After the adjustment of the fiducial centre, complete measurements 
are made over the camera format with points along two diagonals as a 
minimum requirement. Values of '/tan 6 are calculated for each 
measured position and should be symmetrical about the origin. 
The principal distance is now chosen to bring the distortion of the 
lens to the standard value D for the lens type at some arbitrary angular 
position, again 359 is convenient. The value D/tan 6 is calculated and 
subtracted from the ratio '/tan e for the angle chosen. Four values of 
the "principal distance" will result along the two diagonals. The mean 
value is the "calibrated principal distance". 
The calibrated principal distance is subtracted from all "/tan 6 
values and the differences multiplied by tan © to give the lens distor- 
tion values. An example of this calculation is given in Table | and the 
simplicity of the method is obvious. 
There are alternative procedures based upon this equation, including 
a graphical method which is convenient if a simple acceptance or rejection 
of the camera is required. For speed combined with accuracy, the numerical 
method given above is, however, difficult to better when individual distor- 
tion values are to be quoted. A minor criticism of the method is that the 
calibrated principal distance is derived from the measured and standard 
values at an arbitrary angle. In practice this not of great importance 
since departures from the standard values will be small over the entire 
format for an acceptable lens. 
  
4. LENSES WITH ASYMMETRY 
It is out of place to consider the full theory of asymmetrical lenses 
here. It will suffice to state that for small departures from symmetry the 
lens will behave as a symmetrical lens with an "eouivalent thin prism? in 
front of It, 
The separation between the centre of symmetry and the principal 
point of auto-collimation is then given by 
  
A Sm sec? ess id - (8) | 
tan“ © L Cos © | 
where © is the angle made by the ray in the principal section of the 
prism 
R is the corresponding angle of refraction within the prism 
related to o by Snelis Law 
N is the refractive index of the prism 1.5. 
The tangential distortion introduced for a ray in a plane at right 
angles to the principal section is given by 
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