The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
Figure 9 : Histogram extraction of each column
The collection of input radiances and corresponding detectors
responses needed to compute the normalization parameters
according to relation (4) can be deduced from the normalized
cumulative histograms hcj[Z]. For each detector j, the hcj varies
from 0 to 1. Let us define the centile Z(k,j) as follows :
V q k e ]0,1 [, hcj[Z(k,j)] = q k (5)
frequency variations. The consequence is that urban-like
landscape should be avoided for calibration.
Finally, following chart (Fig 10) gives the standard deviation of
the normalization residuals for both linear and piece-wise linear
model (computed according to AMETHIST method).
The latter means that q % of all pixels in column j have a digital
number inferior to Z(kj). In relation (4), YM(k) is the average
values of Z(k,j) for the whole detectors.
2.7 Results based on image simulation
Pleiades-HR images were simulated taking into account the
geometry of the ‘rotated retina’ guidance, the cartography of
the focal plane and the radiometric characteristics of the sensor.
Several varieties of landscape such as cities, forest, agricultural
fields but also homogenous landscape such as snowy expanses
were tested.
The first result is the method sensitivity to the wideness of the
histograms. The widest they are, the most accurate are the
radiometric model. It is difficult to obtain these required
radiometric dynamics on a single-pass. This means that we
need to cumulate data from several pass, maybe 2 or 3,
targeting landscapes covering different level of radiances. For
instance, we could choose ocean for low level, countryside for
medium level, and snowy expanses for high level. In this scope,
the calibration operations remains very light compared to the
previous approach based on numerous uniform landscape
acquisitions.
The second result is that the geometrical residuals induced by
the guidance approximation create radiometric residuals on
normalized images when the landscape contains too high-
Figure 10 : normalization residuals
3. LINE OF SIGHT DYNAMIC STABILITY
ASSESSMENT THANKS TO THE STARS
3.1 Objective
The dynamic stability of the line of sight is to be assessed
during the commissioning phase. These measurements
contribute to the in-flight image geometric budget. The
expected attitude disturbances for Pleiades-HR are
characterized by very low amplitude (less than 0.25 PA pixel)
and numerous frequencies in the range [40-1000] Hz. Several
methods may be performed to estimate some of these micro
vibrations from the images but it remains difficult to achieve a
good accuracy specially for the high frequencies.
3.2 Principle of star acquisition
The idea of our method is to use the stars as references. By
definition, a star is stationary in an inertial frame. If the satellite
sensor remains pointed at the star, it will create a bright column
in the image whose straightness depends on the line-wise
behaviour of the potential micro-vibrations.
Mainly, this kind of acquisition has several operational interest.
First of all, the images are guarantee cloud-free which is very
important when a huge amount of data is required. Then, these
acquisitions are made from night-orbit without disturbing the
satellite commercial mission, given that, both commercial
acquisitions and calibration operations share the same system
resources.
3.3 Stars characteristics
For the sensor, the star is a source point characterized by its
magnitude and spectral response. From now on, we will
consider the spectral responses available in of our stellar
catalogue (HIPPARCOS) compatible with the spectral band of
Pleiades-HR panchromatic mode ([480-820] nm) and we will
make the hypothesis that the provided magnitude can be
converted in equivalent panchromatic input radiance for the
sensor. The conversion in PA digital number is performed
thanks to the numerous sensor characteristics such as the optic
