plants photosynthetic 
iffected by moderate 
iectron pathway [33]. 
In contrast it has been 
its, that the parameter 
' the relative quantum 
ling water during one 
. This treatment was 
is were the following. 
Fm (5000 |j£m'^s‘^, 
mated with intensities 
t different stationnary 
he same part the leaf 
"hen the measurement 
' a few seconds were 
S. and control plants. 
: vanishes on going to 
AF/F m parameters, 
t with the PAM. This 
intensity. 
stress at distance like 
e water-stress on the 
irder of magnitude as 
ed signal is needed to 
complex target may 
tves 
is the case with our 
ppose that all leaves 
¡till expressed as the 
convolution product of F(t), by the complex back-scattered signal Dex(t). In fact, this situation is rarely 
observed, since the laser beam may be intercepted by non fluorescent materials, like stems or the ground. These 
parts may contribute noticeably to the back-scattered signal without any contribution to the fluorescence signal. 
Even when only leaves are illuminated, we have to consider that back-reflectance may contain an important 
specular component which is anisotropic. As the fluorescence emission is isotropic, an amplitude decorrelation 
between Fex(t) and Dex(t) is introduced by the different inclinations of leaves inside the canopy. 
To solve this problem we have developed a new method for the deconvolution of fluorescence by the 
back-scattering signal in the case of complex targets. In a first step we have decomposed the Dex(t) into a sum 
of identical components corresponding to the individual contribution of each leaf. The shape of the elementary 
component D(t) is obtained by measuring an auxiliary signal, generated by the back-scattered response of a flat 
target. In a second step we used these components to fit de fluorescence signal Fex(t). 
6.1. Modeiization of the back-scattered signal 
Let us model the back-scattered signal Dex(t) by a sum of elementary signals D(t). This is expressed by the 
equation: 
Dcal(t) = X a ¡-D(t-tj) 
i=1 
where aj is the relative amplitude parameter for D(t-q) and q is the time delay generated by the actual position of 
the emitting part of the target. The relative amplitude (aj) and the time origin (q) of each elementary flash are 
both fitted, using a Marquardt search algorithm. The number of hit surfaces (n) is increased until the fit does not 
improves. In the majority of situations tested, the best fit corresponds to the actual number of hit surfaces. 
In a second step we introduced Dcal(t) instead of Dex(t) in a modified version of our deconvolution program. 
Fex(t), the experimental fluorescence decay, is then fit by a sum of m exponential components: 
m 
F (t) = £ Fjexp (- i-) 
j= 1 1 , 
convoluted with each elementary flash D(t-q) of the scattering signal, determined in the previous step: 
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