The Jones matrix describes how the components of the radiation field
transform as they go through the instrument. Using equation
(9), one can construct the ``Mueller matrix'' 
[Mueller1948] which tells us how the Stokes parameters transform:
From equations (4) and
(9),
it is easy to compute the elements of the Mueller matrix from the Jones matrix:
It is easily seen that matrix 
is real, as it
should, the Stokes parameters being real parameters, and that the
Mueller
matrix is symmetric when the Jones matrix 
is hermitian.
Expressions
of the general Mueller matrix in terms of the elements of the Jones
matrix
and in terms of its development on the Pauli matrices (equations
(7) and (8)) are given in appendix
A.
The amplitudes 
which appear in Eq. (5) are in
fact the
elements of the first row of the Mueller matrix:
as can be verified by comparing equation (6) with
general expression (24) of the Mueller matrix in appendix
A.