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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
2.4 Linear motion system 
The satellite is moved in two mutually perpendicular directions 
using a servo-controlled linear motion system. The positioning 
and repeatability of the servo system needs not to be the most 
accurate because the satellite position and orientation are 
determined solely using photogrammetry. The satellite cannot 
be allowed to move when images are captured, so the stability 
of the servo system is very important. All dead motion and 
mechanical gaps should be eliminated in order to get reliable 
final results. 
A calibrated servo system, with an accuracy of a few 
millimetres, makes it possible to automatically measure the 
satellite targets from their predicted positions in images. 
3. CALIBRATION 
The measurement system requires careful system calibration to 
get final measurements in a correctly scaled, orthogonal 3-D 
coordinate system. Calibration of the whole system consists of 
the camera calibration, laser calibration, and the calibration of 
the servo system. 
3.1 Camera calibration 
The outer and inner camera systems can be calibrated 
simultaneously using a free-network bundle adjustment 
(Haggrén and Heikkild, 1989). Approximate values for the 
unknown parameters can be obtained using the projective 
adjustment method developed by I. Niini (2000). Normally, the 
absolute scale of the coordinate system is fixed by observing 
the end-points of a known scale bar and by using the known 
distance as a constraint in the adjustment. More information 
about the calibration method can be found in (Niini, 2002). 
Here, due to the scale difference between the two systems (the 
inner system size is less than one tenth of the outer system) 
only one scale bar or distance cannot be used easily. A 
calibration tool containing targets for both systems is 
appropriate. À scale bar with four collinear targets can be used. 
It contains two larger targets in the ends of the bar, and two 
smaller ones close to each others in the middle of the bar. The 
first large target and the first small target are made 
recognisable by adding a smaller index target close to them. 
All targets are white circles in a black background, and they 
can be searched and measured automatically from the images. 
Since the mutual distances of the calibration targets are known 
precisely, e.g., from a coordinate measurement machine, the 
bar can be used to get the systems into a common coordinate 
system and scale. During this part of calibration, the satellite is 
kept at a fixed position, preferably in the middle of the 
measurement area. The targets in the calibration tool are then 
observed from the images so that both systems can see their 
corresponding targets simultaneously. This is made in several 
different positions and orientations. The image coordinates of 
the satellite cover targets are also measured in this fixed 
position, and taken in the adjustment, so that the satellite base 
position also becomes calibrated and can be used later as a 
reference. 
485 
To strengthen the calibration of the outer system, additional 
observations (say 50-100) of the calibration bar are made well 
distributed in the entire measurement volume. The calibration 
of the inner space is also strengthened using another small 
calibration tool, scale of which may be known but needs not to 
be known. It is then only constrained to have a constant, but 
unknown length. 
The overall calibration can be further strengthened with a 
precise calibration plane that contains several unknown 
circular targets for both systems. This plane can be placed in 
several different positions and orientations below the satellite, 
and both systems can observe their dedicated targets. 
Corresponding points can be determined using the epipolar 
geometry obtained from previously determined calibration 
parameters. The image observations of the plane points enter 
the adjustment, and the corresponding 3-D points are 
constrained to lie on the same plane. The calibration also gives 
the relative positions of the plane targets. Then this calibration 
plane can be used to recover an accidentally lost calibration 
between the two systems. 
3.2 Satellite reference position 
The calibration volume has to include the area where the 
satellite targets can move. Additional calibration points are 
generated easily by moving the satellite over the entire linear 
motion area, simultaneously registering the image coordinates 
of the satellite targets. These image coordinates are added into 
the adjustment, along with the constraints that keep the 
relative geometry of the satellite targets constant in all 
measured satellite positions. Thus, the relative geometry of the 
satellite targets will be adjusted using image observations over 
the entire calibration space. 
3.3 Laser calibration 
The laser light planes are calibrated in a simple manner after 
the satellite camera system has been calibrated. It is only 
required that the visible 3-D laser lines are measured from at 
least two distinct object planes. The laser planes are then 
obtained from these 3-D lines. The intersection of the two laser 
planes is the 3-D line that is projected down as the laser cross 
in the object surface. 
After the laser calibration, it is possible to calculate where the 
laser cross locates in any known plane in the satellite 
coordinate system. Using the similarity transformation between 
the satellite base position and current position, the position of 
the laser cross is also known in the outer coordinate system. 
Optionally, the information from the laser planes can be used 
to constrain the measurements, because the visible laser line 
segments have to lie on the same known plane of the 
corresponding laser. 
3.4 Servo system calibration 
The servo system has its own coordinate system and scale. The 
axes may not be exactly straight, or may not have the same 
scale. There may also be minor discontinuities in certain 
positions along the axes, especially when the axes are made 
from several racks. The calibration of the servo system is based 
on a polynomial model for the servo coordinates.