ALMA Memo #588 Inference of Coefficients for Use in Phase Correction II: Using the Observed Correlation Between Phase and Sky Brightness Fluctuations

By observing bright and compact astronomical sources while also taking data with the 183 GHz Water Vapour Radiometers, ALMA will be able to measure the ‘empirical’ relationship between fluctuations in the phase of the astronomical signal and the fluctuations of sky brightness around 183 GHz. Simulations of such measurements assuming only thermal noise in the astronomical and WVR receivers are presented and it is shown that accurate determination of the empirical relationship should be possible in a relatively short time. It is then proposed that the best way of using these empirical coefficients is to include them as a constraint on a physical model of the atmosphere – this allows them to be used for longer period of time, increasing the efficiency of observing. This approach fits naturally into the analysis framework presented in the previous memo, which has now been extended to implement it. The technique is illustrated via simulations and on a short data set collected at the SMA.