Inference of Coefficients for Use in Phase Correction

Paper I

Abstract

We present a Bayesian approach to calculating the coefficients that convert the outputs of ALMA 183 GHz water-vapour radiometers into estimates of path fluctuations that can be used to correct the observed interferometric visibilities. The key features of this approach are a simple, thin-layer, three-parameter model of the atmosphere; priors to incorporate physical constraints and other information; and a Markov Chain Monte Carlo characterisation of the posterior distribution including full distributions for the phase correction coefficients. The outcomes of the procedure are therefore estimates of the coefficients and their confidence intervals. We illustrate the technique with simulations showing some degeneracies that can arise and the importance of priors in tackling them. We then apply the technique to an hour-long test observation at the Sub-Millimetre Array and find that the technique is stable and that, in this case, its performance is close to optimal. The modelling is described in detail in the appendices and all of the implementation source code is made publicly available under the LGPL.

Full text

The full text of the memo will be made available here shortly once he memo is finalised. The memo will be published in the ALMA memo series.

Final version of the memo PDF.

Software

Components

The following software components were used in producing the results presented in this memo:

Licensing/(Lack-of) Warranty/(Lack-of) Support

This software is made available under the terms of the LGPL. Please note that the files”COPYING” in each of the distribution packages have GPL listed but it is in fact LGPL which applies. This will be corrected in future releases.

Please note that there is no warranty of any sort for this software. Consult the text of the LGPL for details of the no warranty condition.

I am not funded to provide general support for this software. If you wish direct question to me, feel free to email, but please understand if I do not have the time to reply.

Raw data

This is the raw data from the SMA used in the analysis shown in Section 4 of the memo.

Paper II

Abstract

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.

Full text

Full text of the memo: PDF

Software

Components

The following software components were used in producing the results presented in this memo:

Licensing/(Lack-of) Warranty/(Lack-of) Support

This software is made available under the terms of the LGPL. Please note that the files”COPYING” in each of the distribution packages have GPL listed but it is in fact LGPL which applies. This will be corrected in future releases.

Please note that there is no warranty of any sort for this software. Consult the text of the LGPL for details of the no warranty condition.

I am not funded to provide general support for this software. If you wish direct question to me, feel free to email, but please understand if I do not have the time to reply.