Introduction to phase correction for ALMA

One of the primary factor limiting the resolution (and to a lesser extent sensitivity) of aperture-synthesis telescopes at mm and sub-mm wavelengths are atmospheric phase fluctuations, that is, errors in the observed phase of the astronomical signal. These errors are due to the refractive effects of the Earth’s atmosphere, specifically due to the (tropospheric) water vapour. Water vapour is the main cause for these phase fluctuation due to a combination of two factors:

  1. Water vapour is poorly mixed in the troposhpere, in other words there is a large variance of total water vapour column along different lines of sight through the atmosphere

    For example, the total water vapour column toward zenith has occasionally been observed to vary at the ALMA site by as much as 50% in a space of only five minutes

  2. Water vapour has a high effective refractive index, with one millimetre of precipitable water vapour retarding the incoming radiation by about 7 millimetres of path

    The 7 millimetres of path can for example be compared to the shortest wavelength at which ALMA will observe which is 0.35 millimetres.

If these phase fluctuations are not corrected they load to loss of resolution, sensitivity and astrometric and photometric errors (see for example ALMA Memo 582).

ALMA Goals

One of the main goals of ALMA is to obtain images with resolution as fine as 0.005 arcseconds, which is about two orders of magnitude finer than is routinely achieved with current mm and sub-mm interferometers. In order to achieve this resolution, ALMA will observe on baselines which are up to 10km long. Making use of information on baselines this long will require very accurate calibration and correction of atmospheric phase errors.

The formal goal for ALMA atmospheric phase errors after calibration and correction is:

\delta l_{\rm corrected} = \left(1 + c/{1\,{\rm mm}}\right) 10\,\mu{\rm m} + 0.02
\delta l_{\rm raw}

where c is the precipitable water vapour column and the result \delta l_{\rm corrected} is the path error per antenna. If this goal is achieved then the stability of the atmosphere will essentially be eliminated as a scheduling constraint on ALMA projects; in other words, if the transparency is good enough for the target frequency then so should be the phase stability of the system after phase calibration/correction.

ALMA Phase correction strategy

ALMA is designed to achieve a high phase stability through a combination of two techniques which will be used together for the majority of observations:

  1. Fast switching

    This is essentially an accelerated version of the normal phase calibration procedure for aperture-synthesis telescopes and involves moving the pointing centre of the array to a known, near-by, and strong, point source and observationally determining the phase of the incoming astronomical signal

  2. Radiometric phase correction using 183 GHz water vapour radiometers

    This works by using a remote sensing system (a 183 GHz absolutely calibrated radio receiver – or “radiometer”) that measures the mm-wave emission from atmospheric water vapour and using this to compute the actual water vapour column along the line of sight of each telescope in the array. This water vapour estimated can then be transformed into an estimate of the path delay due to water vapour, which in turn can be applied as a phase rotation to the observed data

ALMA 183 GHz water-vapour radiometers

ALMA water-vapour radiometers (WVR) are designed to measure the 183 GHz atmospheric water vapour line. They have four double-sideband channels which are distributed from near the peak of the line out to the wings. They are illustrated in the following plot of the 183.3 GHz water vapour line (corresponding to 1 mm of precipitable water vapour) with the filters of the ALMA water vapour radiometers overlaid as hatched rectangles:

The water vapour lines at 183 GHz with the ALMA WVR channels overlaid

The ALMA water-vapour radiometers are not contained within the ALMA cryostats (they are separate un-cooled units), but via a set of relay optics they do form part of the ALMA focal plane. In fact, the WVR beam is the on-axis beam of the telescopes while the astronomical receivers are all off-axis to a small extent (see for example Table 1 in ALMA Memo 573). The design of the ALMA phase correction system is summarised in Nikolic et al 2013.