Test of convergence

Step 7 in the above scheme is another crucial step where we determine if the process has converged. The final product of these iterations will be the model image and the corresponding normalized visibilities ( $X_{ij}=V_{ij}^{Cor}/V_{ij}^{model}$). The Goodness-of-fit of a straight line to $X_{ij}$ as a function of uv-distance $r=\sqrt{u^2+v^2}$ can be used to detect convergence. E.g. a possible measure of convergence can be $\chi^2=\sum_{ij}\vert X_{ij}(r) - (m*r+F)\vert^2$ where $m$ and $F$ should be close to 0.0 and 1.0 and $\sqrt{\chi^2}$ should be equal to the RMS noise respectively. All the three numbers together will probably provide a robust measure of convergence. A gridded version of $X_{ij}$, which is smoothed by the gridding convolution function, is probably more appropriate for this test.

Perhaps, a more fundamental test of convergence is to check the number of closure relations (both amplitude and phase closure) that are satisfied to within the noise level. This can be checked by computing all the possible closure relations from $V^{obs}/g_i g_j^\star$.