In: Wagner W., Szdkely, B. (eds.): ISPRS ТС VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
298 
Eqn. 19 as a function of the winding displacement h, the triangu 
lation angle <p, the distance Z between camera and coil, and the 
quantization of the laser position through the camera. 
Ah — 
dh 
dh . 
dh 
+ 
— AZ 
ÔZ 
+ 
—Ax 
ox 
error due to 
laser align 
error due to 
camera setup 
error due to 
quantization 
(19) 
Before the total systematic error Ah can be calculated by Eqn. 19, 
the acquisition of the coil profile must be defined. Therefore 
Eqn. 2 which describes the calculation of the winding displace 
ment due to the laser light section technique and Eqn. 3 for the 
mapping properties due the central projection theorem are used. 
So the final function for h is shown in Eqn. 20. 
h = 
1 
tan(<^) 
laser light 
section 
/ 
X 
central 
projection 
(20) 
Ah = 
2 
sin(2<^) 
A ip 
• \h\ + 
1 
Z + c 
A Z 
\h\ 
4- 
1 
tan(</?) 
Ax' 
(21) 
200 400 600 800 1000 1200 
Width in pixel 
(a) Coil with a laser line and several (b) Final processed croil profile 
defects. (black), defects (red) and system 
atic error (green). 
Width in pixel Laser position in mm 
(c) Coil with a laser line and a sin- (d) Final processed croil profile 
gle defect in the middle. (black), defects (red) and system 
atic error (green). 
Figure 15: Results of the measurement system for two different 
steel coils. 
elimination of steel coils with packaging material and statistically 
evaluate the defect detection rate of the realized system. 
Equation 21 shows the final result for the systematic error Ah. 
Considering the specifications for p, c, Z and <p (see Sec. 1) an 
uncertainly error of AZ =100 mm, A(p =2 ° and Ax' = p 
results in a maximum systematic error Ah of 1.462 mm for a 
winding displacement h of 5 mm. The main point is that the 
terms belonging to the camera setup error and the laser alignment 
error which are scaled by the winding displacement h are smaller 
than 10“ 1 and the quantization error is a constant 0.487 mm. The 
systematic error Ah is increasing with nearly h/10 + 0.487 mm. 
Additionally the first term in Eqn. 21 shows that the error due the 
laser alignment is minimal for triangulation angles ip between 30° 
and 60°. 
In Fig. 15(a) an example for a unpackaged coil with several de 
fects is shown. The final processed coil profile (black), the de 
tected profile defects (red) and the systematic error (green) is 
shown in Fig. 15(b). It is observable that the calculated coil pro 
file with an insignificantly small systematic error perfectly cor 
responds to the laser line in the image and the major defects are 
detected. Futhermore a second example for an unpackaged coil 
is shown in Fig. 15(c) and processed results in Fig. 15(d). In 
the second image additional edge protection material is attached 
to the coil (visible on the left side) but is excluded from the coil 
profile by the extraction algorithm, as it was demonstrated before. 
6 CONCLUSIONS AND FUTURE WORK 
We have shown that a recognition of winding displacements for 
steel coils using the laser light section technique can be realized 
with a proposed height resolution of less than 1 mm. Further 
more we introduced a mathematical model to eliminate the de 
pendencies from an inaccurate laser alignment and to determine 
the linear trend of the coil front as another quality aspect. Finally 
we also have shown that the designed laser line extraction algo 
rithm extracts reliably with sufficient speed the laser line belong 
ing to the coil front. The next step is to improve the pre-process 
ACKNOWLEDGEMENTS 
The authors gratefully acknowledge the partial financial support 
for the work presented in this paper by the Austrian Research 
Promotion Agency under contract grant 814278 and the Austrian 
COMET program supporting the Austrian Center of Competence 
in Mechatronics (ACCM). Last but not least the authors thank 
the company Industrie Logistic Linz (ILL) for its financial and 
technical support. 
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