The analytical plumb line method excels in overall operational convenience. 
Because the observational equations are independent of elements of exterior 
orientation, one can, if desired, employ multiple exposures of but a single plumb 
line (against a black background) to generate a large number of appropriately 
distributed images (see Figure 5). By employing light sources of various colors to 
illuminate the plumb line, one can conveniently determine the dependence of 
distortion on color. Under certain circumstances a laser beam can be made to serve 
as the straight line in object space to be photographed. 
At DBA we have found the plumb line method to be especially convenient 
for the rapid screening of prospective lenses for use in special projects. The method 
also formed the basis for the investigation reported in Brown (1971) wherein the 
theoretical development reviewed in the first part of the present paper was successful- 
ly subjected to experimental validation. Figure 6 shows the arrangement of plumb 
line images on a typical plate that was reduced in this previous investigation, one 
of the outcomes of which are the results shown in Figure 7. The behavior of the 
various radial distortion curves shown in the figure was found to be in excellent 
agreement with theoretical expectations. Decentering distortion was also investi- 
gated. The experimentally established variation of decentering distortion within the 
photographic field was found to be of no practical significance and so is not shown 
in Figure 7. However, the variation of decentering distortion with object distance 
was found to be somewhat significant. Although a theoretical model for such 
variation has yet to be formulated, it appears to be safe in practice to assume that 
decentering distortion as calibrated at mid-field can be applied to all points within 
the photographic field. 
The primary shortcoming of the analytical plumb line method is that it does 
not yield useful estimates of x, , y, , c (although x, , y, , unlike c, do appear in the 
observational equations, they cannot generally be recovered well). This is not a 
serious drawback if use of the camera is limited to non-convergent photography of 
points lying close to the object plane on which the camera is focussed. In this 
situation, the recovered coordinates of the exposure stations (X^, Y" , Z^) can provide 
effective projective compensation for errors in enforced values of x, , y, , c. 
Aside from operational convenience, the major advantage of the analytical 
plumb line method is that it can, when properly employed, produce a calibration of 
radial and decentering distortion to a greater accuracy than is attainable from any 
other method. Supporting this statement is the fact that the maximum value of the 
standard deviation of each distortion function presented in Figure 7 is under one 
micrometer throughout the format. 
SIMULTANEOUS CALIBRATION AND BLOCK TRIANGULATION 
What we consider to be the most advanced of the methods of camera 
calibration developed at DBA Systems involves a process in which all parameters 
entering the projective equations are recovered simultaneously, namely: