When s, ,s,,s>> f, these expressions reduce to essentially the same form :s (4). 
SPECIAL RESULTS 
The foregoing results show that to account for variation of distortion with 
focal setting, it is sufficient to know the distortion functions for two different object 
distances. Preferably, these distances should bracket any other distances of interest 
(i.e., s, Ss $s,), for then Ory would be obtained by an interpolative process and 
would thus be less affected by errors in 8s, and ôs,. When, as would often to the 
case, s, = =, the expression for ag reduces to 
(13) 
When the other distance s, corresponds to unit magnification (i.e., s, 7 2f), the 
expression for a further reduces to 
(14) 
where m, is the magnification of the image for object plane at distance s. 
VARIATION OF DISTORTION WITHIN THE PHOTOGRAPHIC FIELD 
So far we have been concerned only with distortion of images of points lying 
in the particular object plane on which the camera is focussed. For more general 
applications we need also to be concerned with points in the photographic field 
not lying in the plane of sharpest focus. The above results do not hold for such 
points. Instead, as is also shown in Brown (1270), the following expression applies 
ór, s! = X E vy e Ks 124 eee (15) 
in which 
distortion function for objects in plane at distance s' 
for camera actually focussed on plane at distance s 
(see Figure 1); 
distortion coefficients that would have applied if 
camera actually had been focussed on object plane 
at distance s'; 
and where the parameter y, ,! is defined by 
sf s 
Ye, s'-f 5