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Implications for the MMA

Under the assumption of baseline independent Gaussian residual phase errors, such as might exist if Welch's total power monitor scheme or Woody's water vapor spectrometer scheme were employed, a simpler decorrelation correction might suffice. If the residual phase errors were antenna dependent or time dependent, then one of the decorrelation correction methods described here might improve the imaging.

In the case of fast switching, the residual phase errors are equal to the square root of the phase structure function for short baselines and saturate at a value of for baselines longer than the effective switching length (Holdaway and Owen, 1995). Since the decorrelation is baseline dependent under fast switching, the decorrelation correction methods described above would be helpful.

Currently, it is believed that reasonable imaging with the 40 element mma should be possible with 30 degree rms phase errors, assuming the phase errors do not maintain some systematic value over long times. The 30 degree rms phase error per baselines specification comes from point source simulations (dynamic range = 200:1; Holdaway, 1992) and from sensitivity arguments (down to 0.87). These simulations show that the MMA will be able to make high fidelity, moderate dynamic range images of complex sources with rms phase errors of 70 degrees per baseline (the worst baselines in this simulation actually had rms phase errors of 100 degrees). The 70 degree phase errors will result in a stiff penalty in sensitivity since the decorrelation is down to 0.47 on the typical baseline. A modest resolution loss of 17% also occurs.

We propose that we have two levels of phase error specifications:

The primary phase error specification of 30 degrees rms per baseline will permit excellent imaging with almost no loss in sensitivity from decorrelation. This should be the primary goal of our phase correction schemes.
The secondary phase error specification of 70 degrees rms per baseline will still permit very good imaging with a loss of 50% in sensitivity (a factor of four in time). This secondary phase error specification reminds us that atmospheric conditions which do not allow us to meet the primary phase error specification are not lost. This will be particularly important for an instrument which is built on a suboptimal site and for observations at very high frequencies.

In Table 4 we explore what the 30 degree and 70 degree phase error specifications mean for observing on a 300 m baseline at Chajnantor in Chile without any phase calibration. We list the phase stability quartiles measured on the NRAO 300 m, 11.2 GHz site test interferometer for the month of June 1995, and then determine what frequency can be observed with 30 degree and 70 degree phase errors. Fast switching can achieve an effective calibration baseline

of about 50 m (Holdaway and Owen, 1995), and typical phase structure function power law exponents are 0.7, so the post-calibration phase errors would be

lower than the rms phase errors measured on the 300 m baseline. These lower phase errors would pertain to all baselines longer than 50 m, and would boost the peak observing frequencies given in Table 4 by a factor of 3.5.

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