16 
The two angles a and ß which establish the direction of the ray OP in two 
orthogonal planes through the camera axis can be determined from the for 
mulas 
Ax 
tan a = — 
c 
(47) 
n Az 
tan ß = —cos a 
c 
(48) 
But A x and A z are determined as differences between the measured image 
coordinates x, z of the actual point P and the image coordinates jc 0 , z 0 of the 
principal point H', the position of which was determined through the camera 
calibration procedure. The expressions (47) and (48) are therefore written 
A Aq 
tan a = 
c 
(49) 
Z — Z 0 
tan ß — cos a 
(50) 
An investigation of the geometrical quality of the reconstruction of the 
bundles of rays according to this procedure must consider not only the 
geometrical quality of the image coordinate measurements in the actual 
photograph but also the geometrical quality of the location of the principal 
point and the geometrical quality of the principal distance c. These data are 
functions of measurements and adjustments in connection with the camera 
calibration procedure and are therefore affected with regular and irregular 
errors. Very seldom, if ever, information is given about the geometrical quality 
of the elements of the interior orientation and, moreover, the camera calibra 
tion procedures in practice are not always particularly well suited for a reliable 
and realistic estimation of the geometrical quality of the elements of the 
interior orientation under actual operational conditions. The interior orientation 
is often determined under laboratory conditions only and is mainly a check 
of the geometrical quality of the lens and a determination of the relative 
position between the inner perspective center of the lens and the coordinate 
system defined by the fiducial marks. It is of course most important that all 
the elements of the interior orientation which are necessary for the reconstruc 
tion of the bundles of rays be determined under actual operational conditions 
as far as possible and in particular that the geometrical quality with which 
these data have been determined be expressed in well defined terms.The method 
of least squares is of the greatest importance for this purpose and should 
be used as a general method. In particular the basic geometrical quality of