By choice of principal distance, Ar will be small; and by choice of the origin of 
coordinates, Ar will be approximately independent of 9, although still a function of r. 
The origin in the negative plane is then the principal point of symmetry. About this 
origin, we further find 
R/H = tan a (2) 
so that 
r — F tan a (3) 
where a is the angle at the camera between the point R and the origin. This with 
our transform allows the distortion to be defined in terms of the incident angle a. 
A further definition is important. This is the principal point of autocollimation, 
which is the point in the negative plane for which the incident beam is perpendicular 
to the negative plane. 
3. Calibration 
The process of determining the relationship between the positions of images on 
the negative and the positions of the corresponding objects on the ground is known 
as calibration. Clearly there will be many factors involved over which the photo- 
grammetrist has no direct control, such as atmospheric refraction and camera 
temperature. Thus, for the whole system to be calibrated, photographs will need to 
be taken of an accurately surveyed target area, in which there are a sufficient number 
of well-defined, properly positioned and accurately measured targets. Equation (1) 
above is then used to determine principal distance and distortion. 
While this form of calibration is extremely valuable, particularly as a research 
tool, it is too expensive and slow for the routine checking of camera systems. It is 
usual, therefore, to think in terms of camera calibration, where the camera is isolated 
from the rest of the system, and the transform between object and image is found from 
equation (3) above under closely controlled laboratory conditions. This is usually 
done without using the actual film magazine, and probably the majority of calibra 
tions performed throughout the world are purely visual. From this, the practice has 
grown up of defining distortion purely in terms of these laboratory measurements on 
the optical unit of the camera, while the effects of atmospheric refraction, aircraft 
windows, temperature differences, film shrinkage in processing, and so on, are looked 
upon as errors or deviations from the “true” distortion. 
The procedures for camera calibration are well known; there is an I.S.P. 
Standard covering the subject and the literature contains a number of papers on the 
details necessary for accuracy. Up-to-date accounts are given by Washer, 121 Hall 131 
and Carman. 141 
Washer [5] subsequently has given some interesting results from the calibration 
of one camera by four alternative methods. He shows that a precision of ± 2 p can 
be achieved by any of the methods if attention is paid to sources of error, and further 
that the four methods give identical answers. He concludes that if one is to be sure 
that the distortion values obtained are accurate to ±2 p, then two independent 
methods should be used to see that the values given by each method agree within 
the ±2 p. 
4. Radial Distortion 
The lens designer aims to eliminate radial distortion by proper choice of glass 
types, component curvatures and separations. He can never achieve this to perfec 
tion and he is always left with the design distortion. Older lenses had design distor 
tions as high as 200 p. More modern designs have brought distortions down to 
380