64 
N a ae right target : 
X(a) - X(a) in pixels with LSQ fit 
left target 
  
0.5 
  
  
  
  
  
  
  
  
  
  
  
  
  
‘—40 —30 —20 —10 0 10 20 30 40 
angle œ [deg] 
Figure 9 Theoretical minus measured distance between the centre target and the left or right punched 
reference target. The centre target is a retro-target with painted mask. 
Interpretation of results: 
The punched retro-target in the center shows no significant shift to the left or right (Figure 8). 
As the target carrier is tilted a retro-target with painted mask shows a clear linear shift with a slope a towards the left or 
right punched reference target (Figure 9). This will be designated a transverse target shift. 
Transverse target shift in the image plane: 
Si(a) [pix] 2 a [pix/*] * a [*] (4) 
Transverse target shift at the target position, normal to the line of sight: 
Sy (x)[um] = b [um/°] * a. [*] (b 2 a * 8[um/pix] * D/F) (S) 
The transverse effect leads to a longitudinal shift if, for example, the target position is determined by intersecting two 
lines. 
The longitudinal shift is given by: 
  
  
  
  
  
  
  
  
  
  
  
  
  
zy (a)[um] = b [um/°] * a [°] * ctg(a) (x = B = O, see Figure 10) (6) 
distance D focal length F a b transversal shift longitudinal shift 
[mm] [mm] [pix/^] [um /°] [um] [um] 
3280 307 0.010 0.86 for a=30° for o.23098 230? 
2260 283 0.012 0.80 approx. 25 approx. 43 
1690 258 0.015 0.79 
Table 1 Measurements made at different distances, retro-target & 8mm. 
Same results have. been found by using targets with diameters of 4mm and 2mm. 
theodolite 1 . pos 1 pos 2 
viewing directions 
measured length 
le 
: End 3e 
    
2m 
x longitudinal shift 
7 
  
  
  
  
transversal shift 
  
theodolite 2 ‘7m |= 2.00 m 
Figure 11 Effects of shifts in a practical case. 
Figure 10 Transverse and longitudinal shift, caused 
by movements of edge elements. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences”, Zurich, March 22-24 1995 
  
L