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61 
2. MICROSCOPE VIEW OF A RETRO-REFLECTIVE TARGET 
Figure 1 and Figure 2 indicate the operation of retro-targets. 
A light source, coaxial with the line of sight or mounted close to the camera lens, illuminates the retro-target. Part of the 
light is reflected back along the incoming direction. Each sphere generates a bright ring of radius r and width Ar with a 
small bright dot in the center. Along the target contour individual spheres are partially covered by the edge mask. The 
degree of coverage is randomly distributed. 
   
target contour light from 
camera position : 
> : left edge right edge 
i edge sphere: not - partially - totally / totally - partially - not 
E | / visible \ | A 
4 
  
     
      
: 50 to 80 um 
; ~110|um : 
fed partal uded — 7 » off reflected 
magnified partially occlude es 
a) edge glass-sphere . back to CCD edge mask: painted or —glue glass sphere: 50um 
) thin black paper foil paper 
Figure 1 Retro-target: 
; ; » Figure 2 Retro-target cross section showing the 
e) Front view wit à magnifed edge sphere, g isibili pa e spheres, when mS from 
b) Cross section with ring and dot forming dift t EVI gt pr tic 9 
light rays. ifferent viewing directions. 
When the target is tilted, the pattern of rings and spots moves over the surface as x changes and thus for partially 
occluded edge spheres the reflected light intensity F changes with the tilt angle o. (Figure 3). 
The radius r and thus the maximum reflection FO area depends on the index of refraction n. 
Tests have shown that r = 0.80 sphere: thus n « 1.8. Each glass sphere reflects approx. 1 96 of the incoming light back 
to the camera, if the target at 1m distance is illuminated by coaxial parallel light (camera aperture @ = 50 mm). 
The intensity F(x) of the reflected ring is given by : 
Fo) s F'ozrAr(- 2 aMccos (oj (1) 
x r 
X 
with sin(a + ao) = : ao indicates edge position when a = 0° 
sphere 
  
F(x) can then be approximated by : 
F(a) = F°2 7 rsphere Ar (a ao) ; 0 < a + aos arcsin( 
  
) = 0.80 (= 53°) (2) 
n 
sphere 
(The intensity of the center dot can be neglected) 
The approximation in (2) shows a linear change of the reflected light intensity F. 
What are the consequences if the reflected light intensity of a contour pixel changes when an observer views the target 
from different positions? 
directions of changed edge intensity after a tilt 
a + cQ 
intensity or 
gray levels 
  
  
= pixels 
  
7 target 
"^ *. tilted target 
Figure 3 Target tilted by a. 
Figure 4 Intensity profile of the reflected light from a retro-target. 
The profile shifts when the target is tilted, i.e. viewed 
from a different direction. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences”, Zurich, March 22-24 1995