set up about the origin. The fiducial centre and in particu- 
lar, where the camera has a register glass, the central cross 
is the logical choice. 
(b) Any residual distortion should be small and symmetrical around 
the chosen or igin. 
When the lens possesses asymmetry, the choice of origin is rather 
arbitrary but the best choice undoubtedly has symmetrical residual dis- 
tortion, since other elements of the photogrammetric process such as the 
corrector plate in the reduction printer, the distortion of the plotting 
machine, etc. are all symmetrical. The aim is, therefore, to adjust the 
centre of symmetry of the distortions to the fiducial centre during 
calibration. Then all residual distortions and the lens constant f, the 
principal distance, will be quoted relative to this centre. 
Until measurements have been made, the centre of symmetry will not 
be known and it is suggested that the camera should be set up initially 
with the principal point of auto-collimation adjusted accurately to the 
fiducial centre. 
The basic calibration equation can be rewritten as 
r D 
= f + 
tan 6 tan 6 
  
  
(5) 
Having measured values of r and © , values of "/tan © can be computed 
and in the absence of distortion should give a constant value f. In- 
equality of the value "/tan 6 as a function of the angle 9 will indi- 
cate residual distortion, while inequality for a given angle 8 along 
diagonals of the camera format will indicate asymmetry. We assume that 
measurements have yielded four values f4fgfcfp of the ratio "/tan o 
along the diagonals AB, CD, for some angle 6 towards the edge of the 
field, perhaps 359 for a wide angle lens. The co-ordinates of the centre 
of symmetry relative to the centre cross are then 
fa 7 fg 
AaB = 2 tan 8A (6) 
with a similar equation for Acp - A positive value of Apg indicates 
that the centre of symmetry is displaced towards the point B. 
The total displacement of the centre of symmetry is given by 
Al = [ofp + 83; [7j 
If necessary, the register glass is moved by amounts apg and ACD 
to make the centre of symmetry coincident with the fiducial centre. The 
displacement Al is a measure of the asymmetry of the lens and should be 
subject to some tolerance. 
  
  
  
  
  
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