between the direction of the
thrown particles in the simulation in terms of 
and 
, and the
direction of the reconstructed shower origin coordinates in terms of
and 
. From Equ. 1.26, this angular
difference 
takes the form:
The optimization of for each detector has been done with
respect to two parameters: the ADC weighting
exponents 
and 
from Equ. 5.1,
and the parameters 
and 
which are related to
the shower penetration depth in each detector. The latter are used to calculate an angle
of incidence correction in the shower origin reconstruction (see
Sec. 5.2.2).