation of this line is rotated by ½¿¾À relative to the
primary image. This behaviour is similar to that shown in figure 4.9 and can be studied best
by probing throughout the focus while observing non-axial particle images.
Aberrations introduced by means of the optical components within the laser, as the frequency
doubler crystal or for the generation of the light-sheet, are more difficult to observe
but of similar importance for PIV. Both systems have to be carefully aligned in order to obtain
the best possible signal in the image-plane as information loss in this stage cannot be reconstructed,
especially not by software solutions. The first testing procedure on any lens, after it
FIGURE 4.12: Top row: Intensity distribution of a Nd:YAG beam behind a tilted converging lens for
three different angles of rotation. Bottom row: dependence of the light-sheet profile on the magnitude
and direction of the aberration.
has been set up in the light-sheet-optics, is to rotate the optical elements about their own axis
while examining the image. If there should be any de-centreing or tilt, lateral asymmetries in
the point image will appear to rotate with the lens. This is shown in the top row of figure 4.12
for three different angles of rotation. The bottom row of the same figure reveals the same
operation, but a fixed cylindrical lens was placed behind the rotating lens in order to highlight
the direct dependence of the light-sheet profile from the magnitude and direction of the
aberration. Generating an extremely thin light-sheet, which is necessary for high resolution
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