52 BALLISTIC PHOTOGRAMMETRY, AUTHOR'S PRESENTATION 
parameters. An evaluation method based on 
the condition of colinearity will as a by- 
product, warrant the numerical analysis of this 
problem. Generally speaking, we may say that, 
the fact that the general problem of photo- 
grammetry can be based on such a simple 
geometrical theorem as that of the colinearity 
of three points justifies the conclusion that the 
difficulties in photogrammetry are not of geo- 
metrical nature, but like in most precision 
measuring methods, are caused by physical 
  
lomparator measurements 
of selected Star images 
  
  
  
  
Computer 
  
Plate coordinates corrected 
for comparator errors and 
referred to fiducial marks system 
  
  
  
  
c. there is no limitation to the angle under 
which the objects are seen. 
This means that a smooth transition from 
terrestrial to astronomical refraction for ele- 
vation angles from 0 to 90? must be possible, 
In addition, it is necessary to incorporate any 
meteorological data as they may become avail- 
able from local measurements. While this 
problem in its complexity is far in excess of the 
requirements for, lets say, topographic ap- 
plication, nevertheless it becomes evident that 
  
Star catalogue data 
(right ascension, declinatian) 
of measured stars 
Standard coordinates ( and 7) 
referred to the locatien(@ and A) 
  
  
  
  
      
    
  
  
  
  
  
Least Sim for 
the elements of orientation 
&, C), K,C, Xp, yy. and 
radial distortion coefficients 
Ko: Ki, Ka, Ks. 
  
  
  
  
Graphical presentation of 
radial distortion curve 
and distribution of residuals 
  
  
  
   
the elements of orientation 
C, C9, CK, C, Xp, Yp 
  
  
  
  
  
  
Graphical presentation of 
L) radial and tangential compo - 
nents of residuals 
2) contour lines for the radial 
resi 
3) contour lines for the tangential 
residuals 
  
  
  
Fig. 3. Data Reduction Steps. 
properties which act as perturbations on the 
chosen geometrical model. This brings me to a 
third area, where the efforts in Ballistic Photo- 
grammetry may be of general interest. The 
problems to which I refer are obviously the 
problem of refraction and the problem of 
camera calibration including the determination 
of distortion. First refraction: In Ballistic 
Photogrammetry, due to the wide range of the 
observational conditions encountered, it is 
necessary to approach the refraction problem 
in a very general way. We must take into con- 
sideration, that 
a. the camera can be either on the ground, 
in the air or outside of the atmosphere, 
b. in each of these cases, the objects photo- 
graphed can be anywhere between the neigh- 
borhood of the camera and infinity, and finally 
aerial precision photogrammetry cannot ignore 
it. It may be of interest to state that for an 
observer in the air, there is a maximum amount 
of refraction from flying heights of about 14 
km. A rather high percentage of the maximum 
refraction is still effective in the heights of 
7-10 km which are typical flying heights for 
topographic application. The refraction cor- 
rection, especially with regard to super wide 
angle photography, amounts to about 20-25 
seconds of arc for edge rays under such con- 
ditions, or to about 11 y, in terms of image 
position. In any triangulation, including aerial 
triangulation, the rays intersecting at a certain 
point do not necessarily have the same inclina- 
tion and therefore different refraction amounts. 
As a matter of fact, corresponding tangents to 
the light curves at the center of perspective are 
screw lir 
showing 
on the c 
In co 
concerni 
listic Ph 
camera « 
help to 
problem 
a photo; 
The pat 
the poss 
star im; 
pattern. 
square « 
ment of 
photogr: 
of the e 
mittent 
and clo: 
recordec 
The 
calibrati 
in Figu