by leveling. The discrepancies between the photogrammetric and ground
surveys of the check points were computed by the DOT and are summarized
in Table 2. Separate breakdowns are given for targets and monuments, for
the latter were not triangulated directly, but, as mentioned above, were
computed from the coordinates of the targets and the offset measurements.
It is seen from Table 2 that RMS errors for targets at plate
scale are 5.4, 3.9 and 2.4um in X,Y and Z respectively; for the monuments
the corresponding figures are 4.0, 2.4 and 1.6um. The relatively higher
accuracies obtained for the monuments are consistent with expectations.
because errors in the coordinates of the two offset targets are essentially
averaged in the reduction leading to the coordinates of the monument (the
error in the offset measurements themselves are of no practical significance).
With optimal geometry (i.e., monument equidistant from offset targets and
subtending a 90° angle), the theoretical improvement in accuracies for the
horizontal coordinates of the monument over those of the offset targets is
about 25 percent; for the vertical coordinate it is about 30 percent. This,
then, constitutes still another advantage of the offset target method.
Because of the smallness of the sample of check points (especially
for vertical coordinates) one should not draw overly strong conclusions from
the above results. In particular, the extraordinarily good results for
vertical accuracies must partially be regarded as fortuitous because they
exceed theoretical expectations by almost a factor of two. The analytical
error propagation performed in conjunction with the photogrammetric tri-
angulation and carried through the computation of the positions of the
monuments yielded the following results: targets, 04,0, « .19 to .24 ft.
(3.3 to 4.2um at plate scale), o7 = .21 to .26 ft. (3.7 to 4.5 ym);
monuments, 04,0, x .14 to .19 ft. {2.4 to 3,3 um, c4/s .13 to 18 FL. (2.3
to 3.1 um). Except for the overly optimistic outcome for vertical coordi-
nates, results from the check points are seen to be fairly consistent with
theoretical expectations. One rather firm conclusion to be drawn from the
Atlanta Project is that the potential superiority of the super wide angle
camera with regard to accuracies of vertical coordinates can indeed be
realized through the use of the bundle adjustment with self-calibration.
INVESTIGATIONS OF FLATNESS OF FILM PLATENS
As mentioned, the hypothesis that the large correction for
radial distortion could be explained by thermally induced changes in the
lens itself became untenable as a result of the outcome of the Atlanta
Project. Accordingly, an alternative explanation had to be sought.
Renewed consideration was then given to another possibility that had
earlier been dismissed, namely, curvature of the platen. To the degree
that such curvature is radially symmetric, it is projectively equivalent
to radial distortion. The DBA Reseau Platen used in both the Vermont and
Atlanta Projects had been designed to be at least as sturdy as the original
Zeiss platen which it was to replace. As measured, following completion of
its fabrication, it was extraordinarily flat with an rms departure from a
best fitting plane of only 1.5um. Following the Vermont Project the platen
was remeasured and found to have changed its figure somewhat to an rms
departure of 2.6 um — still exceptionally good and totally inadequate to
explain the recovered radial distortion. Following the breakdown of the
‘thermal’ hypothesis resulting from the Atlanta Project, the platen was
once again measured. This time, its rms departure had deteriorated to
5.3um and its actual figure was decidedly concave. This still was not
enough to explain the matter under investigation, but it did establish a
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