Model fitting is the oldest way of analyzing interferometer data. It
was effectively used in the times where the coverage of the
plane was too scarce to even think of creating an image by Fourier
transform. One assumes a simple source model depending of a few
parameters (source position, flux, size) and fits the visibility
function of that model to the visibility data. Of course one may use
a linear combination of several source models since the Fourier
transform is linear. This is performed using the GILDAS task UV_FIT. The result may be displayed with the procedure PLOTFIT. Both are available in the panel ``Interferometric UV
operations'' from the GRAPHIC standard menu.
Table 14.1 gives examples of a few models and their visibility functions. For source models with a circular symmetry, the visibility function is split into a radial dependent amplitude and a phase factor which depends only on the source position.
Some sources are actually so simple that this method may be used to a good accuracy (fig. 14.6).
Quite often this method is used for sources that are unresolved or not well resolved at a given frequency; for instance a SiO maser may consist of several point-source components at different velocities. Fitting a point source in each channel one derives a ``spot map'' (figs 14.7,14.8).
For a source with central symmetry the task UV_CENTER determines the source position by using only the phases. Alternatively the task UV_FIT may be used to fit the amplitudes and phases at the same time, or e.g. to simultaneously fit a pair of sources.