Issues and Method for In-Flight and On-Orbit Calibration (only geometry)

1. 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

2. 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 Camera Calibration

3. t‘ Inner Orientation photographic camera – fiducial marks t CCD-line sensors Inner orientation only for 1 CCD-line digital array camera – principal point F(line, sample)

4. 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“ Deformation of the bundle of rays - “systematic image errors“ image averaged image company 2 company 1 coordinate residuals (66 images, 1484 image points)

5. 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

6. 4 5 1 2 3 Additional parameters Jacobsen (program system BLUH) angular affinity affinity mathematic justification 7 8 9 10 6 mathematic tangential distortion radial symmetric distortion mixture between physical and mathematical justification – parameters less correlated like with Ebner set if image points randomly distributed 11 12 radial sym. mathematic

7. 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 11 9 - -0.36 0.24 10 - -0.32 radial symmetric additional parameters same data set: correlation K1 – K2 = 0.94 correlation matrix only K1 P9 – P11

8. Bundle adjustment with self-calibration by additional parameters • based on the over-determination of the bundle adjustment + control point information in-flight calibration of photographic aerial cameras • 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

9. 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) determination of focal length and principal point hg1 – DZ1 hg2 – DZ2 control points GPS-SHIFT STANDARD DEVIATION X Y Z SX SY SZ GPS DATA FOR DATA SET 1 .010 -.113 -.278 .008 .008 .004 GPS DATA FOR DATA SET 2 -.069 .124 -.460 .014 .015 .006 CHANGE OF FOCAL LENGTH .039 = CORR. FOR F -> 153.383 GPS-SHIFT ABSOLUT -.094

10. No problems with film deformation, CCD-array usually perfect flat, main problem caused by optics + affinity of CCD (will never change) Digital aerial array cameras “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 CCD-array camera Rollei Q16 typical strong radial symmetric distortion of off-the-shelf optics

11. “systematic image” errors of the ThermScan camera – tangential distortion Digital aerial array cameras 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

12. 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

13. IRS-1C Pan-camera 3 combined CCD-lines CCD-line cameras 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

14. “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

15. 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 conclusion