Universität Hannover Institut für Photogrammetrie und GeoInformation Issues and Method for In-Flight and On-Orbit Calibration (only geometry) Karsten Jacobsen

Universität Hannover Institut für Photogrammetrie und GeoInformation

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

Karsten Jacobsen

Institute of Photogrammetry and GeoInformation

University of Hannover

[email protected]


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


Inner Orientation

photographic camera – fiducial marks

digital array camera – principal point F(line, sample)

CCD-line sensors

Inner orientation only for 1 CCD-

line

‘


Deformation of the bundle of rays - “systematic image errors“

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 company 1 coordinate residuals (66 images, 1484 image points)

image

deformed bundle of rays


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


Additional parameters Jacobsen (program system BLUH)

angular affinity affinity mathematic justification

mathematic tangential distortion radial symmetric distortion

radial sym. mathematic

1 2 3 4 5

6 7 8 9 10

11 12 mixture between physical and mathematical justification – parameters less correlated like with Ebner set if image points randomly distributed


radial symmetric additional parameters

Often used: r = K1* r3 + K2* r5 + K3* r7

disadvantage: highly correlated, K2 and K3 effective only in corner

Program system BLUH:

r = P9* (r3 – A*r) + P10*r*sin(r*A/(2) + P11*r*sin(r*A/(4)

9 10 11

9 - -0.36 0.24

10 - -0.32

correlation matrix

same data set: correlation K1 – K2 = 0.94

only K1 P9 – P11


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


determination of focal length and principal point

hg1 – Z1

hg2 – Z2

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

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)


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 CCD-array camera Rollei Q16

typical strong radial symmetric distortion of off-the-shelf optics


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


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


CCD-line camerasIRS-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


“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


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

Documents

Universität Hannover Institut für Photogrammetrie und GeoInformation Issues and Method for In-Flight and On-Orbit Calibration (only geometry) Karsten Jacobsen