For direct detection (or additive) interferometry, as in the optical domain,
an interferometer measures on-source on the baseline
:
After doing an on-off (also called the ``sky calibration''), Eq.21.1 becomes:
Where
is the visibility of the astronomical source measured
on baseline
of amplitude
and phase
.
The visibility to calibrate can be expressed by:
is the contrast which takes into account the calibration of all the system
(instrumentation + atmosphere). The photometric term is given by
(note that
and
are relatively easily measured).
The visibility
appears as a fringe contrast (which is flux calibrated), therefore
it is normalized to unity. Note finally that in the optical case
.
For heterodyne or multiplicative detection, the output of
the interferometer (correlator) gives a correlation rate
which is a dimension less number (this uses a simple correlation
between two antennas, not a ``bi-spectrum'').
The correlation corresponding to
is the term of
astronomical interest, and is related to
by:
At mm waves,
because the atmospheric thermal
emission strongly dominates with typically
(except for the Sun and bright planets).
Therefore, Eq.21.3 simplifies as:
The heterodyne technique does not allow to measure the continuum term but preserves
the phase (thanks to the use of a complex correlator, see Chapter
2). can be seen as the correlation efficiency of the
interferometer (instrumental + atmospheric). The calibrated visibilities (as defined
in previous chapters)
are expressed in unit
of flux density (Jy) while
can by considered as the photometric
term (including the photometric calibration of the atmosphere).