19
It can be seen that five translations in combination
with six or seven rotations are necessary to correct for the
following influences: proper motion of stars; their radial
velocity; precession and nutation of the earth's axis; annual
and diurnal aberration; parallax; astronomical refraction;
earth rotation; and polar motion.
After computing the Z vectors for all stars measured
on a specific plate, the parameters simulating the photo-
grammetric bundle, as shown in Figure 6, are computed by a
least squares solution, allowing for weighting of the star
coordinates as well as for the corresponding plate measure
ments. The introduction of three sets of (cc,u),r) orienta
tion elements is necessary to detect and account for any
possible camera movements during the observational period,
which typically spans a period of about 20 minutes. These
sets correspond, respectively, to star images taken before,
during, and after the satellite passage. In essence each
such reduction is a camera calibration and, therefore, the
method provides, in addition to its use for satellite triangu
lation, the means to calibrate aerial cameras. It is being
used for this purpose by the Coast & Geodetic Survey in its
effort to develop a precision aerial photogrammetric trian
gulation system.
It may be of special interest to inspect the distortion
model which involves both radial and decentering distortion,
the latter in accordance with Conrady's results derived by
ray tracing. Figure 3 shows schematically the situation for
a specific radial distance d. In order to provide more
flexibility for the mathematical model, the point of origin
of these distances has been separated from the principal
point, an approach which appears especially advantageous
for the calibration of wide-angle systems. Furthermore, it
is possible to correct the astronomical refraction coefficients
when the angle of view covers an extended range in zenith
distance.
After obtaining the parameters simulating the photo
grammetric bundle it is a straightforward procedure to
reduce the measured coordinates of the satellite images to
fictitious images whose locations correspond to the principle
of central perspective.
However, before these coordinates can be introduced into
the final triangulation it is necessary to add further
corrections, the purpose of which is to apply