An heterodyne system preserves the phase information, therefore
one major interest of the heterodyne detection is to allow high
resolution spectroscopy. Some interferometers working at 10m
such as ISI use heterodyne technique. However they have a low
efficiency and can only observe very bright sources.
Direct detection at optical wavelengths uses delay lines which are
well suited to the wavelengths and baseline lengths. In the mm
range, due to the low wavelengths and the long baselines, the size
of the mirrors would be prohibitive. To avoid losses due to
diffraction in the delay lines, the mirror size must be larger
than about
. For example, at
mm and assuming a baseline of
meters (which is of
medium size), the mirror should be larger than 1.1 meters. For
ALMA, assuming baselines of 14 km and a wavelength 3mm, the
required diameter goes up to 6 m. Using electronic compensating
delay is definitely easier for the purpose of mm interferometry.
Note finally that the term white fringe in the optical is similar to the fringe stopping, at mm waves.
Since is typically of order several 10 minutes at
mm, the atmospheric phase can be regularly calibrated by
reference to a nearby source close to the astronomical source.
This allows phase retrieval.
This is not possible in the optical because is of order a
few 10-100 milli seconds, and also because the angular scale over
which the atmospheric phase is coherent (the isoplanetic patch) is
too small. Instead as soon as optical arrays have three telescopes
(or more), opticians use the phase closure relations in order to
retrieve the astronomical phase.
In this sense, the phase closure relations are not applied in mm interferometry because individual visibilities are very noisy (dominated by the atmospheric noise, as explained above). Hence applying such a method does not really bring new constrains on the phase.
However a careful reader of Chapters 7, 9 and 12 should have noticed that mm interferometric data are mostly calibrated per antenna and not per baseline, the interest being to reduce the number of unknowns and therefore increase the SNR. This calibration technics implicitly assumes that the closure relations in phase and in amplitude are applied on the calibrators. This remains possible because the closure relations are indeed respected by the instrumentation.