We first need to set the elementary box sizes
and
(in pixels) in which correlations will be calculated along each direction
and
. To estimate the minimum value required for
these parameters, open an image (see section 3.6),
and look at the minimum size of a square which always contains at
least 5 particles. In practice a value of
and
between 21 and 31 is chosen. Larger values lead to lower spatial resolution:
the velocity obtained is an average in this elementary box. In addition,
the actual motion is a pure translation only in a local limit: deformation
effect increases in proportion with the box size, leading to deterioration
in the quality of the correlation (see section 3.5
for a discussion of this effect).
For a seeding with particles at a uniform mean density
(in particles per pixel), the probability of finding n point particles
in a rectangle
is the Poisson distribution
,
where
is the mean particle number
in the square. For
=0.05 and
=21,
we have
=20. Then the Poisson distribution gives a total
probability 1.6 10
to get n< 5 particles. For a twice lower
density,
=10, this probability rises to 2.9 %, resulting
in a significant number of false vectors(3.3)
(even for a uniform seeding). We need then to use a larger box, or
increase the particle density. Choosing different values of
and
is justified for rectangular pixels (e.g. with the
Pulnix camera) or in the presence of a strong shear. For instance
in a boundary layer, we can reduce the size transverse to the wall
and increase the streamwise size.