into the outgoing field 
, also a 2 dimensional
complex vector. Therefore, the action of the instrument can in
general be
represented by a 
complex Jones matrix
[Jones1941a, Jones1941b, Jones1942]:
If the instrument can be split into successive parts, through which
the radiation travels before it reaches the bolometer, then the total
matrix is the product of the matrices of the parts. For
instance if the radiation goes first through the telescope, then through
a first horn, then through a polariser and finally through a second horn,
the total matrix of the instrument is:
If the
Stokes parameters of the incoming radiation are 
and 
, a bolometer behind the instrument receives an intensity:
where
Amplitudes 
satisfy the inequality: 
which again expresses the
fact that the instrument does not induce a polarised energy
larger than the total energy.
The
Jones matrix in terms of Pauli matrices: It is sometimes convenient to
write the
Jones matrix in terms of the Pauli matrices:
where
a can be taken real and 
is a complex vector. To keep
track of
the reality properties of the Jones matrix, which are related to the
circular polarisation induced by the instrument, we write
the components of in terms of 3 parameters 
, 
and
which are real when the Jones matrix is:
Then the Jones matrix
writes: 
Note on the reference systems: Of course, the Jones matrix
depends on the ``in'' and ``out'' reference systems which are in
general
different. For instance the ``in'' reference system is some
conventional
``Co-Cross'' reference system orthogonal to the direction of
propagation of
the incoming radiation, whereas the ``out'' reference system lies in
the
focal plane
``Co(
), (Cross(
))'' directions being parallel (orthogonal) to
the presumed direction of the polarizer.
Transformation of the coherence matrix by the instrument:
By going through the instrument, the coherence matrix 
of
radiation
is transformed to:
