ALMA Memo 503 Antenna position determination: Observational methods and atmospheric limits

We discuss the accuracy to which ALMA antenna relative positions can be determined via astronomical observations of phase and delay toward multiple strong calibrators. We show that delay induced phase gradients across the bandpass can be used to resolve turn ambiguities so that accurate delays can estimated from the phase. At low frequencies this demands only modest stability of the bandpass phase. For this and other reasons we argue that 90GHz is the best frequency for position calibration observations. The proposed specification for short time instrumental phase stability is adequate for antenna position determination. We discuss in detail the effect of the wet troposphere and derive how position errors scale with baseline length in the case of single-baseline calibration. We then generalise to a full calibration of the whole array. It is found that the resulting position errors between two antennas is the same as if these two antennas participated in there own single baseline calibration. We find that because of the geometry and the need to solve for instrumental phase that even on short baselines the rms error on the vertical or z-component is twice as large as for the x and y components. In addition for > 1km baselines while the x and y rms errors rapidly saturate the z components rms errors continue to increase. Some uncertainly in estimating errors on long baselines comes from our lack of knowledge of the outer scale of turbulence at the site. The effects of systematic gradients in the zenith wet or dry delay and methods of calibration are briefly considered. We propose that when in the intermediate ’zoom’ array configurations an initial calibration of the moved antennas is made in late afternoon lasting 30minutes. Later in the early hours of the morning, when phase stability is best, we propose a 30 60 minute calibration of the whole array. Because of the need to apply phase corrections for antenna positions retro-actively even continuum data should always be stored in spectral line mode with channel widths < 1GHz. Final pipelining for the highest dynamic range imaging may have to wait for up to 12 hours until good antenna positions are obtained. With good ’a priori’ positioning of antennas on pads and/or the acceptance of delayed pipelining as the norm after reconfiguration the first late-afternoon calibration might be avoided. For the smallest configurations we expect that the troposphere will not be a limitation on achieving the proposed goal of 100μm relative positioning on all baselines. For larger configurations we estimate that while most baselines will achieve the target accuracy those baselines to recently moved antennas will have much larger errors. Further work is required to understand the effects of this on imaging and astrometry.