Tropospheric phase calibration in millimeter interferometry

We review millimeter interferometric phase variations caused by variations in the precipitable water vapor content of the troposphere, and we discuss techniques proposed to correct for these variations. We present observation s with the Very Large Array (VLA) at 22 and 43 GHz designed to test these t echniques. We find that both the fast switching and paired array calibratio n techniques are effective at reducing tropospheric phase noise for radio i nterferometers. In both cases, the residual rms phase fluctuations after co rrection are independent of baseline length for b > b(eff). These technique s allow for diffraction-limited imaging of faint sources on arbitrarily lon g baselines at millimeter wavelengths. We consider the technique of troposp heric phase correction using a measurement of the precipitable water vapor content of the troposphere via a radiometric measurement of the brightness temperature of the atmosphere. Required sensitivities range from 20 mK at 9 0 GHz to 1 K at 185 GHz for the millimeter array (MMA) and to 120 mK for th e VLA at 22 GHz. The minimum gain stability requirement is 200 at 185 GHz a t the MMA, assuming that the astronomical receivers are used for radiometry . This increases to 2000 for an uncooled system. The stability requirement is 450 for the cooled system at the VLA at 22 GHz. To perform absolute radi ometric phase corrections also requires knowledge of the tropospheric param eters and models to an accuracy of a few percent. It may be possible to per form an "empirically calibrated" radiometric phase correction, in which the relationship between fluctuations in brightness temperature differences an d fluctuations in interferometric phases is calibrated by observing a stron g celestial calibrator at regular intervals. A number of questions remain c oncerning this technique, including the following: (1) Over what timescale and distance will this technique allow for radiometric phase corrections wh en switching between the source and the calibrator? (2) How often will cali bration of the T-B(rms) - phi(rms) relationship be required?