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 <1 GHz. 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 100 microns 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.
View a pdf version of ALMA Memo #503.
Last modified: 2004-09-08