We consider now the simplest case of a composite detector. It will be an incoherent composition of two simple ones. Thus we will take:
Remark Notice that if 
, then coherent and incoherent
compositions are indistinguishable, as in this case, with 
we have that 
For 
we have now the formula:
and to compute the complex amplitudes 
we
will use the Laplace transform method as in the case of one detector.
To this end one applies 
from the left and 
from the right to Eq. (11) and solves the resulting system
of two linear equations to obtain:
where we used the notation
and where 
stands for
The probability density 
is then given by
where 
is the inverse Fourier transform
of
By the Parseval formula we have
that 
is given by:
