2.2.5. Calibrated Principal Distance or Calibrated Focal Length: An adjusted value of the principal 
distance, chosen so as to distribute the distortion in the manner best suited to the plotting 
conditions to be employed. The report shall state the way in which the calibrated principal 
distance has been chosen. 
2.2.6. Average Radial Measured Distortion: Average radial measured distortion at any field angle is 
the average of all radial measured distortions occuring at that field angle. In practice it 
will usually be adequately determined as the average of the radial measured distortions found 
for four or more points equally spaced along the circumference of a circle centred at the 
principal point of autocollimation. à 
2.2.7. Principal Point of Best Symmetry: The principal point of best symmetry is a point near the 
principal point of autocollimation chosen so that when it is used instead of the principal 
point of autocollimation as a new origin for distortion measurement it makes the largest 
absolute difference between new radial measured distortion and new average radial measured 
distortion as small as possible along each diagonal of the image format. 
Discussion 
Cameras with front-projected reseau and film flattening, based on pressure differences on both 
sides of the film, i.e. by the removal of the air between the back of the film and the magazine 
reference platen, feature a separation between image plane and reference plane. The image plane is 
defined as in other cameras by the image frame. The reference plane is no longer defined by fiducial 
marks located in the image plane but by a net of markings on the lens-element surface nearest to but 
not identical with the image plane; this surface is plane in the two known types of such cameras, 
hence, a reference plane exists in addition to the image plane. The separation of the reference plane 
from the image plane poses the question of which plane is to be used for the determination of principal 
points of autocollimation and best symmetry, the calibrated focal length and the lens distortion. 
Since the two authors differ in their preference in the selection of this plane, they will not 
recommend either. 
During the discussions at the 1952 congress, it was suggested that the theoretical distortion 
should be replaced by "the average distortion of a series of cameras of the same model". This is done 
at National Research Council of Canada with the definition of lens distortion reference data. We 
suggest the introduction of a lens distortion reference curve and the concept of determination of the 
deviations of the actual lens distortion from that curve. The latter would reduce the number of 
angular positions desirable in calibration, and would avoid extrapolation when the lens distortion 
cannot be determined to the format corners. An investigation has shown that all lens distortion 
reference curves ever accepted or proposed for acceptance in Canada can be defined well by polynomials. 
- In addition, it appears possible with the small lens distortion of modern lenses, that theoretical 
distortion and actual average radially symmetrical lens distortion for a certain lens type may not be 
nearly identical. 
The acceptance of a standard reference lens-distortion for each lens type, e.g. defined as 
polynomial using manufacturer's data, would make it possible to use the same criterion for the 
selection of the calibrated focal length and to introduce the equivalent focal length. —While the 
criterion for the selection of the calibrated focal length and the resulting positioning of the lens 
distortion curve is not a matter of importance, the introduction of the equivalent focal length, i.e. 
that focal length obtained when positioning the lens distortion curve such that a tangent on the curve 
at the origin r' = 0 is horizontal, is desirable in view of- the use of stellar calibration procedures. 
The location of the principal point of best symmetry is dependent upon the locations of the points 
used in its determination. Using only points "...along each diagonal of the image format...” may not 
do justice to calibration procedures providing a nearly-uniform distribution of points throughout the 
format as do for example - at least potentially - stellar calibration, artificial stellar calibration 
and systems calibration over a test field. More work is needed to clarify the extent of possible 
differences before reformulating this section. 
Since the selection of a principal point of best symmetry does not affect the tangential component 
of the lens distortion which is in its size related to the asymmetrical radial component, the 
elimination from a camera calibration report of the point of autocollimation and the.lens distortion 
referenced to it, as recommended occassionally, cannot be supported by the authors. 
The location of fiducial marks is at present reported by some camera calibration institutions in 
the form of distances between fiducial marks. The increasing use of comparators and analytical 
plotters makes it desirable to report the location of the fiducial marks, the principal points and the 
fiducial centre in the same image coordinate system. We feel that this system should be related to the 
film transport direction. This image coordinate system could also be used for the reporting of the 
lens distortion including the decentering distortion. 
Summing up our comments to the definitions, we suggest to replace the theoretical distortion with 
lens distortion reference data, and to introduce a distinction between reference plane and image plane, 
the equivalent focal length and an image coordinate system. 
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