water surface
glas window f=
m D adiuti miei A
oxi ert stop |
scattering plate
LED array
CCD camera — |
uu s
CONS
water tight housing
flume bottom
Figure 3: Sketch drawing of the optical bubble measuring device.
The left tower contains the illumination optics with the pulsed
LED array, the right tower contains the camera together with the
imaging optics. The height of the towers can be adjusted from
45 to 100 cm to allow measurements in different distances to the
mean water surface.
less than 1000 um are of nearly spherical shape and therefore
imaged as dark circles (Fig. 4).
The illumination consists of an array of LED's. Synchro-
nized with the image acquisition, they were pulsed with a
duration of 20 us. In addition, the camera is shuttered to
an acquisition time of 1/2000 s to completely suppress scat-
tered light from the environment. The short illumination time
avoids any motion blur in the images of fast moving bubbles.
With a single pixel imaging an area of 10.1 um x 16.7 um,
bubble velocities up to 0.5 m/s in x-direction and 0.8 m/s in
y-direction cause motion blur of less than one pixel. Since
typical bubble velocities are less than 30cm/s and do not
exceed 1 m/s motion blur is nearly completely suppressed.
Image sequences of 5000 to 8000 images were taken for each
measuring condition. They were stored on laser video discs
for later processing.
3.2 Position ambiguity
A principal problem of depth-from-focus is that it is not pos-
sible to distinguish whether a bubble is located in front or
behind the focal plane. The calculation of the true size of
a bubble from its blurred size and the amount of blur may
therefore result in an ambiguity of the radius measurement.
To overcome this problem, we use a telecentric path of rays
both on the illumination side as well as on the camera side.
With this setup, the aperture stop is located at the rear focal
point of the respective optics. The effect is that all princi-
pal rays in object space are parallel to the optical axis. Only
narrow and axis-parallel ray bundles contribute to image for-
mation. Then, the size of blurred bubbles becomes indepen-
dent from the grade of the blur or the location along the
optical axis. The size of a blurred bubble is hereby defined
at the gray values that are the half of the maximum gray
value. Furthermore, the grade of blurring becomes indepen-
dent from whether the position is in front or behind the focal
4000p
3000p
2000p
1000p
On 1000p 20004 30004 4000p 5000p
ou 1000u 2000p 3000u 5000p
Figure 4: Two images taken with the IBG device. Both well
focused as well as out of focus bubbles can be seen. The bright
spot which can be seen in the center of well focused bubbles arises
from the small fraction of light (less than 0.1 %) which passes
through the bubble.
plane. Because of the symmetry introduced by the telecen-
tric path of rays, the position ambivalence can be completely
disregarded in the measurements.
defocused focused
object point
— optical axis
ree principal ray for telecentric stop
== marginal rays for telecentric stop
z principal rays for stop at lens
lens telecentric stop CCD
Figure 5: Comparison of standard and of telecentric path of rays:
the displacement of an object point along the optical axis causes
changes in the size of the image only with standard optics, but not
with telecentric path of rays.
4 IMAGE PROCESSING TECHNIQUE
The processing of the images to determine the size distrib-
ution consists of two main steps: segmentation and depth-
from-focus. Before these steps are performed, a brightness
normalization is applied to the images to eliminate inhomo-
geneities and brightness variations of the illumination.
4.1 Brightness normalization
A good understanding of the image formation process and
a normalization of the gray values, which is independent of
brightness fluctuations and inhomogeneities is an essential
requirement for the depth-from-focus technique. The nor-
malization is done by applying a linear illumination model
assuming that the measured gray values g(&) are further pro-
portional to the irradiance I(Z). Then
g(z) — a(z)1(z) 4 b(z). (2)
The unknown quantities b(Z) and a(&) are obtained by tak-
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
ing a backgro
(I(Z) = 0) ar
present (I(z)
If we describe
r(X) in the
ordinates and
their image is
I(Z)
with v(Z) des
tion.
Then, the lin:
AL 9
(E) = 0. @)
results in a ne
4.2 Segme
The image pr
objects from
(blurred) size
been perform
particle size.
the objects tc
is not a priori
to be at these
the 1/g-th of
used to segm
combines a p
algorithm. E
measuring vo
the normalize
the plateau s
distance from
the size of th
reason it is nc
the blurred in
segmentation
which may b
15
08.
0.6.
0.44 =
02.
fis
Figure 6: D.
As an example
given by the i
