In: Wagner W„ Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Voi. XXXVIII, Part 7B 
295 
according to this law. By evaluating the inequation it follows 
that a diffuse reflection appears if R a >77.842 nm. The mean 
roughness index R a of the coil front surface is between 6 /im and 
11 fim and therefore it is sufficient to guarantee diffuse reflec 
tion. 
To proof the assumptions made in this section an experimental 
setup has been designed. The coil windings are modelled by sev 
eral steelplates of the same thickness which are stacked upon each 
other and then deferred fixed. First a frontal photograph of the 
coil winding model including the laser line was taken to calculate 
the displacements with the laser light section technique, shown in 
Fig. 7(a). Because of the good illumition conditions only an op 
tical red filter was used. Additionally a photograph from the side 
was taken as reference image for the coil winding model, shown 
in Fig. 7(b). 
1000 2000 3000 
Width in pixel 
(a) Frontal photograph of the 
coil winding model showing 
the laser line. 
1000 2000 3000 
Width in pixel 
(b) Lateral photograph of the 
coil winding model. 
Figure 7: Photographs of the coil winding model. 
To determine the winding displacement, the first step is to extract 
the laser line from the acquired image data. Therefore the image 
is cropped to the probe edges and then the position of maximum 
intensity in every row is determined. For the experimental setup 
a commercial photo camera was used, whos images were down- 
sampled to obtain a comparable resolution to typical video cam 
eras. The reference for the coil winding model is obtained from 
the lateral image by using a canny edge detection algorithm (Gon 
zalez and Woods, 2008). In Fig. 8 the results of the previous steps 
are shown. The laser light section curve is close to the reference 
curve and also the desired resolution limit is almost reached. 
suits in a maximum error of 6 mm for the displacement determi 
nation. Futhermore the coil windings can also be affected by a 
linear trend due to a non-conform rolling-up process. This lin 
ear trend can be used as a quality characteristic too and should 
therefore also be measured. To estimate the influence of the laser 
alignment and the linear trend of the coil front on the laser line a 
model of the setup is introduced in Fig. 9. Here two coordinate 
systems are considered, a fixed-place coordinate system given by 
x, y, z and a laser coordinate system given by £, rj, The laser 
coordinate system is rotated by the angles a, ¡3, 7 which allow 
a free rotation of the laser in space with the corresponding ro 
tation matrices (Cook, 2007) shown in Eqns. 5, 6 and 7. For a 
solvable system of equations it is necessary to pose the following 
constraint on the coil windings and the laser line. The additional 
linear trend resulting from the non-conform rolling-up processes 
is represented by a rotation of the coil front around the y-axis 
by an angle 0 with the corresponding rotation matrix shown in 
Eqn. 8. That means that when the laser line is projected onto the 
axis of symmetry in the lower half of the coil only a linear trend 
is present in the x-direction. This can be achieved by an exact 
triggering and a limitation on the ROI. 
Camera 
Figure 9: Advanced model of the setup with a fixed-place coordi 
nate system given by x, y, z and a laser coordinate system given 
by & V, C 
The following rotation matrices R 1 , Rp, R a and Re represent 
the degrees of freedom in the setup: 
• Rotation around £, for up or down tilting of the laser. 
( cos(7) — sin(7) 0\ 
sin(7) cos (7) 0 (5) 
0 0 1/ 
• Rotation around 77, for rotation of the laser around its sym 
metry axis. 
/ cos(/3) 0 sin(/?)\ 
Rf, = 0 1 0 (6) 
y— sin(/2) 0 cos(/3 )J 
Figure 8: The red colored curve is the result for the displace 
ment recognition by using the laser light section technique and 
the green colored curve is the reference derived from the frontal 
probe image (see Fig. 7(a)). A good agreement can be seen. 
3 ADVANCED MODELING OF THE SETUP 
• Rotation around £, for tangential deviation of the laser due to 
the laser light section technique in the following form a = 
f — 7t/2. 
(10 0 \ 
R a = 0 cos(a) sin(a) 1 (7) 
\ 0 — sin(a:) cos(a:) J 
During the experimental setup the influence of the laser align 
ment on the result was very low because of the small-sized probe 
with a height of only 32 mm (a typical coil profile length can 
be up to 700 mm). Considering a profile length of 700 mm a 
slight rotation of the laser around its symmetry axis by 0.3°, re- 
Rotation around y, for skewness of the coil front. 
R a = 
0 sin(0) N 
1 0 
0 cos(0) 
(8)