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Method xp [mm] yp [mm] c [mm]
interior orientation -0.009 (20.011) -0.409 (20.011) 20.281 (40.019)
w/radial -0.141 (40.004) -0.434 (40.004) 20.354 (40.006)
w/radial and decentering -0.152 (20.008) -0.337 (20.009) 20.371 (40.006)
Table 1: Results of the pre-calibration of the Hawkeye camera: interior orientation
parameters (principal point xp, yp, focal length: c) were derived by different versions of the
bundle adjustment. The values in the brackets give the estimated precision.
Zu G
| 20 Az
|
| A
| e- =
le EL peer
IG N grid
Xp
XL YLo4CL 9 local grid coordinate system,
X, Y, 2 eet image coordinate system.
Figure 3: Calibration of the offset vector in the image
coordinate system.
All measurements in the airplane were done in the hangar
with the airplane strapped to the floor in a position which
comes close to the one it would assume during flight. A test
grid was laid out beneath the aircraft to define a local
coordinate system (Xy, Yr, Zı) in which the offset vector
AO was determined. First, an image of the grid was
captured by the Hawkeye M-3 camera in its mount. This is
possible as the short focal length of the digital camera has a
large field of view and thus creates a sharp image of the grid
even at this short distance of about 1.5 m. Then, a number
of theodolite intersections were measured to locate the GPS
antenna's phase center G, its vertical projection onto the grid
(G^), and a number of grid points on the floor. All
coordinates were determined in the local grid system.
Additionally, we marked a point G' at the bottom of the
airplane, which is used to initialize the GPS survey of the
mapping flight over a known target with a plumb. The
image coordinates were measured in the grid images.
Together with the interior orientation from the pre-calibration
they were used to compute the perspective center (O) and the
camera attitude in the grid system. The offset AO] is
defined as the vector from O to G. By applying the rotation
matrix it is transformed into the image coordinate system (3).
AO - RL: AOL (3)
with: AQ... offset vector in the image system,
AO, offset vector in the local grid system,
Ry rotation matrix of the captured image.
During our first test flights the offset vector was
calibrated as AO = (1.695, - 0.269, 1.434).
3.3 Time Delay of the Shutter
During our first test flights we found that there is a delay
between the exposure time recorded by the computer and the
time when the shutters actually opened. This is due to the
fact, that the PC sends a signal to the Hawkeye and records
the GPS time of this signal. However, the exposure is
somewhat delayed due to the electronics transmitting the
signal. This delay can be as large as 1 millisecond, which
corresponds to an offset of 5 cm if the aircraft is traveling at
a velocity of 160 km/h.
There are two ways to calibrate this delay At: first, one
can try to measure it with an oscilloscope and a light
sensitive diode behind the shutter. This would tell us, how
long the camera takes to respond, once the signal was
transmitted from the PC. The other approach would try to
correct for At by an additional block-invariant parameter in
the bundle-solution. The problem is that this parameter is
fully correlated with the principal point coordinate xp (if the
camera's x-axis is parallel to the flight line). This would
only be a problem, if a self-calibration is computed during
aerotriangulation.
4. OPERATION OF MAPCAM AND POST-
PROCESSING
For the test flights conducted with the first version of the
MapCam system we used a Cessna 207 aircraft. It had a
hole and camera mount in the bottom, so that we only had to
install a small adapter for our Hawkeye camera. The
installation of all equipment takes about half an hour, not
including the calibration which was done separately. Once a
basic operation test was performed in the hangar, the
airplane was taxied to a known target on the runway of the
airport. By using a plumb line the horizontal offset between
this position and the GPS antenna is determined, the vertical
offset is already known from the original calibration. By
this procedure the GPS survey is being initialized. From
this time on the pilot must try to maintain continuous satellite
lock, which is possible if the airplane is not tilted more than
109 during the flight. We managed to avoid cycle-slips
during both test-flights which lasted more than one hour
each. After the flight the known point was revisited to close
the survey.
Once airborne, the operation of MapCam is straight
forward: the operator simply hits a button to start capturing
images. This can be done at time intervals larger than one
second, or at a constant, user-defined overlap. In the latter
case MapCam uses on-line navigation data from GPS to
determine the airplane's speed and relative position changes.
After the flight, post-processing of the GPS
measurements is completed by combining observations of
base and rover stations. Either pseudo-ranges or phase
measurements can be analyzed, dependent on the
requirement. As a result we obtain the flight-lines with the
images attached as attributes (figure 4).