These are gefined as
Closure phase (triple phase): arg( V12*V23*conjg(V13) ) Closure amplitude (quad amplitude): abs( (V12*V34)/(V14*conjg(V34)) ) Triple amplitude: abs( V12*V23*conjg(V13) )**0.3333 Quad phase: arg( (V12*V34)/(V14*conjg(V34)) )
The closure phase, quad phase and closure amplitude should be independent of antenna-based errors, and for a point source should have values of zero phase or unit amplitude. The triple amplitude is independent of antenna-based phase errors (but not amplitude errors), and for a point source is a measure of the flux density.
The task works by averaging the quantites that are the argument of the abs or arg function. These are always averaged over the selected frequency channels and over the parallel-hand polarizations. Optionally the averaging can also be done over time and over the different closure paths.
CLOSURE also prints (and optionally plots) the theoretical error (as a result of thermal noise) of the quantities. Note this assumes a point source model, and that the signal-to-noise ratio is appreciable (at least 10) in each averaged product.
amplitude Plot the amplitude quantity (the default is to plot phase). quad Plot the quad quantity (the default is to plot the triple quantity). avall Average all quantities from different triangles together. Note the theoretical error estimates are incorrect when using options=avall. notriple Plot data from all quantities on a single plot. rms Plot theoretical error bars on the points. The error bars are +/- sigma.The following give control over calibration to be applied to the visibility data before the triple correlations are formed. Note that applying phase calibrations does not affect the closure phase!
nocal Do not perform gain calibration. nopol Do not perform polarisation calibration on the data. nopass Do not perform bandpass calibration on the data.