The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
It is apparent that any spectral binning will reduce the number 
of bands. The instrument is delivered usually with a default 
spectral binning pattern, defined upon the general mission 
requirements; frames are Mx B matrixes, where B <= P. 
An instrument model based on the following variables is 
introduced: 
• Noise sources (i.e. dark noise, amplifier noise, read 
out noise, photon noise) 
• Transmission of optics and chip quantum efficiency. 
• Unbinned configuration of the chip (i.e. CCD or 
CMOS) in terms of both bandwidth and 
corresponding center wavelength. 
• Other parameters (i.e. flight altitude, field-of-view 
(FOV)). 
Those variables are grouped within a typical SNR equation that 
will be later on subjected to an optimization process. 
The approximated signal equation is: 
Equation 1: Signal equation. 
S°cF* 
L*A*4*tan 2 (FOV/2)*r*T*X*ri*S 
he* N - 2 
e 
where: 
L 
is the radiance. 
A 
is the instrument aperture. 
FOV 
is the Field Of View. 
T 
is the integration time. 
S 
FWHM. 
is the spectral sampling interval, related to the 
h 
is the Planck constant. 
c 
is the speed of the light. 
N e ' 
is the number of collected electrons. 
T 
is the optical transmission. 
X 
is the center wavelength. 
is the detector quantum efficiency. 
F 
is the filter efficiency (if any). 
It is apparent that the integration time as well as the binning 
pattern can increase the signal level and then the SNR 
performances by acting directly on the variables T and S. 
The logic scheme behind the optimization tool is shown in 
Figure 3. Scientific requirements (on the extreme left) are the 
input for the instrument model based on the SNR equation; 
therefore the optimization algorithm will suggest how to 
configure the instrument in terms of integration time and 
binning pattern. 
Scientific 
Instrument Model 
. 
Optimal configuration I 
Requirement* 
n 
r 
■Spectral Resolution 
Center Wavelength 
Spatial Resolution 
SNR 
L 
Spectral Binning 
IT 
Filters 
SN'U equation 
IT range 
Frame period 
NeAI. 
Figure 3: Software logical model. 
The spectral binning is usually applied to CCD detectors, 
mostly adopted for the sensing in the visible or near infrared; 
the read out process can be in fact adjusted in a way that group 
of lines are summed up and read out at once. 
CMOS detectors, mainly used in the short wavelengths domain, 
have a different reading architecture where every pixel is read 
independently from any other one; therefore on-chip spectral 
binning cannot be applied easily. Nevertheless off-chip binning 
can be applied. 
Whenever a requirement cannot be met for any combination of 
unbinned spectral pixels then backup solutions must be adopted. 
The easiest one would be to relax the requirement until the 
performance is met. If the requirement is not met because of 
saturation then an ad-hoc filter could be design. 
Theoretically, the ideal result of such an optimization would be 
the narrowest bandwidth with the highest SNR. The narrower is 
the bandwidth, and the finest are the spectral details that can be 
distinguished. Case studies are presented in next section. 
3. CASE STUDIES 
The model has been applied to different scenarios, each one 
coming with its own requirements. The case studies are the 
following: 
A. Sensor default configuration: the instrument is tuned 
in a way that the largest variety of targets can be 
sensed with very high performances. 
B. Application driven: requirements are generated by 
considering a typical vegetation application, and the 
spectral binning pattern is generated accordingly. 
Results are shown mainly through tables; the subscript R stands 
for requirements while the C stands for calculated. 
3.1 APEX requirements 
APEX 1 , the ESA Airborne Prism Experiment is a flexible 
hyperspectral mission simulator and calibrator for existing and 
upcoming or planned future space mission. Operating between 
380 nm and 2500 nm in 300 freely configurable bands (up to 
508 bands in full spectral mode), the system offers a 28° FOV 
and 1000 spatial pixels. 
Variable frame rates and integration times allow adjusting for 
specific flying heights, speeds and patterns. The choice of 
predefined or user defined programmable binning patterns is 
offered and will be driven by the specific application and SNR 
needs. 
The general APEX requirements for a medium radiance level 
are illustrated in Table 1, indicated by the variables with the 
subscript R. 
The results of the simulations are shown in Table 1 whereas the 
final binning pattern is described in Table 2; the model results 
are indicated by the variables with the c subscript. The center 
wavelength requirements are all met with a very high accuracy 
as in shown in column 2. Thanks to high number of unbinned 
spectral bands the instrument is able to ensure most of the 
requirements with a spectral resolution less or equal than the 
required one. The performances are not satisfying at 780, 850 
and 1000 nm. The requirements at 780 and 850 can be met only 
if a dedicated filter is designed at such wavelengths; the 
instrument would need to attenuate of 20% and 39% the signal 
respectively at 780 nm and 850 nm (the filter absorpitivity is 
shown in Figure 4); it does mean that, even if the SNR 
requirement is met, the noise-equivalent-delta-radiance is not, 
therefore decreasing the resolution in distinguish between small 
quantities of chemical components into the targets. The 
requirement at 1000 nm is not met at all and it’s because we