the precise angles or focal plane distances will not always be attained 
and the tabulation in itself cannot be used for intermediate values. A 
more important consideration however is that it quite unnecessarily 
restricts the lens manufacturer who, in optical terminology, is not able 
to control the focal length of the lens to the accuracy necessary for 
this pure comparison process. 
The plotting process therefore incorporates a variable element, 
which allows the negative taken in the camera to be enlarged or reduced 
slightly to obtain the best match to the plotting machine characteristics. 
(Often this variable element is in the plotting machine itself but this 
does not vitiate the argument.) The extent of the scale change is deter- 
mined by the camera constant - sometimes called the principal distance or 
focal length. This constant arises from the relationship between the 
focal plane distance r and the incident angle 6. Separating the two 
variables we can say 
r « f F(e) (1) 
where f is a constant having the dimension of a length 
F(e) is a complicated function of the angle. 
Differences between production cameras can then be treated as 
variations of the lens constant f superimposed upon variations of the 
angular function F(0). The former can be easily compensated and can be 
allowed a wide tolerance, the latter cannot be compensated easily and 
therefore must be controlled to close limits, to ensure that the angular 
functions for camera projector etc. are the same. For convenience, the 
angular function F(6) should be simple and we may then define a further 
function, the distortion D, depending upon the departure of this function 
from a simple form. The camera relationship can then be stated in the 
form 
r =f F(a) + D (2) 
where F(8) is à simple angular function, 
D the distortion having the dimensions of à length. 
The actual values of D depend upon the choice of the angular 
function F(6). This should be chosen so that, with real lenses, the 
distortion values D are as small as possible and are simple for computa- 
tion. Here we may call upon optics and suggest that the relation 
r = f fan 9 (3) 
is approximately followed if measurements are taken from a point in the 
centre of the camera field. This is usually the best choice of function, 
although there may well be special lenses for which some other functions 
are more convenient. Thus in the case of a lens with a spherical focal 
plane the function F(8) = 0e might be more desirable. 
  
  
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