21.2 Getting the fringes

For details about both techniques, we invite the reader to read Chapters 2 and 4. We only focus here on some basic points.

21.2.0.1 Additive detection versus Heterodyne technique

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 10$\mu$m such as ISI use heterodyne technique. However they have a low efficiency and can only observe very bright sources.

21.2.0.2 Electronic compensating delay versus delay lines

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 $\sqrt{B \times \lambda}$. For example, at $\lambda = 3$mm and assuming a baseline of $B=400$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.

21.2.0.3 Phase calibration

Since $t_o$ is typically of order several 10 minutes at $\lambda \sim 1.3$ 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 $t_o$ 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.

21.2.0.4 Phase closure relations

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.