The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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diameter, spectral bandwidth, time of integration, detector 
quantum efficiency, TDI lines number and electronic gain. In 
an inertial acquisition scheme the star is seen by only a few 
lines of the TDI matrix as shown in Figure 11. 
Figure 11 : Source point seen in the PA TDI device 
The number of pixels illuminated in the matrix depends on the 
modulation transfer function of the instrument whose level is 
expected to be 0.10 at Nyquist frequency. Given that for a N 
line TDI matrix, a single line response is only 1/N of the total, 
and that for a source point most of the signal is concentrated on 
one or two lines, the integrated signal of the star is rather low. 
The expected maximum digital number in a PA image versus 
the magnitude of the input star is given in Figure 12. 
Expected maximum digital number 
Star magnitude 
Figure 12 : Maximum digital number versus magnitude 
The radiometric signal-to-noise ratio required to use the ‘star’ 
pixels is about 10. Considering the sensor radiometric 
performance, a digital number level higher than 25 LSB is 
required for those pixels. The corresponding magnitude limit is 
4 according to Fig 12. 
3.4 Dedicated star guidance 
The satellite guidance has to fulfil the main condition which is 
that the star remains stationary long enough in the TDI matrix 
to ensure a dynamic measurement. However, the target 
acquisition guarantee depends on the satellite pointing accuracy. 
Thanks to many dedicated onboard equipments, Pleiades-HR 
performs a pointing accuracy better than 30 micro-radians in a 
30° off-nadir cone. For specific off-nadir viewing such as those 
needed to point the stars, this accuracy is expected to be better 
than 100 micro-radians. A dedicated pitch steering is to be 
found, on one hand to scan the sky with an excursion higher 
than the satellite pointing accuracy and, on the other hand, to 
approach the inertial pointing scheme. The pitch angular rate 
for a standard acquisition is about 10000 micro-radians/s. A 
slowdown of this rate by 200 fulfils our conditions. A 50 micro 
radians/s pitch rate allow to scan the 100 micro-radians pointing 
accuracy in 2 seconds. The 13 lines TDI matrix defines a 13 
micro-radians viewing angle which is scanned in 0.26 seconds. 
This time of acquisition corresponds to about 2600 PA image 
rows, which is sufficient for our measurement. Moreover, the 
20 available lines of the TDI device could be used, after a 
specific payload control, to increase the observation period. 
The total acquisition duration, including image recording and 
payload tranquilization is less than 4.5 seconds. About 10 stars 
may be shot per night-orbit so that a hundred acquisitions is 
achievable per day without disturbing the nominal satellite 
mission. 
3.5 Star image simulations 
The dedicated star guidance has been implemented through PA 
image simulations. Radiometric parameters were set to : 
• MTF at Nyquist frequency = 0.10, 
• signal-to-noise ratio for a 100 W/m 2 /sr/pm radiance=150 
• TDI device monitored with 13 lines 
• Compression rate = 2.5 bits/pixel 
The simulations cover a set of input star magnitude and a set of 
line-wise and column-wise direction micro-vibrations. The 
magnitude are in the range [0,4]. Each micro-vibration is an 
addition of several sinusoidal signals. A temporal shift is 
introduced between the two directions of the micro-vibration. 
As an example, simulated microvibrations with less than 0.20 
prad cumulative magnitude have been used to assess the 
measurement accuracy. 
An example is given in Fig 13 for a magnitude 0. 
3.6 Micro-vibration measurement 
For each row, as shown on Fig 13, the star line-wise absolute 
location can be given by the digital number profile barycentre, 
generally close to the profile peak. This approach gives relative 
stability wathever the instrument PSF symmetry : the only 
required hypothesis is the PSF temporal stability. 
The barycentre profile measurement accuracy depends on the 
digital number level of the peak closest neighbours. Obviously, 
this level is related to the star magnitude. Anyway, the measure 
is always noisy. The noise can be filtered by a low-pass filter 
(as shown on Fig 14 for a magnitude 1) given that we want to 
preserve frequencies lower than 1000 Hz (expected micro 
vibrations).