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Huang, Yi Dong 
When working in the theodolite mode, the theodolite part of the video-theodolite is used as the measuring device. Three 
dimensional coordinates of object points are determined by space intersection using angular readings taken from the 
theodolite rather than image coordinates from the camera. This principle of measurement is familiar to most and well 
documented. The new features added to this traditional way of measurement by video-theodolites are that the camera 
provides visual interface for easy field operation and the possibility of development into tele-operation and automation. The 
camera offers an alternative method for theodolite orientation, which is suitable for automation. This method is explained in 
Section 4.2. 
3 SYSTEM CALIBRATION 
The task of system calibration is to determine the camera interior orientation parameters and the camera-to-theodolite 
orientation parameters. The camera-on-theodolite method proposed previously by the author is most suitable for this 
calibration. This method involves capturing multiple frames of images of one or two targets set some distances away 
while rotating the telescope to various directions so that the target images are well spread in the image format. The three 
dimensional coordinates of the target in the rotating telescope coordinate system are obtainable for each of the target 
images from the theodolite readings at the moment of capturing that image and the constant target to theodolite 
distances. The photogrammetric space resection is applied to solve for the camera exterior orientation parameters in 
reference to the telescope coordinate system and the camera interior orientation parameters. For the detail of the 
camera-on-theodolite calibration method, see the author's previous papers (Huang and Harley, 1989) 
4 SYSTEM ORIENTATION 
The task of system orientation is to determine the position and attitude of the theodolite in the video-theodolite system with 
respect to other video-theodolite stations in the measurement network or with respect to a user specified object coordinate 
system. The former is termed as relative orientation and the latter absolute orientation. Either orientation can be achieved by 
means of theodolite observation or via the video camera in the system. One may think of a large variety of different methods 
based on the adaptation from geodetic surveying methods or from photogrammetry methods by treating the theodolite like a 
camera. If an EDM or GPS is used, more methods are possible. In the following, we collect a few typical methods based 
on theodolite observations and contribute with new collinearity equations that can be used for theodolite orientation via 
the mounted camera. 
4.1 System Orientation by Theodolite Observation 
Discussion is restricted to the cases with only angular observations using the theodolite. There are classifications in 
relative and absolute, with leveled or unleveled theodolites. 
4.1.1 Space resection with an unleveled theodolite. Three full control points are sighted with the theodolite, both 
horizontal and vertical angles are recorded. These angles are converted into equivalent pseudo image coordinates and 
the photogrammetric space resection method is applied to determine the six orientation parameters of the theodolite 
with respect to the control point system. This is an absolute orientation. 
4.1.2 Space resection with a leveled theodolite. As above, but now two angular parameters are set to zero. Only four 
parameters need to be determined. Thus only two control points are required to be sighted. 
4.1.3 Five-point relative orientation for two unleveled theodolites. The horizontal and vertical angular readings of a 
theodolite can be transferred into their corresponding rectangular coordinates of a pseudo photo if a focal length is 
assumed. That is the "pseudo-photo" principle of theodolite observations. By this principle we can transplant many 
methods and algorithms in photogrammetry into use for theodolites. Among these is the analytical relative orientation 
method for photo-pair, which can be used straightforwardly for the orientation between two theodolites. 
The analytical relative orientation method is based on the coplanarity condition that the two rays (or lines of sight) from the 
two theodolites to a common object point are coplanar with the base line that links the rotational centres of the two 
theodolites. An equation of coplanarity condition can be formed for each observed object point (Wolf 1983). Observing five 
points is necessary for the five relative orientation parameters. More points may be needed to observe for a better accuracy 
and blunder detection. A known distance between any two of those points or a measured base line is necessary for scaling. 
4.1.4 Three-point relative orientation for two levelled theodolites. For levelled theodolites the number of orientation 
parameters to be determined reduces from five to three. Thus only three points are necessary to be observed. As is seen, 
there is a trade-off between levelling the theodolites and observing two more points. If possible, the former is preferred 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 391