i ATE
6
5. The size of the quantity p,
From (3) we find that
dr, d (21)
dro . v2 d.
Consequently such orientation points can be found where the distor-
tion has no influence upon the y-parallaxes.
(21) can be transformed in different ways. We find for instance
b dr, : (22)
V dra? EI dr,?
p, 0 11
But the reliability of the relative orientation due to the accidental
errors is much dependent upon the quantity d. It 1s always desirable
from this point of view to choose d as large as possible. Compare the
weight numbers of the elements of the relative orientation in [3]. The
shape of the actual distortion curve will decide how d, according to the
expression (22) has to be chosen in order to obtain p, — 0. Obviously
also the overlap will play an important role in this connection.
Due to these circumstances it might be necessary to choose d without
attention to the desired condition p, — 0. In such cases the empirical
relative orientation will be afflicted with systematic errors since it is not
possible to leave certain y-parallaxes according to expression (3) in the
orientation points. Consequently also the elevations of the model will
become afflicted with systematic errors, see expression (20) for the
assumed number and location of the control points as given in (17).
This systematic influence upon the elevations of the model can be nu-
merically corrected via the measured y-parallaxes of the model. The
procedure has been demonstrated in [4] and [5] in connection with an
adjustment of the orientation.
6. The effect of the distortion upon the aerial triangulation
Since des and dbz» according to (10) and (11) can be expressed as
direct functions of the distortion quantity p, we can easily from the
wellknown Bachmann formulae find the influence of the radial distor-
tion upon aerial triangulation strips.
From for instance [4], equations (7.2), (7.5) and (7.6) we find the
errors of the orientation elements of the n-th picture
2hn (23)
bd Pa
hn? (24)
LHbz = = d D,
AN,
