Issues and Method for In-Flight and On-Orbit
Calibration (only geometry)
Karsten Jacobsen
Institute of Photogrammetry and GeoInformation
University of Hannover
jacobsen@ipi.uni-hannover.de
Universität Hannover
Institut für Photogrammetrie und GeoInformation
Camera Calibration
Reconstruction of the bundle
of rays from the projection
center to the object based on
measured image positions
Inner orientation of sensor
Exterior orientation = location
of projection center + attitude
information
System calibration = inner
orientation + relation to
positional sensors
Universität Hannover
Institut für Photogrammetrie und GeoInformation
Inner Orientation
t‘
t
CCD-line sensors
photographic
camera –
fiducial marks
Inner orientation
only for 1 CCDline
digital array
camera –
principal point
F(line, sample)
Universität Hannover
Institut für Photogrammetrie und GeoInformation
Deformation of the bundle of rays - “systematic image errors“
deformed
bundle of rays
deformation of bundle of rays causing
“systematic image errors“ = effect in images
“systematic image errors OEEPE test block
“direct sensor orientation“
averaged image
company 2
coordinate residuals (66 images, 1484 image points)
Universität Hannover
image
company 1
Institut für Photogrammetrie und GeoInformation
Self calibration by additional parameters
Set of additional unknowns for
fitting systematic errors
Additional parameters from
Gotthard / Ebner
optimal if image points located in
Gruber points – only mathematic
interpretation
Universität Hannover
Institut für Photogrammetrie und GeoInformation
Additional parameters Jacobsen (program system BLUH)
1
angular affinity
6
mathematic
11
radial sym.
Universität Hannover
2
3
affinity
7
mathematic
5
mathematic justification
8
tangential distortion
12
4
9
10
radial symmetric distortion
mixture between physical and mathematical
justification – parameters less correlated like
with Ebner set if image points randomly
distributed
Institut für Photogrammetrie und GeoInformation
radial symmetric additional parameters
Often used: Dr = K1* r3 + K2* r5 + K3* r7
disadvantage: highly correlated, K2 and K3 effective only in corner
Program system BLUH:
Dr = P9* (r3 – A*r) + P10*r*sin(r*A/(2p) + P11*r*sin(r*A/(4p)
9
10
9
10
11
-
-0.36
0.24
-
-0.32
correlation matrix
Universität Hannover
same data set: correlation K1 – K2 = 0.94
only K1
P9 – P11
Institut für Photogrammetrie und GeoInformation
in-flight calibration of photographic aerial cameras
Bundle adjustment with self-calibration by additional parameters
-
based on the over-determination of the bundle adjustment + control point
information
1. Standard block configuration – only parallel flight
lines: affinity parameters depending upon control
points, other just by over-determination
2. Crossing flight lines – also affinity parameters just by
over-determination
 OEEPE test block “direct sensor orientation”,
image scale 1 : 5000, 1 : 10 000
Universität Hannover
Institut für Photogrammetrie und GeoInformation
determination of focal length and principal point
under standard conditions of aerial images determination of focal length
not possible
– strong correlation Zo – focal length
Z of projection centers required – possible by GPS, but problems with
GPS datum shift, no separation of GPS datum and focal length
- 2 different flying height levels required (like in OEEPE test block)
hg1 – DZ1
hg2 – DZ2
control points
Universität Hannover
GPS DATA FOR DATA SET 1
GPS DATA FOR DATA SET 2
GPS-SHIFT
STANDARD DEVIATION
X
Y
Z
SX SY SZ
.010 -.113 -.278
.008 .008 .004
-.069 .124 -.460
.014 .015 .006
CHANGE OF FOCAL LENGTH
GPS-SHIFT ABSOLUT
.039 = CORR. FOR F -> 153.383
-.094
Institut für Photogrammetrie und GeoInformation
Digital aerial array cameras
No problems with film deformation, CCD-array usually perfect flat, main
problem caused by optics + affinity of CCD (will never change)
“systematic image errors” of synthetic ZI-DMC
images (flight over test area) – small affinity
deformation, has been confirmed by following
laboratory calibration
- original distortion of 4 single optics always
respected
“systematic image errors” of CCDarray camera Rollei Q16
typical strong radial symmetric
distortion of off-the-shelf optics
Universität Hannover
Institut für Photogrammetrie und GeoInformation
Digital aerial array cameras
“systematic image”
errors of the ThermScan
camera – tangential
distortion
wide angle optics
normal angle optics – largest vector 1.7 pixels
If optics are exchanged, focal length and principal points have to be
calibrated again
focus has to be fixed, after change of focus and going back, not same inner
orientation
calibration of zoom-lenses not possible, inner optical system has no
sufficient stability, may change after shaking the camera
Universität Hannover
Institut für Photogrammetrie und GeoInformation
line scan cameras
HRSC CCD-line camera
linearity of CCD-line by
laboratory calibration
can also be calibrated
under flight conditions,
higher number of control
points or crossing flight
lines required
real problem: boresight
Universität Hannover
Institut für Photogrammetrie und GeoInformation
CCD-line cameras
IRS-1C
Pan-camera
3 combined
CCD-lines
available configuration for calibration
determined geometry
most CCD-line cameras used in space equipped with a combination of shorter
CCD-lines, calibration under flight conditions required, with combination of
images taken from different orbits reduction of required number of control points
Universität Hannover
Institut für Photogrammetrie und GeoInformation
“level 1A” space images
QuickBird
SPOT
ASTER
“systematic image errors” of the orientation of level 1A space images
- no calibration, dominated by exterior orientation
- in general sub-pixel accuracy possible
Universität Hannover
Institut für Photogrammetrie und GeoInformation
conclusion
Perspective aerial cameras can and should be calibrated under flight
conditions by bundle block adjustment with self-calibration by additional
parameters – optimal set of parameters should be used, statistical
analysis of parameters required
Stability of film-camera calibration limited, only parts stable over time
focal length and principal point can only be determined by 2 different
flying heights + GPS-projection center coordinates
Digital CCD-array cameras mainly influenced by optical distortion
CCD-line cameras used in space usually do use a combination of shorter
CCD-lines, has to be calibrated under flight conditions
Universität Hannover
Institut für Photogrammetrie und GeoInformation