The need to correct phase fluctuations

Variations in the column density of water vapour along the line of sight to the different ALMA antennas cause variations in the interferometric phase resulting in:

• Reduced spatial resolution
• Reduced sensitivity
• Pointing errors and problems with flux calibration

ALMA's target angular resolution at mm-wavelengths is a factor of ~50 smaller than the current leading mm-interferometers; 0.005 arcsec compared to the 0.25 arcsec reached at the SMA, Plateau de Bure interferometer and CARMA. However, Table 1 demonstrates that without phase correction methods, this target resolution will be unattainable.

Table 1: Measured phase fluctuations on 300-m baselines at Chajnantor alongside the maximum (uncorrected) usable baseline and seeing with these fluctuations at 345 GHz, from [Evans03].

RMS fluctuations/deg	Maximum usable baseline/m	Seeing/"
5.3	52	2.40
2.5	181	0.69
1.2	625	0.20
0.7	1691	0.07

Figure 1 illustrates some of our work (published in ALMA Memo 582 see also the publications page) modelling the effect of atmospheric phase fluctuations on ALMA's sensitivity. In the series of images as the magnitude of the phase fluctuations increases (from left to right) you can see the degradation in resolution and peak flux.

Figure 1: Variation in the apparent point-source peak intensity (2, 0.98 and 0.45 Jy from left to right) and size on increasing the magnitude of the atmospheric phase fluctuations (from left to right)

ALMA Phase Correction Strategy

ALMA will use two methods to correct phase fluctuations:

1. Fast-switching
   • the antennas switch to a nearby point source rapidly (every few sec) to get a reference phase measurement
   • corrects fluctuations on timescales of tens of seconds
2. Water vapour radiometry (WVR)
   • measure the water emission above each antenna
   • hence infer the change in path length to each antenna
   • correct the phases (in the correlator, or off-line)
   • corrects rapid fluctuations on timescales of ~1 second

ALMA WVRs

The ~66 ALMA WVRs (to be mounted on every 12-m ALMA antenna) take measurements of the sky brightness around the 183-GHz atmospheric water line (see Figure 2). From the shape and strength of the line profile the amount of water vapour along the line of sight of any particular antenna can be determined.

Figure 2: Filter design centres and bandwidths of the production ALMA WVRs with the 183 GHz water vapour line also shown (in red).

The Cavendish Astrophysics Group in partnership with the Onsala Space Observatory built two prototype WVRs for the ALMA project. Previously, Richard Hills' group at the Cavendish had been the first to demonstrate the feasibility of WVR around the 183 GHz line, using the single-baseline JCMT-CSO interferometer (see [Wiedner01]). The two prototype ALMA WVRs had distinct designs:

• WVR1 Correlation radiometer
  • Sideband separation, pseudo-correlation design
• WVR2 Dicke radiometer (basis of production WVRs)
  • Double sideband, chop-wheel at about 20Hz

although both WVRs had integrated cold and ambient calibration loads. These two prototypes were installed on two SMA antennas for testing in 2006 (see below for results).

Figure 3: Prototype WVRs being readied for installation on the SMA.

WVR Testing at the SMA

The tests with the prototype WVRs on the SMA were mostly on a 200-m baseline, while the antennas were tracking a bright quasar. This allows an estimate of the phase fluctuations, independent of the WVR data. Some sample results for the variation in path are shown below in Fig. 4 (for further information on the SMA tests see Bojan Nikolic's 2007 talk, available here). The graph shows the variation in path length over an hour-long observation, as predicted by the interferometer (in red) and the radiometers (in blue). On subtracting the estimated path from the WVRs, the fluctuations reduce from a sigma of 207 micron to 62 micron.

Figure 4: Sample result from the SMA WVR tests. The variation in path over an hour, estimated from the interferometer phase (in red) and WVRs (in blue) is shown.

References