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

4.7 Monochromatic aberrations
reflected ghost-images superimposed on the desired image result in a reduced signal-to-noise
ratio accompanied by a lower correlation coefficient. To solve this problem, the time separation
method can be applied as long as the separation between the first orthogonal polarised
light pulse pair is negligible, e.g. the position of the particle image remains constant in terms of
digital registration. In this case, which holds for a wide range of flow velocities, a difference
between instantaneous and time separated measurements cannot be observed. Technologically,
this can be done by transferring the first image right behind the first illumination.
4.7 Monochromatic aberrations
Before the light scattered by the particles can be recorded it interacts partially with optical
elements like glass-window, mirror, beam-splitter and various lenses in order to alter the orientation
of the field, to separate the incoming light according to the state of polarisation and
to generate an image of the tracer particles. Beside a possible loss of light due to absorption
or reflection, these components introduce aberrations of different type, direction and magnitude
which may limit the measurement accuracy [8]. Although it is impossible to eliminate
all aberrations completely in any real system of finite aperture, a basic understanding of their
origin and dependence from optical parameters is the key to reduce these undesirable effects
under the resolution of the recording medium or to eliminate certain aberrations completely
by accepting aberrations of other types which are of no harm in PIV. The last point is of primary
importance because higher order aberrations like distortion 1 and curvature of the field
just influence the position and form of the image but do not lower the resolution. They can be
completely eliminated by calculations according to section 2.4 and do not need to be considered
here. Primary aberrations on the other hand like spherical aberration, coma and especially
astigmatism deteriorate the image and alter the shape in a characteristic way. This leads to an
increased measurement error as the performance of the peak-fit for sub-pixel accuracy strongly
decreases for particle image diameter not equal 2-3 pixel. Before the optical aberrations can be
reduced or eliminated, they have to be identified first. Using the PIV equipment this is easily
possible as higher order aberrations become clearly visible by analysing the image of a regular
grid, according to section 3.2, whereas the main primary aberrations can be easily observed
by examination the image-symmetry of small particles within a thin light-sheet. For
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three
different field-coordinates figure 4.9 shows the images of olive-oil Ÿ è
droplets, with m,
through a tilted BK7 glass-plate of constant thickness (10 mm). The most striking feature is
the variation of the magnitude and direction of the dominant aberration by probing continually
through focus and across the field of view.
When the optical system is perfectly aligned and the aberrations are below digital registration,
the diffraction limited image of a particle appears as a bright circular core surrounded
by several rings of rapidly diminishing brightness. This is shown in the central column of
figure 4.9 but the small variations of the intensity distribution are smeared out by the low resolution
of the used CCD sensor. As the object moves further off-axis, the diffraction limited
particle image pattern alters from a bright central area surrounded by dark and bright rings to
a dark central area surrounded by bright and dark rings as shown in the lower image. On the
other hand, particles, located an appreciable distance apart from the optical axis deform into a
line of certain orientation due to the tilted glass-window, see outer image pair of top row. By
1 Distortion occurs when off-axis points are not formed at the location predicted by the paraxial equations.
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