ured grid. The grid itself had been tested with a special procedure, see
reference [4], and had proved to be very accurate. The standard error
of the coordinates of the grid points is of the magnitude 1 micron. The
statistically determined errors of the measurements of image coordina-
tes in the autograph A 7 evidently also contain the errors of the instru-
ment itself. Therefore the standard error of unit weight of the image
coordinate measurements which will be demonstrated below would be
somewhat lower if the image coordinates had been measured in a more
accurate instrument, for instance in a modern stereocomparator. The
measurements in the precision single image comparator SIP were rather
inconvenient since the format of the instrument was too small for the
size of the negatives. Therefore the measurements in this instrument
had to be made in sections followed by coordinate transformations.
2.5 The computations
The computations are founded upon numerical projective relations
between two planes. Therefore, first the geodetic coordinates of the
control points had to be transformed into one and the same horizontal
plane as seen from the exposure station. For these very simple calcula-
tions the elevation differences of the control points and the radial dist-
ances of the points from the nadir point of the exposure station are of
importance.
Since the camera was well adjusted in position and direction at the
photography only comparatively small corrections to the preliminary
data of the elements of the external orientation are to be expected. The
determinations of these corrections is demonstrated in the grid method
see reference [3]. According to this method the determination of the
corrections is performed with redundant observations and in accor-
dance with the method of least squares.
In particular the radial distortion is determined from points which
are located upon circles around the center point. Also the center point
is included in the individual point combinations. According to Fig. 2
there are ten circular point combinations, nine of which consist of five
points and one of nine points. The latter one is particularly intended
for the determination of the standard error of unit weight of the image
coordinate measurements. The number of redundant coordinate obser-
vations is in this case 12.
We will here briefly demonstrate the formula systems which have
been used for the actual computations.
In reference [3] the complete formula systems for the combinations
of five points are demonstrated.
[For the three translations dx , dy , dz of the perspective center and
for the three rotations dx, de and do of the camera we have with the
notations of reference [3] the following corrections:
EE LEE EE ESI
=”
E M RM TV ET SS SE:
=
