The empirical value for the X-coordinate of object points 
is higher than expected. The reasons for this are the de- 
viations from ideal measuring conditions, which influence 
mainly the X-direction. A not totally compensated varia- 
tion in temperature or vibrations could be such deviations. 
Furthermore a less precise reseau grid was used for these 
measurements. Additional tests of layout 2 with high pre- 
cision reseau grids haven given an accuracy of 2 um in 
Y-direction and accordingly to the base-to-height ratio 6 
pm in Z-direction. 
Layout 2 proves to be the more stable one, therefore it was 
chosen as final configuration. In cases where only a reduced 
accuracy is required layout 1 might also be suitable. 
3. Calibration of the Optical System 
The procedure described above assumes, that the position 
of the components of the imaging system remain stable 
and that the relative orientation of each single bundle of 
rays is known. 
Furthermore the control points of both reseau grids must 
be known in one coordinate system, so that the position 
of one reseau grid in relation to the other must also be 
determined. 
This can be achieved by replacing the unknown object 
(i.e. the tool) by a third precise reseau grid. Then the 
camera system is shifted systematically over this additional 
reseau grid and at different places the reseau crosses of 
all 6 images, which can be taken at a single position are 
measured. Then all the observations can be put into an 
adjustment with following unknowns: 
vi, wi, Ki, Xoi, Yoi, Zo; : parameter of the exterior orienta- 
tion for each independent image 
I 
dp;, dw;, dk;, br;, by;, b.;:parameter of the relative orienta- 
tion for each dependent image j- 
1,5 
Q1, 91, K1, Xi, Yi, Z1: transformation parameters for the 
first two reseau grids 
P2, Wa, K2, X2, Y2, Z3 : transformation parameters for the 
third reseau grid onto the first re- 
seau grid 
As the unknowns are highly correlated it is often enough 
to adjust only the rotation angles of the transformation 1 
and 2 and to keep the translation parameters which must 
be known in advance with an accuracy of about 1 mm, 
which can be easily measured manually. 
The determination of the first transformation parameters 
become superfluous, if the position of the reseau grids is 
not influenced by vibrations. As there is up to now only 
a laboratory setup the calibration of these parameters is 
sometimes necessary too. 
The parameters of the transformation of the third reseau 
grid onto the first reseau grid can also be eliminated if 
there is an appropriate three-dimensional calibration field 
available. The problem is that for each new configuration 
a new calibration field is necessary and reseau grids with 
certain dimensions are not made in series and have terms 
of delivery of up to one year. 
  
For one of the configurations which were tested in the 
course of the investigations a calibration field was made 
of ultra flat glass with reseau crosses that were projec- 
ted onto the glass with photographic means. The crosses 
were measured with an analytical plotter and after four 
glass plates had been fixed together, the calibration was 
made with photogrammetric methods. This procedure is 
very time consuming. Comparisons of the calibration of the 
optical system with and without calibration object have 
shown, that there is no difference for the measuring of 
unknown object coordinates, so the calibration with single 
reseau grids is prefered. 
The procedure of the calibration can be easily done auto- 
matically, if there is a shifting device for the cameras and 
if the light can be switched on and off automatically. 
4. Measuring of Cutting Edges 
One of the most frequently used forms for cutting edges 
are triangle shaped inserts which can be replaced when all 
three sides are damaged or worn out. 
  
Fig. 7: triangle shaped insert of a cutting tool 
Fig.7 shows such an insert the way it is seen by the CCD- 
cameras. [he cutting edges are clearly visible and can be 
easily measured automatically with digital image proces- 
sing techniques. To minimize the time used for the image 
processing the procedure is parted into two steps. At first 
the location and the orientation of the triangle is deter- 
mined to get the approximate position of the edges, then 
the precise edge detection with linear edge operators is 
performed. 
The task to find approximate values for the desired edges 
in a reasonable time is not as simple as it seems [Wang et 
al., 1991]. In the image there are several additional edges 
and a line structure and circles inside the triangle. So this 
task was also parted into single steps. At first the image 
with a size of 768 x 512 pixels is squished to a quarter 
of its original size. This reduces the data considerably and 
eliminates most of the image noise. Then single edge pixels 
are extracted and in a next step all those edge pixels that 
do not lie on a straight line are eliminated. From these 
straight lines triangles are reconstructed and the smallest 
equilateral one is selected. 
The part of the approximate search may later be repla- 
ced by using the information of a CAD-system where the 
construction data of the tools are stored.