aspects, from instrument calibration through to 
inner orientation of the analogue imagery. 
The core of the calibration, however, is a geometric 
transformation between the digital image and the 
stage plate coordinate systems. For a full 
calibration, a radiometric relationship would also 
be included, but for the present application and also 
for on-line DTM generation, this takes on less 
significance since in general only small areas of the 
images will be used at any one time. The 
transformation falls into a local and global part 
since the pixel coordinate system moves within the 
stage system. A local stage coordinate system is 
defined with origin as the current stage position. In 
an ideal case an invariant transformation between 
this system and the digital system can be defined, 
which is equivalent to saying that the measuring 
mark, if visible, remains at a fixed position in the 
image, independent of the stage coordinates. 
The global part concerns the relationship between 
the local and the full stage systems, which by 
definition is only a translation. The accuracy of 
this relationship is to be found in the instrument 
calibration. 
3.2 S9AP Instrument Calibration 
The accuracy of the instrument calibration between 
the linear encoders and the stage coordinate system 
is influenced by the opto-mechanical design. It is a 
limiting factor of the overall calibration. 
The calibration is done as a manual procedure, 
requiring the measurement of all 25 or only 9 stage 
crosses. An affine transformation is determined by 
least squares adjustment, resulting in an RMS 
residual of 1.0 to 1.3 }im. It would be possible to 
perform this procedure automatically, but it is 
unlikely that a significant improvement to the 
accuracy level could be obtained as some 
systematic tendencies in the residuals are evident. 
3.3 Calibration of the CCD Cameras 
3.3.1 Position of the Measuring Mark 
The ideal case of the local stage and digital image 
coordinate systems remaining fixed relative to one 
another for all stage positions does not hold true on 
the S9AP. This is a consequence of the opto 
mechanical design: as the optical unit moves in the 
X direction, shifts of up to 2 pixels in the position 
of the measuring mark in the digital image are 
observed. The movement is systematic in nature 
and so can be compensated. 
The measuring mark movement is determined 
directly in an automatic procedure known as profile 
measurement. At constant intervals along the X 
axis, the position of the mark in the image is 
determined by least squares template matching, the 
accuracy of which is high (~ 0.05 pixel) relative to 
the range of the movement. 
The result is handled as a list of the original pixel 
coordinate measurements. No further modelling is 
considered necessary if the density of measurement 
is high enough; an interval of 2 mm is usually used 
on the S9AP. Corrections are determined by 
interpolation on these values. 
The shapes of the profiles are a characteristic of a 
stage’s measurement system: they remain constant 
in time. Those for the left stage of the S9AP in 
Zurich are shown in figure 2, transformed into the 
stage frame. 
-too o too 
Figure2. Profiles on the S9AP left stage. 
Microns on the stage: x above, y below. 
There is some similarity between the pattern of 
these profiles and the instrument calibration 
residuals, pointing to a possible common source of 
the observed effects. As the optical unit translates 
in the X direction, it may also be subject to very 
small movements in other directions. The 
remaining five possible movements (ie including 
rotations) will have different effects, some on the 
digital image, some on the manual measurements 
and some on both. Separation into the component 
movements would, however, be very difficult. This 
and the acceptable accuracy level of the instrument 
calibration have justified the relatively simple 
modelling employed. 
3.3.2 Calibration Transformation 
The method of deriving a transformation between 
the digital image frame and a local stage frame is 
based on a procedure used originally on the AC1 in 
Zurich (Baltsavias, 1988). One of the engraved 
stage crosses is used as a fixed point within the 
stage system; in a grid-wise fashion it is imaged 9, 
25 or 81 times, the size of the grid being slightly 
smaller than the image size projected onto the stage 
so that all of the sensor is used. The coordinates of 
the grid positions are taken relative to the central 
position, which becomes the local system origin. 
In each position, the coordinates of the cross are 
determined using a two-stage method of coarse 
then fine matching: the coarse match will give the 
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