Invited Paper, Commission V* 
  
CALIBRATION OF CLOSE RANGE CAMERAS 
By 
Duane C. Brown 
DBA Systems, Inc. 
Melbourne, Florida 
ABSTRACT 
With the increasing application of analytical methods to close-range photo- 
grammetry, the problem of camera calibration has assumed increasing importance. 
This is particularly so in applications exploiting the superior geometry afforded by 
highly convergent photographs and in applications calling for moderately large 
photographic scales (say, greater than 1:50). With high convergence, errors in the 
elements of interior orientation (x, T , €) are not offset by the process of projective 
compensation that operates so effectively with non-convergent photographs. Similarly, 
with the exercise of moderately large photographic scales, the variation of lens 
distortion with varying object distance can assume appreciable significance. Such 
considerations indicate the need for special methods of calibration tailored to the 
specific requirements of close-range photogrammetry. |n this paper a general review 
is made of a number of such methods that have been developed in recent years. 
INTRODUCTION 
Although distortion varies with object distance, the variation is ordinarily 
insignificant in mapping and other applications in which photographed points are 
removed by a large number of focal lengths from the camera. Here, one can safely 
employ the infinity calibration of distortion for all photographed points. On the 
other hand, when object distances are within a few tens of focal lengths of the 
camera, moderate to severe variation of distortion with object distance may be 
experienced. Here, one must not only allow for change of distortion with focal 
setting, but must also take into consideration the change of distortion occurring 
within the photographic field itself. The two are not equivalent, as we shall 
presently see. 
VARIATION OF DISTORTION WITH FOCUSSED OBJECT DISTANCE 
In an earlier paper (Brown, 1971) we showed that if ór, and ór, denote the 
radial distortion functions of a lens when focussed on object pldnes at distances of 
s, ands,, respectively, the distortion function ór, for the lens when focussed at 
object distance s is given by 
6^ o, 6,0 - @, ) Ôr (1) 
/ 
$2 
* Presented to the XII Congress of the International Society of Photogrammetry, 
Ottawa, Canada, July 23 through August 5, 1972. 
-]-