neighbouring image areas being equally distant to their
respective projector. Therefore, this type of radiometric
adjustment has not been applied during the initial prototype
stage of panorama generation.
5. CALIBRATION OF CAMERA AND PROJECTORS
The calibration of the camera (Nikon with 28 mm lens) has
been performed with the help of a special test field and the
versatile bundle adjustment programme ORIENT [Kager
1989]. As the focus was set to infinite no problem is to be
expected when the camera must be reset to the calibrated
settings. The accurary of the interior orientation may be
described by the residuals in the image plane of the control
points. After modeling principal distance, location of
principal point and lens distortion the residuals were within
x5 um (i.e. about 2 mm on the projection surface).
The outer orientation of the camera is well-known because
of the exact pointing direction during image capture. The
local coordinate system is that of the planetarium (see
section 4). The projection centre is assumed to be the same
for all pictures, although minor displacements are likely. The
projection centre will probably vary within a few cm that
does not cause any troubles.
For the calibration of the slide projectors a different
approach has been chosen though the projector could have
been assumed as inverse camera and ORIENT might have
been employed in a slightly modified way. It turned out that
it is not necessary and even not feasible to perform a
complicated calibration procedure either on-site or under
laboratory conditions. The projector calibration should be
kept as simple as possible, firstly because of the limited
possibilities in the planetarium, and secondly for reasons of
an uncomplicated and easy maintenance by the
planetarium's staff. Practice showed that the very projectors
are used for different types of slide projection and are
subject to adjustments according to the requirements now
and then.
The standard test slides provided for the projector adjust-
ment for utilization of blending and fading proved to be very
accurate and offered proper means for restoring the initial
positions and settings of projectors within the required
accuracy. Visual differences by replacing one test slide by
another one are not detectable. Fortunately, the slide
holders of the projectors behave in the same accurate way.
Hence, no additional developments were necessary for a
simple and easily performable restoration process. Firstly,
test slides were inserted in each projector. Thereafter, the
lens settings and the positions of the projectors were
manually adjusted in order to cover the entire panorama
area, with small overlaps (some 20 cm) of adjacent slides
and without occlusion by the star projector. Then small,
nearly invisible reference targets were glued permantently
onto the dome surface at the projections of selected check
points of the test slide (figure 7). In case of later changes
the operator just needs to match the target positions by
inserting the test slides again and by moving the projectors
and/or by varying the focus or zoom settings without taking
care of any (obscure) calibration data and without support
by a photogrammetric expert.
112
Check Points
Figure 7: Test slide and check points
The next step deals with the determination of the interior
and exterior orientation of the slide projector. Again the
reference system for exterior orientation is the planetarium
system as defined earlier. Therefore, with the help of
theodolites the front lenses of the projectors (as
approximations of the projection centres), the reference
targets, other points of the dome (in particular the pole), and
selected points of the audience hall were measured. The
observations were adjusted as a network in a local system
with an accuracy of +2 cm. Although a photogrammetric
bundle arrangement would have been a certainly faster and
more convenient way for the determination of the required
point coordinates, the’ poor lighting conditions in the
audience hall made it impossible to take pictures of suitable
quality.
The shape and size of the dome have been assumed to be
the ideal hemisphere as originally defined by the speci-
fications of the building company and were not remeasured
in the course of this project. For the definition of the
reference coordinate system (i.e. the projection system) a
sphere was adjusted by least squares to the measured
dome points. The residuals were again in the order of
+2 cm, thus indirectly proving the correctness of the
preassumptions. By laying the Z-axis through the pole we
find the equatorial plane which will serve as XY-coordinate
plane. For the definition of the X-direction we select a
reference meridian. All geodetically determined points can
now be transformed to this new reference system (the so-
called projection system or planetarium system).
Finally the exterior orientations and interior orientations of
the projectors were computed in a simplified way. The
coordinates of the projectors’ front lenses are treated as
projection centres. We further assume that the principal
point is identical to the centre of the slide. As we know for
certain points (for instance the targeted check points) the
coordinates in the reference system and in the slide (image)
coordinate system, we are able to compute the principal
distance and the rotation angles. Since the projection of a
upper and its respective lower projector are visually
identical, we do not distinguish between upper and lower
projector any more.
6. RECTIFICATION OF PICTURES
We now know all parameters necessary for rectification that
is to be performed in the way explained in section 4. Firstly,
a regular square grid need to be defined in the slide plane
only once. For each individual projector this grid is
mathematically projected to the dome surface and then
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
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