Fitting Gaussians to Visibilities

UV-Plane Model Fitting (uvmodelfit)

It is often desirable to fit simple analytic source component models directly to visibility data. Such fitting has its origins in early interferometry, especially VLBI, where arrays consisted of only a few antennas and the calibration and deconvolution problems were poorly constrained. These methods overcame the calibration uncertainties by fitting the models to calibration-independent closure quantities and the deconvolution problem by drastically limiting the number of free parameters required to describe the visibilities. Today, even with larger and better calibrated arrays, it is still desirable to use visibility model fitting in order to extract geometric properties such as the positions and sizes of discrete components in radio sources. Fits for physically meaningful component shapes such as disks, rings, and optically-thin spheres, though idealized, enable connecting source geometry directly to the physics of the emission regions.

Visibility model fitting is carried out by the uvmodelfit task. The inputs are:

The user specifies the number of non-linear solution iterations (niter), the component type (comptype), an initial guess for the component parameters (sourcepar), and optionally, a vector of Booleans selecting which component parameters should be allowed to vary (varypar), and a filename in which to store a CASA component list for use in other applications (outfile). Allowed comptypes are currently point ’P’ or Gaussian ’G’.

The function returns a vector containing the resulting parameter list. This vector can be edited at the command line, and specified as input (sourcepar) for another round of fitting.

The sourcepar parameter is currently the only way to specify the starting inputs for the fit. For points, there are three inputs: I (total flux density), and relative direction (RA, Dec) offsets (in arcsec) from the observation’s phase center. For Gaussians, there are three additional inputs: the Gaussian’s semi-major axis width (arcsec), the aspect ratio, and position angle (degrees). It should be understood that the quality of the result is very sensitive to the starting inputs provided by the user. If this first guess is not sufficiently close to the global χ2 minimum, the algorithm will happily converge to an incorrect local minimum. In fact, the χ2 surface, as a function of the component’s relative direction inputs, has a shape very much like the inverse of the absolute value of the dirty image of the field. Any peak in this image (positive or negative) corresponds to a local χ2 minimum that could conceivable capture the fit. It is the user’s responsibility to ensure that the correct minimum does the capturing.

Currently, uvmodelfit relies on the likelihood that the source is very near the phase center (within a beamwidth) and/or the user’s savvy in specifying the starting parameters. This fairly serious constraint will soon be relieved somewhat by enabling a rudimentary form of uv-plane weighting to increase the likelihood that the starting guess is on a slope in the correct χ2 valley.

Improvements in the works for visibility model fitting include:

• User-specifiable uv-plane weighting
• Additional component shapes, including elliptical disks, rings, and optically thin spheroids.
• Optional calibration pre-application
• Multiple components. The handling of more than one component depends mostly on efficient means of managing the list itself (not easy in command line options), which are currently under development.
• Combined component and calibration fitting.

Example (see Figure 1):

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Type	Figure
ID	1
Caption	Use of plotxy to display corrected data (red and blue points) and uv model fit data (green circles).

 

Citation Number	1
Citation Text	Marti-Vidal et al. 2014, A&A 563, 136 (arXiv:1401.4984)