Huang, Yi Dong 
  
for two reasons. The first is that modern electronic theodolites have precise self-correction device for inclined vertical 
axes within some range. In these theodolites, the magnitude and the direction of the inclination of the vertical axis are 
determined and corrections added to each theodolite reading. The accuracy is believed to be higher than that of 
determination with five-point orientation method. The second reason is that levelling is one of the requirements to 
ensure a theodolite to work properly. 
4.1.5 Theodolite relative orientation with reciprocal pointing. The relative orientation between two unleveled 
theodolites can be fulfilled by pointing the theodolites at each other's centres and an object point. If the theodolites are 
levelled, on object point is needed. The scale factor is determined by measuring a distance between one theodolite and 
the other or the object point. Kyle (1988) has described some reciprocal pointing methods. Reciprocal pointing is 
generally easier if only horizontal readings are required. In this case, the theodolites need to be leveled and need to point 
at one object point. 
4.2 Theodolite Orientation via the Mounted Video Cameras 
All the methods mentioned above use theodolite observation to fulfil orientation among theodolites. For a calibrated video- 
theodolite system, it is possible to perform orientation for the theodolite via the mounted video camera. There are two 
different ways of performing this orientation. One involves capturing only a single image from each theodolite station, the 
other uses multiple images taken from each theodolite station with the camera pointing at different directions. 
In the single image method, the camera captures an image on each theodolite station of sufficient control points or tie 
points. The exterior (absolute or relative) orientation of the image, namely Rew, Tew in Eq.2-8, Eq.2-9 are determined 
using the standard photogrammetric algorithms (space resection or relative orientation). The theodolite readings are 
taken at the moment the image is captured so as to evaluate R. The theodolite orientation R, and T, can then be solved 
using the following equations which are derived from equations (2-8,9). 
R: = Rew R.' RT 9 4-1 
TET. RIRT. 4-2 
The shortcoming of this method is that when a narrow angle camera is used, the weak camera orientation will lead to 
weak theodolite orientation and, in turn, poor orientation for other images taken from that theodolite station. 
The multiple image method is possible to avoid this shortcoming of the single image method by capturing multiple images at 
various theodolite directions to cover wide spread control points or tie points. This method may use the collinearity 
equations derived below. 
5  COLLINEARITY EQUATIONS WITH THEODOLITE ORIENTATION PARAMETERS 
Suppose that there is an object point P and that its corresponding image point is p. According to the collinearity principle the 
coordinates of these two points and the image projective centre O, in the theodolite coordinate system have the following 
relationship (see Section 2 for the notations): 
Xp) - Xqo; 7 5(Xq,, -Xq5)) 5-1 
where s is a scale factor. Substituting from Eq.2-2 - Eq.2-6 the above equation turns to 
Re (Xy-T:)-RT.=sRR,x' 5-2 
u X= Xo 
v ERR, Y- Yo 5-3 
w f 
  
392 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.