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Next: Open and unresolved questions Up: The Generic Interferometer: I Overview of Calibration and Previous: The Generalized Dirty Image

Image and Calibration Solvers

The sky brightness and the calibration matrices now appear in the formalism on an equal basis. This is in accord with our experience that one can use interferometers to image the sky or to calibrate the interferometer.

Deconvolution can now be described as a processing of solving for the sky brightness $\vec{\cal I}\,$ . It is probably better to use a term such as Image Solver since the connection to classic deconvolution is getting harder and harder to follow. Image Solvers such as CLEAN, including all variants such as the Clark and Schwab-Cotton algorithms, and MEM, can be written in terms of $\chi^{2}_{}$ and the gradient terms described above. Thus the machinery for deconvolution can be separated from the machinery for the measurement equation. This is the essence of abstraction.

Solving for calibration is conceptually much more straightforward than imaging. Let us assume that we have a model for the sky brightness, $\widehat{\vec{\cal I}}$ . We then find those calibration matrices that minimize $\chi^{2}_{}$ . I described above, how one might imagine doing this by a simple gradient search method analogous to that using in imaging. One caution is in order: since the calibration matrices are parametrized by other free variables and since such parametrizations are likely to be strongly non-linear, it is likely that a simple approach like that advocated for imaging will be ineffective and so a more complicated algorithm may be required. Even if this is true, it is probably also true that all that is required from the measurement equation is knowledge of first and second derivatives.

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