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

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4 Multiplane Stereo Particle Image Velocimetry
FIGURE 4.9: Images of tracer particles (¢ ›£¤ m) observed through a tilted glass-plate (BK7) of
constant thickness 10 mm for three field locations as a function of the focus. The lines of constant
intensity (isophote) are circular near the centre of the field but have a more complex form in the outer
part of the image. The size of each sample is 128 pixelî .
changing the focus this line becomes elliptical and out-of-focus effects start to occur like the
decreased brightness and the intensity gap in the centre of the particle-image, compare outer
image pairs of figure 4.9.
The mentioned deformation is the main aberration the experimentalist has to deal with
in praxis. It appears already when a non-collimated light-front enters or passes planar optical
elements of different index of refraction, such as glass windows which separate the test-section
from the laboratory, and it becomes even more pronounced for curved interfaces like lenses
[6]. Although a detailed analysis of aberrations requires the theory of diffraction in order to
account for the intensity distribution, the main features become evident by using the principles
of geometrical optics which identify the image by the points of intersection of the geometrical
rays with the image plane. Using this approximation, the starting point of this consideration
is the law of refraction ZCç]ê|ë2¥]¦ŽçÙèsZmîgê|ë2¥§¦0î
which describes the direction of a light ray after
diffraction at the planar interface between two homogeneous, isotropic media of differing
index of refraction. To obtain the image position n of an object located on the optical axis
at ¨ , this law has to be applied for each ray emerging from this point. Using the relations
¦Žç è©«ª ç and ¦0î è¬]ªCî according to figure 4.10, the following formula can be derived.
Zmî ¨
(4.7)
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