65 
What is the significance of this effect in a length measurement ? 
Consider the measurement setup sketched in Figure 11. A target moves from position pos1 to position pos2 by exactly 
2.00m. What is the measured deviation Al of | (b = 0.8 um /°) ? 
The angles a(pos1) = 55° and a(pos2) = 20° leads to longitudinal shifts of: z,(pos1) = 30.8 um and z(pos2) - 44.0 um. 
The deviation is calculated as: AI = Z(pos1) - z(pos2) =-13jyum i.e. the measured distance will be too short. 
4. CONCLUSIONS 
The position of a retro-target, defined transversely by the edge elements and longitudinally by the plane through the 
center of the glass spheres, is in practice not fixed relative to the physical target. 
The measurements confirm a linear shift of the retro-target center from - 30um to + 30um, normal to the line of sight, 
when the target is tilted from - 40° to + 40°. This result is in good agreement with the qualitative demonstration of 
Figure 5. 
This systematic shift is independent of the target size and distance, as indicated by the approximately constant value b 
in eqn. (5) (op. ~ 5 % of b) The center target moves towards the more distant reference target. 
The effect does not depend on the pointing method, for example image processing or by manual pointing if the target is 
illuminated from the camera position. 
In a real application this shift can be corrected if the orientation of the target is in known relation to the camera position. 
Positions of retro-targets measured by intersection are dominated by the longitudinal shift whereas alignments are 
dominated by the transverse effect. 
The maximum shift depends on the mean distance between two glass spheres on the retro-reflective target foil. A 
saturation of the linear trend is around 50° tilt, depending on the flatness of the target surface. 
Punched targets could be used to avoid the problem but the fuzzy edge is not resistant to mechanical contact. 
for If the edge mask is black paper, thicker than about 10 um, additional shadowing effects will further affect the shift. 
This demonstrated effect is seen as a limiting factor if the pointing accuracy should be better than 20 um. 
Acknowledgments 
two 
This work is part of the project 'Development of test and calibration procedures for automatic theodolite systems 
in production metrology', supported by the European Program ‘Measurements & Testing’. The project was a 
cooperation together with the Physikalisch-Technische Bundesanstalt in Braunschweig, Germany, managed by 
Dr.K. Wendt. 
References 
Wester-Ebbinghaus, W., 1989. Trends in Non-Topographic Photogrammetry Systems. In: Non-Topographic 
Photogrammetry. American Society for Photogrammetry and Remote Sensing. 
Tabatabai, A.J., Mitchell, R., 1984 Edge Location to Subpixel Values in Digital Imagery. IEEE Transaction on Pattern 
Analysis and Machine Intelligence, Vol.PAMI-6, No 2, pp.188-201. 
5 IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995