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ALMA Memo # 535

Simulation Series of a Phase Calibration Scheme
with Water Vapor Radiometers for the Atacama Compact Array


We have carried out a series of simulations of a phase calibration scheme for the Atacama Compact Array (ACA) 1 using water vapor radiometers (WVRs). In the proposed scheme the WVRs devoted to measurements of tropospheric water vapor content are attached to the 12-m antennas. The excess path length (EPL) due to the tropospheric water vapor variations aloft is fitted to a simple two-dimensional slope using WVR measurements. Interferometric phase fluctuations for each baseline due to the turbulent water vapor are obtained from differences of inferred line-ofsight EPL and subtracted from the interferometric phases for the correction. We have estimated residual root-mean-square (RMS) phases for 30-m baselines after the correction for various values of WVR measurement errors, wind velocities, coefficients and power-law exponents of the spatial structure function of the EPL, and extents of the distribution of the WVR instruments. From the simulations we found that, for WVRs with no measurement errors, the proposed calibration scheme shows an excellent performance for all tropospheric conditions, and that a simple relationship between the residual RMS phase and the extent of the WVR distribution exists: the closer the extent to the interferometer array is, the more effective the calibration scheme will be. When WVR measurement errors are added, although the RMS phases are still improved in unstable tropospheric conditions (50-percentile conditions), the proposed calibration scheme may not be needed in good conditions (25-percentile conditions). We found that, if the performance of the WVR achieves the expected level (a factor of about three better than the current ALMA WVR specification), the proposed scheme is quite promising for the ACA. In addition, we provided a simple statistical model to explain the simulation results. The simulations and the following analyses with the statistical model show that radio seeing data with baselines of 10?30 m is important to determine the optimum extent of the WVR distribution around the interferometer array. Monitoring of the radio seeing as well as the WVR measurement errors during observations will be useful to judge whether pre-calibrated data with the proposed calibration scheme should be used in the following ACA data reduction or not. For observations at lower elevations made by the ACA, the expected performance of the WVR is also important.

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Last modified: 2005-09-19