Phase calibration and water vapor radiometry for millimeter-wave arrays

Correcting for the fluctuations in atmospheric path length caused by water vapor is a major challenge facing millimeter- and submillimeter-wave interferometers, and one that must be overcome to obtain routine sub-arcsecond resolution. Using the model for the power spectrum of phase fluctuations developed in Lay (1997), the existing technique of phase referencing to a bright calibrator object is analysed. It is shown that the phase errors after calibration have comparable contributions from both the target and calibrator measurements. The technique of water vapor radiometry, where the amount of emission from water vapor in the beam of each antenna is used to estimate a path correction, is also examined. It is found that there are two levels on which a correction can be made. The simplest corrects just the fluctuations within each on-source period; the calibration requirements for the radiometers are modest, and this partial correction can give a substantial improvement in the resolution and coherence time of an interferometer. The atmospheric fluctuations on longer timescales remain uncorrected, however, and are significant. To remove these, a full correction is required, which measures the change in the path difference that occurs when moving between the calibrator and the target, in addition to the on-source fluctuations. Since there can be a large difference in air-mass between the calibrator and the target, measuring this change requires that the radiometers have the same response to a given column of water vapor to within similar to 0.1% Two possible methods of achieving this very stringent limit are outlined. For reasonable observing conditions at 230 GHz, it is predicted that the effective atmospheric ''seeing'' (the apparent smearing of the sky brightness distribution due to the atmosphere) is improved from 0.6 '' (phase referencing every 25 minutes) to 0.3 '' (phase referencing and partial radiometric correction). A full radiometric correction would, in principle, restore perfect seeing.