The overlap of the astronomical and WVR beams

The variation of the overlap of the astronomical and water-vapor radiometer beams with height in the atmosphere is investigated for the current BIMA setup, and is compared with similar calculations for OVRO and a proposed system for ALMA. The findings are that at BIMA, the 3-mm and 1.3-cm beams essentially do not overlap above a height of 1 km. The linear separation of the beams is 35 m at a zenith height of 4 km. The dominant factor in determining the beam overlap is the angular offset between the beams, with the overlap decreasing very rapidly with increasing offset. Under conditions where the dominant source of water-vapor fluctuations has a scale greater than the beam separation, the small beam overlap will generally not pose a serious problem to correcting the phase. However, we do find that the current 28-arcmin beam offset at BIMA potentially places a limit on the measurement of path length differences achievable with the APHID water vapor radiometer, although this is dependent on the height of the dominant source of fluctuations in the water vapor content. For a number of reasons, the beam separation will not be a problem for an instrument which has recently been proposed for ALMA. Finally, we also suggest that, if possible, future instruments should have beams which are offset in azimuth to minimize the error introduced by looking through atmospheric lines of sight of unequal length.