Geoscience Reference
In-Depth Information
As shown in Fig.
11
, errors (noise, actually) may be caused by particles leaving the
interrogation area or arriving to the interrogation area in the interval between the
laser pulses,
Dt
. These particles will have no pair and will reduce the correlation
peak. Several techniques are employed to mitigate the effects of loss-of-pairs.
Figure
12
shows a flow chart with the sequence of processes necessary to find the
mean planar displacements and, thus, the velocity vector in each interrogation area.
The key aspect is the cross-correlation algorithm between each two consecutive
images (Westerweel
1993
). Before the correlation algorithm is applied the optional
step of windowing may be carried out. This is basically a selection of a subarea in
the core of the interrogation area, leaving out, for instance, 10% of the area adjacent
to the borders, to limit in-plane loss-of-pairs.
Windowing will have no effect on errors committed because of out-of-plane
loss-of-pairs, i.e., particles that, at any position, will leave the laser sheet because of
3D motion. If out-of-plane is dominant relatively to in-plane loss-of-pairs, window-
ing is not recommended. Obviously, both types of loss-of-pairs can be minimized
by a selection of a shorter time between pulses
Dt
.
Correlation-based algorithms actually compare gray levels of consecutive
images in a given interrogation area and surrounding area. The result of a correla-
tion analysis is seen in Fig.
13
. Evidently, the better contrast between the illumi-
nated particles and the background, the less noisy becomes the signal, i.e., the
smaller the secondary peaks. Common algorithms comprise simple cross-correlation
and adaptative correlation. In the latter case, a large interrogation area is employed
first and subjected to simple cross-correlation. The correlation peak is then used to
re-center (offset) a smaller interrogation, again subjected to correlation. The pro-
cess can continue while there is enough illuminated seeding particles. This tech-
nique is now standard and is especially useful when flow gradients are large. The
first steps determine the direction of the flow, and the last step finds the correct
displacements even with few illuminated particles in the interrogation area.
At each step in the correlation process, filters may be applied to reduce noise and
to enhance the peak width. If peak width is too low, subpixel interpolation may
render integer values (the associated error becomes the size of the pixel). It is
convenient that illuminated particles occupy an area of more than 4 square pixels.
The values of the displacements are lastly divided by the time between pulses to
be converted into velocities. The process is repeated to all the interrogation areas in
the image.
Entrada no
sistema
Transformada
rápida de Fourier
Determinação
do pico e
interpolação
Conversão em
velocidades
Correlação
f
(m,n)
F (u,v)
Imagem 1:
t=t
0
FFT
(d
x
, d
y
)
? (u,v
)
V
x
(i,j)
Cross-correlation
Φ
(u,v)=F(u,v)
.
G(u,v)
FFT
−
1
Ficheiro de
saida
V
y
(i,j)
G (u,v
)
g (m,n)
Imagem 2:
t=t
0
+
FFT
Δ
t
Função Janela
(Opcional)
Função Filtro
(Opcional)
Fig. 12 Sequence of processes involved in the PIV data processing
