and 8.6 ¡um. Using Bartlett’s test we test the hypothesis that they are equal. The
test gives an almost significant difference among them. A difference can be
explained in the following way. The standard error of unit weight includes the
errors of the co-ordinates of the test object. This test object is not the same for
the three pairs, as the grid has been in three positions in every exposure. The
positions are determined by the glass scale of the A6 and the setting may have a
standard deviation of some hundredths of a millimeter. The movement may not
be straight and this introduces errors in the co-ordinates. If the movement is not
perpendicular to the glass plate this is compensated for by the parameters (prin
cipal point and nadir point) in the adjustment. Such lack of perpendicularity
will result in systematic errors in the parameters. This problem has been treated
in [30].
8.2.6. Exterior Orientation
The elements of exterior orientation are given in the co-ordinate system of
the test object although this is not of particular interest. But the relative orien
tation of the cameras and the base (see below) for every pair of pictures can be
computed from the exterior orientation. This will be discussed a little.
Testing the variation of orientation elements, it must be remembered that
they are correlated. This correlation is sometimes very strong e. g., between
principal point and rotations, between camera constant and distance of photo
graphy. This holds for vertical photography and examples are given in Tables
1—3. For oblique photography, which is the case here, the relations are diffe
rent. In Table 8 a correlation coefficient matrix of the parameters is shown
as an example. In this case we want to test the constanc of the interior and re
lative orientation and the base. As the elements are correlated in all combina
tions there is no simple test available to study the variation between pictures,
and at the same time take account of the algebraic correlation. Therefore,
each orientation element is studied separately, i. e. we use the corresponding
marginal distributions for the tests. The variance between the pictures is deter
mined from observations that are independent of each other. The variance wit
hin pictures is determined from the separate standard errors of the correspon
ding element. The values of the elements, their standard errors and the analyses
of variance are shown in Tables 11 and 12. The test between picture pairs 1 and
2 is introduced as the same aperature, f:45, was used.
8.2.7. Interior Orientation
In this case the interior orientation has been defined by five elements, x 0 Jo
c as «5. Radial distortion and camera constant are inseparably related to each
other, because a small change in the camera constant can be converted to a
radial displacement. This is evident from the relation