HYBRID METHODS 
The various methods that have been reviewed can be employed in combi- 
nation with each other. For example, the Plumb Line Method and Se lf-Calibration 
Method can jointly be employed in a common calibration of a camera. t is merely 
necessary to: 
a) use the same approximations for those parameters common to both 
reductions; 
b) add the two systems of reduced normal equations together (after 
duly augmenting the plumb line system with zero elements to account 
for those parameters not common to both methods); 
c) solve the combined system of normal equations and iterate the above 
process to convergence. 
In this hybrid approach one may either employ plates taken separately for the two 
methods or plates on which both types of images are exposed together (i.e., plumb 
lines against a wall containing a target array). In conjunction with a horizontal 
target range it is even possible to employ horizontal lines by tightly stretching a 
set of lines radially from a common stake located at or close to the nadir of the 
entrance pupil of the lens; with this set up the slight sag of the system of horizontal 
lines will not compromise the required projective linearity. Nothing, of course, 
prevents one from also or alternatively employing vertical lines (plumb lines) in 
conjunction with a horizontal target range. 
The foregoing example illustrates but one of several possible hybrid ap - 
proaches. Most, however, would make practical sense only under very special 
circumstances. 
CONCLUSIONS 
Close-range photogrammetry affords wide ranging opportunities for 
application, innovation and experimentation. One can obtain special results 
(sometimes including calibration) by pressing into service appropriate combinations 
of plumb lines, glass grids, theodolites, mirrors, flat surface plates, spirit levels, 
micrometers, mercury pools, collimators, translation stages, reflections from spheres, 
beamsplitters, known geometrical shapes, falling bodies, ultra violet florescence, 
laser beams, particle kinematics, rigid body dynamics, stroboscopic illumination, 
and so forth. In all applications of close-range photogrammetry, however, one 
must somehow cope with the basic problem of variation of distortion with object 
distance that we have addressed in this paper. 
ACKNOWLEDGEMENTS 
The programming support provided by Bill Harp and the data processing 
support supervised by John Kenefick contributed greatly to the above investigation.