Under certain circumstances, especially if oversized targets are 
used, the distance between the true and measured target center 
(offset) can be larger than the measurement accuracy of 
photogrammetric industrial measuring systems. Two different 
cases can be differentiated. 
    
  
  
   
elliptical target image 
_center of target image = measured target center 
— - offset 
\ image of target center = true target center 
image plane 
7 circular target 
target center 
Figure 3: Measured and true target center 
In those cases in which the image plane is parallel to the target 
plane a circular target is projected as a circle into the image. 
Thus, the true target center is identical with the measured 
target center. 
In those cases in which the image plane is not parallel to the 
target plane, which happens in most convergent 
photogrammetric networks, the expected target center is not 
necessarily identical with the actual target center. The offset 
between the true and the measured target center (Fig. 3, 4) can 
be estimated by equation (2). 
Using the parameters of a digital photogrammetric 
measurement system (e.g. /Brown and Dold 1996/) the offset 
will be estimated. In (Fig. 5, 6) the variation of the offset is 
shown for different lenses (15mm, 25mm; e.g. lenses for 
Kodak DCS camera), the maximum image radius (18mm; e.g. 
Kodak DCS460), typical distances between camera and target 
(2 m, 5 m) and different target diameters (5 mm, 10 mm, 15 
mm, 20 mm). Assuming that the image measurement accuracy 
of digital photogrammetric systems is for real applications 
larger than 0.2 microns, 10 mm targets have no influence if 
recording distances between 2 m and 5 m are used. Target 
diameters of more than 10 mm should not be used for these 
recording distances. It has also to be considered that the 
recording direction using retro refelctive targets is between 
+60 gon because those targets do not reflect the light for larger 
angles 
(-5) 
g=n 2 
m 2 
R, + 2) sin(90-a) R,- d sin(90—a) 
£27 — apr 2 + 2 
m d d (2) 
h==-cos(90-a) he -cos(90-a) 
  
€: offset between true and measured target center 
d: diameter of target 
r: image radius of P', 
fr: image radius of P’, 
image radius of P", (true target center) 
recording direction 
distance between target center and optical axis. 
distance between camera and target 
focal distance. 
J 
9 = #92 
S 
    
/ . 
\ / image plane 
/ 
Mm na at = on Tepe 
1 
Figure 4: Relation between target and target image 
  
  
  
| 
| 
  
alpha (gon) 
= 2m/5mm 
—n/5mm 
——5n/0mm 
——Sm/5mm 
—— — 5m /20mm 
—_— 2m / mm 
2m / 15mm 
2m /20mm 
  
  
  
  
Figure 5: Estimation of offset for a 15 mm lens and a maximum image radius of 18mm. 
120 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
5 Influenc 
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