(38) 
ince 
s of 
(39) 
(40) 
(41) 
(42) 
(43) 
cles 
The 
the 
44) 
45) 
46) 
4T) 
115 
The distortion curve can immediately be plotted after the determination of the 
quantities dr; — dry. The radii of the circles give the distances on the abscissa axis. 
See Diagrams 2 and 3. 
If we want the curve to intersect the abscissa axis in a certain point (zero-point) the 
following procedure can be used. 
The relation between small changes of the f and the distortion amounts is given by 
the wellknown differential formula: 
df r 
dr = 7 (49) 
  
Consequently, the amount df which makes the distortion dr zero at a certain r can 
be determined. The corrections of the distortion curve for arbitrary values r can then be 
determined from (49) and the new distortion curve can be drawn. 
The weight-numbers of dr, — dr, can easily be determined directly from (44)—(48) 
with the aid of the special law of error propagation. We find 
  
f 
= = = En 50) 
Ay Dr, Dry rr, 4h2 ( 
f 
=... 51 
Qr. 8h2 (51) 
The standard error of the distortion amounts are then found 
as 
= = = = f (52) 
Ta un m a pi = 25.4 
"irc u (53) 
T4 2h V2 
The standard error of the measurements p is found from the expressions [vv] for 
the different cases. For case 5 the expression [vv] is given in (86) and the standard 
error u in (37). 
If the grid is denser as shown in Fig. 2 other combinations of points can of course 
be used. A suggestion for a standardised set of points will be made later on. 
Simultaneously with the determinations of the distortion amounts also the elements 
of orientation according to (25)—(26), (28)—(30) which are valid only for the case 5, 
should be computed. The results will show if there is any assymmetry present. The assym- 
metry will cause systematic errors .that cannot be compensated with the distortion cor- 
rection but can be taken into account numerically. 
The described procedure can be used for all types of cameras and projectors as soon 
as suitable and accurate grids are available. The accuracy of the grids has of course to 
be carefully checked. The errors of the grids can easily be introduced in the computations 
if necessary. 
[1] Hallert, B.: Fifth interim technical report. Basic factors limiting the accuracy of 
mapping and aerotriangulation by photogrammetric procedures. 1 Jan. 1954 
through 31 March 1954. Mapping and Charting Research Laboratory, Ohio State 
University, Columbus, Ohio. Contract placed by Engineer Research and Develop- 
ment Laboratories. Fort Belvoir. Virginia. 
[2] O’Brien, L.: Theoretical calibration of the Kelsh-Plotter. Diss. Institute of Geodesy, 
Photogrammetry and Cartography. Ohio State University, Columbus, Ohio 1954. 
  
  
  
  
  
  
  
  
   
  
  
  
   
   
   
  
  
  
  
  
  
  
    
   
    
     
     
    
   
  
  
  
  
   
   
    
  
  
  
  
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