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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