Atmospheric Dispersion and Fast Switching Phase Calibration

2001/12/19

The differential atmospheric phase of an interferometer has an approximate linear variation with frequency up to about 300 GHz. However, near absorption lines, and especially in the sub-millimeter wavelength atmospheric windows where the absorption lines are very strong and always near, the assumption of a non-dispersive atmosphere breaks down markedly.

We present simulations performed with the ATM atmospheric transmission model (Pardo et. al, 2001), tailored to the specific observing conditions at the Chajnantor site and we propose specific observing strategies to employ for the ALMA telescope. While the *absolute* wet and dry dispersive phase (ie, the part of the phase which deviates from the phase which is linear with frequency) can be very large through the atmosphere, the *differential* dispersive phases (ie, the difference in the dispersive phases above two antennas paired in an interferometer) are much smaller. We find that the differential dry atmospheric dispersion is essentially zero at all frequencies of relevance to the ALMA for the expected pressure fluctuations within the area covered by the interferometer. The differential wet dispersion can be large enough to be of concern in the 350, 400-500, 650, and 850 GHz windows.

In fast switching, we expect to observe a calibrator source at 90 GHz and scale the phase solutions to the target frequency. If time dependent wet and dry phase errors occur, ALMA has a potential problem because the wet and dry phases will scale differently with frequency in the sub-millimeter windows. Separation of the phases into wet and dry components may be possible, but this sounds very messy and uncertain, requiring multi-frequency calibrator observations or associated radiometric measurements and good atmospheric modeling. If dry phase errors are negligible and the phase errors can be split between electronic and atmospheric components, then the frequency-dependent phase scaling factor can be determined by a model such as ATM to accurately account for the dispersion. As we do not have a good handle on the magnitude of dry phase errors, we cannot estimate the success of such a strategy. A worst case scenario would be to assume that the dry phase errors are larger than the dispersive phase. By using the ratio of the frequencies to scale the phase solutions to the target frequency, we correct for the dry errors, but miss the differential wet dispersive phase. The differential wet dispersive phase will manifest itself as some fraction of the phase errors which are just not calibrated. These residual phase errors will be larger during unstable atmospheric conditions, at the edges of the transmission windows, and on longer baselines. During the 10th percentile atmospheric stability conditions, on baselines of 1000 m, the fast switching residual phase will be dominated by the uncompensated dispersive phase at the edges of the sub-millimeter windows (ie, at frequencies where the transmission is less than 50% of the peak transmission for that window). This will markedly affect the ability of fast switching to correct atmospheric phase errors for sub-millimeter observations. Longer baselines could be accommodated by observing during better conditions or by observing near the window center where the dispersive phase is close to zero. If dry phase fluctuations are smaller than the dispersive phase, as will almost certainly occur far from the window centers, the dry phase can be ignored and a correct accounting for the dispersive phase from a transmission model such as ATM can be applied.

If radiometric phase correction were used, a differential dry delay could be quite damaging for sub-millimeter observations. However, if the dry phase were very small, the differential dispersive phase could be calculated from transmission models and applied to correct the phase more perfectly, just as in fast switching with a negligible dry term.

View a pdf version of ALMA Memo 404.

Download a postscript version of ALMA Memo 404.

* Last modified: 2002-01-02*