The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
launch. These activities cover many topics gathered in two
families : radiometric and geometric Image Quality.
Radiometric activities concern the absolute calibration, the
normalization coefficients computation, the refocusing
operations, the MTF assessment, the estimation of signal to
noise ratio and also the tuning of the ground processing
parameters in order to fit the images to the users needs.
Geometric activities deal with the geometric model calibration,
the assessment of localization accuracy, focal plane cartography,
multi-spectral and multi-temporal overlapping, static and
dynamic stability, planimetric and altimétrie accuracy.
These operations require specific control of the payload and, for
some of them, dedicated guidance of the satellite platform. The
new capabilities offered by Pleiades-HR agility allow to
imagine new methods of image calibration and performances
assessment. Two of them are described here.
2. NORMALIZATION CALIBRATION ON NON
SPECIFIC LANDSCAPE
2.1 Objective
The aim of normalization is to correct raw images for relative
inter-detector sensitivities, so that a uniform landscape gives a
uniform image. Normalization residuals may cause vertical
stripes.
Where : C(j) is the dark current of detector j (L=0)
g(j) is the relative sensitivity of detector j
A is the absolute calibration coefficient
With a linear model, normalization function F can be easily
performed to get the normalized digital number Y as a function
of X :
YG,L) = F (X(j ,L),g(j ),C(j)) = [X(j,L)-C(j)]/g(j) = AL (2)
This relation shows that normalized images are proportional to
input radiances.
Dark currents C(j) are computed thanks to specific images
acquired over the oceans when the satellite is in the dark (night
orbit). To make it simple, starting from this section, only Z=X-
C will be used in the normalization model.
Because high resolution optical satellites like Pleiades-HR have
to face a lack of signal, which may move the useful signal
range towards the non-linear part of the detector response,
normalization may have to be run with a non-linear model.
Considering the computational constraint, we use for F a
piecewise linear function designed to fit the detectors relative
responses :
Y(j) = al(j) Z(j) ifZ(j)<Zs(j) (3.1)
Y(j) = a2(j) (Z(j)-Zs(j))+al(j)Zs(j) if Z(j) > Zs(j) (3.2)
Figure 4 : Pleiades HR normalization model
The calibration consists in computing for each detector j, the
triplet p(j)={al(j), a2(j), Zs(j)} used in the normalization
function F / Y(j) = F(p(j), Z(j)).
2.3 Resolution principle
In this non-linear case, we need for each detector the response
to different radiances. Then the parameters are computed in the
least-squares sense.
Given N different input radiances, let us define Z(kj) the
corresponding response of detector j where index k points to
the input radiance value. For each radiance index k, the average
response of the whole line is YM(k). The unknown triplet is
determined in order to minimize the following least-squares
criterion LSC(j):
Figure 2 : Raw image
Figure 3 : Normalized image without residuals
2.2 Radiometric model and normalization function
When the camera observes the top-of-atmosphere radiance L,
the output digital number X(j,L) delivered by detector j is
modelled by the following relation:
(1)
LSC(j) = £
fc=l
/ YM(k)-F(p(j\Z(k,j)) V
y <r(Kj) y
(4)
where cr(kj) weights can be used to balance the residuals
according to the signal level.
X(j,L)=A.g(j).L+C(j)