7.3.1 Phase referencing by a nearby point source

This is the standard, traditional way to calibrate the phases with current interferometers. A point source calibrator is typically observed for $\ensuremath{T_\mathrm{\scriptscriptstyle I}}$ (a few minutes) every $\ensuremath{T_\mathrm{\scriptscriptstyle C}}$ (20-30 minutes). One fits a gain curve to the data observed on the calibrator, this gain curve is an estimate of the actual gain curve $\mbox{\ensuremath{g_\mathrm{\scriptscriptstyle C}} }_i(t)$. This enables removing most long-term phase drifts from the observation of the target source.

7.3.1.0.1 Decorrelation

It can be shown that the decorrelation factor for a given baseline is approximated by:

$$f \sim 1-\frac{1}{2}\int_{-log{2.5 \ensuremath{T_\mathrm{\scriptscriptstyle I}} }}^\infty{\nu P_\phi(\nu) d(\log{\nu})}$$ (7.22)

The decorrelation is fundamentally a baseline-based quantity: it cannot generally be expressed as a product of antenna-based factors. Both the target source and the calibrator are affected, so amplitude referencing will correct for decorrelation. However, the amount of decorrelation will vary from an integration to the next, so that the amplitude uncertainty is increased.

7.3.1.0.2 Phase referencing

The slow component of $\mbox{\ensuremath{g_\mathrm{\scriptscriptstyle C}} }_i(t)$ to be calibrated out is sampled at intervals $\ensuremath{T_\mathrm{\scriptscriptstyle C}}$ so that only variations with periods longer than $2\ensuremath{T_\mathrm{\scriptscriptstyle C}}$ can be followed. However one fits a slow component into the data points so one is sensitive to errors due to the presence of the fast component: the fast component is aliased into a slow component. It is essential to fit a curve that does not go through the points.

7.3.1.0.3 Fast phase referencing

One may reduce $\ensuremath{T_\mathrm{\scriptscriptstyle C}}$ as much as possible to remove a larger part of the atmospheric fluctuation spectrum. Time scales of the order of 10s may be used, at the expense of:

• the time efficiency is decreased (relatively more time is spent on the calibrator resulting in a larger overhead)
• caution must be taken than the time may become comparable to the time it takes to water eddies to drift along the apparent distance between source and calibrator.

7.3.1.0.4 Water vapor radiometry

A radiometry system may be used to monitor the emission of water vapor at a suitable frequency in front of all antennas (dedicated instrument or astronomy receiver; water line or quasi continuum). The fluctuations in the path length can be of a few % of the total path length due to water vapor.

The fluctuations of the water emission are converted into fluctuations of path length by using an atmospheric model (see lecture by M. Bremer, Chapter 9). In principle one could hope to correct for all phase fluctuations this way. However limitations due to receiver stability, to variations in emission from the ground, and to uncertainty in the determination of the emission to path length conversion factor have the consequence that it is not yet possible to consistently correct for the variation of path length between the source and the calibrator.

So far this method at IRAM/Plateau de Bure is used only to correct for on-source fluctuations. Its main effect is to remove the decorrelation effect due to short-term phase fluctuations, improving the precision of amplitude determination.