applied. The principal distance can then be calculated from the 
simple geometry of similar triangles once the distances between 
the imaged targets, the targets themselves and the camera to 
target have been measured. The only correction which must be 
applied is for lens distortion and one presumes this has been 
previously computed by a method such as the plumb-line 
technique. 
If the camera and lens are being calibrated using the self- 
calibration technique, then from a 3-D target array and/or a 
convergent multi-station configuration, a value of c will be 
produced from the adjustment. 
The effect of not considering radial distortion when attempting 
to solve for c has been demonstrated by Webb (1987). With a 
simple non-metric *point-and-shoot" Canon AF35M camera he 
reduced the rms value for the plate residuals and the uncertainty 
in c by a factor of two by considering only the Kj term. When 
radial distortion is ignored, the image locations of points in the 
control field will all be affected by varying amounts of radial 
distortion and the derived value for c will, consequently, be in 
error or, at least, have a poor precision. 
For much work in close-range photogrammetry, an accurate 
knowledge of the principal distance is not warranted. Given 
accurate 3-D control and an estimate of c, the bundle 
adjustments with AP's will derive the “best” value for that 
configuration. In situations where stereophotogrammetry is 
being employed on objects such as building facades which are 
essentially planar, control points around the periphery will be 
used to scale the model for the object space and an a priori value 
for c will not be significant. As discussed earlier though, an 
allowance for lens distortion must be applied in this case. 
6. FIDUCIAL MARKS 
One of the distinguishing features of non-metric cameras is, 
often, their lack of fiducial marks. A commonly used technique 
to overcome this shortcoming is to compute pseudo fiducial 
corners of the image frame by digitising some points along the 
edges of the frame during the interior orientation procedure. 
Lines describing the frame edges are calculated and their 
intersections computed. The corners of the frame are not 
directly digitised as they often appear “furry” in nature. 
Analytical stereoplotters which cater for the small format market 
possess software to aid this process (for example, the ADAM 
Technology MPS-2). 
The next stage of the interior orientation is, usually, to calculate 
an affine transformation to define an image co-ordinate system. 
In this paper, the use of the affine transformation is questioned, 
in light of several recent tests undertaken by the author and also 
the experience of Robson (1992). Lens distortions, and film 
unflatness effects have their largest impact at the frame edges. 
To “blindly” apply an affine transformation to frame corners 
which have not been observed, but only calculated, is to 
transfer and distribute spurious image corrections across the 
entire frame. 
A much more satisfactory approach is to apply a conformal 
transformation which does not make the assumptions which are 
inherent in an affine. Recent tests on non—metric camera data 
have shown improvements up to two—fold in the final values for 
object co-ordinates, even in situations with four slightly 
convergent camera stations and eight photographs. Robson 
(ibid) similarly shows the affine transformation to produce 
inferior results, especially in situations of weak geometry. 
The case against the use of the affine transformation with non— 
metric cameras can be argued on the grounds of “over— 
parameterisation”. The level of redundancy arising from four 
fiducials is too low, given the assumptions made in the 
derivation of those corner fiducials which may not have been 
observed but computed. With tests done on metric cameras 
with well-defined fiducial marks, no such problems have 
arisen. The misuse of the affine transformation with non- 
   
metric cameras is one more error source which awaits the 
inexperienced user of close-range photogrammetry. 
Several authors report the addition of fiducial marks to non- 
metric cameras. Warner and Carson (1991) detail the addition 
of V-shaped notches to the edge of the frame of a Pentax 645 
camera and also along the small cylindrical rollers at the edge of 
the format area. A weakness in their system was the projection 
of the V-shaped fiducials a distance of 0.7 mm from the roller 
to the image plane. The authors concluded that fiducial marks 
cut into the frame edge were more precise and suited to affine 
transformations. However the fundamental difficulties which 
can arise from the affine transformation were noted and they . 
suggested the incorporation of a reseau plate would allow for 
the determination of film deformation over the entire format 
area. 
Chandler, Cooper and Robson (1989) experimented with, 
respectively, local bi-linear and second order polynomial 
techniques for interpolation from either the surrounding four 
reseau crosses or across the entire format. The best 
improvement in object point co—ordinates was achieved by the 
use of an interior orientation comprised of a local bi-linear 
computation based on the surrounding four reseau points. 
In this way, local out-of-plane film deformations were 
constrained and systematic errors not introduced into the 
remainder of the image co-ordinates. 
7. CONCLUSIONS 
The formulae pertinent to the close—range calibration of cameras 
and lenses has been detailed. The techniques of self-calibration 
and plumb-lines has been discussed and their strengths and 
weaknesses evaluated. The influence of lens distortions on a 
range of close-range photogrammetric camera-object 
configurations has been explored and advice presented to new 
users of photogrammetry as to how these error sources may be 
eliminated or otherwise recognised. 
Experimental results which indicate the relevance or importance 
of parameters such as the offsets of the principal points, the role 
of fiducials and methods of interior orientation were discussed. 
The influence of film deformations, including unflatness, were 
examined and the weaknesses caused by over-parameterisation 
when the affine transformation was used for interior orientation 
without fiducial marks explained. 
8. REFERENCES 
Brown, D.C., 1971, "Close-Range Camera Calibration", 
Photo. Eng., 37(8):855-866. 
Brown, D.C., 1984, “A Large Format Microprocessor 
Controlled Film Camera Optimised for Industrial 
Photogrammetry”, Int. Arch. Photo., 25(A5):29 pages. 
Chandler, J.H., Cooper, M.A.R. and Robson, S., 1989, 
" Analytical Aspects of Small Format Surveys Using Oblique 
Aerial Photographs”, J. Photo. Science, 37:235-240. 
Donnelly, B.E., 1988, “Film Flatness in 35 mm Cameras”, 
M.Surv. Thesis, The University of Newcastle, New South 
Wales, 2308, 116 pages. 
Ekelund, L., 1956, “Some Investigations into Distortions of 
Air Cameras”, Int. Arch. Photo., Stockholm, 12(4). 
Elfick, M.H., 1986, “MPS-2 — A New Analytical 
Photogrammetric System for Small Format Photogrammetry”, 
Int. Arch. Photo., 26(2):8. 
Fraser, C.S., 1982, “Film Unflatness Effects in Analytical 
Non-Metric Photogrammetry”, Int. Arch. Photo., 24(5):156- 
166.