Task: gpdof Purpose: Compute Degrees-of-freedom for calibration solutions. Categories: calibration GPDOF estimates the likely error in a calibration solution, by calculating the errors in the "Degrees-of-Freedom" (dofs) of an interferometer. This is useful for calibration of high-precision circular polarization observations. What GPDOF does is to determine the average calibration solution of several input solutions. Then, assuming that this average solution is "ideal", GPDoF determines the error in each of the input calibration solutions, using the degrees-of-freedom notation. Finally, GPDoF calculates the std and standard error of the derived dofs, which you can use to estimate the errors in the Stokes V of a target observation. The input calibration solutions should have been processed using the method outlined in the "Circular Polarization User's Guide" (see References below). Obviously, the more calibrators you have, the more accurate the dof estimates will be. Explanation: The degrees-of-freedom (dofs) are linear combinations of leakage (delta) or gain (gamma) errors. The advantages in the dofs over other measures of calibration consistency (eg. rms scatter in the leakages) is that the dofs actually describe how the calibration error would affect a target observation. Thus, for the dofs delta-+, delta--, and gamma--, and equatorially-mounted antennas: Stokes V error = delta-+ * Stokes I + delta-- * Stokes Q + gamma-- * Stokes U For the ATCA, the parallactic angle \chi comes, in so it isn't quite so elegant: Stokes V error = delta-+ * I + delta-- * ( Q.sin(2\chi) + U.cos(2\chi)) + gamma-- * ( U.sin(2\chi) + Q.cos(2\chi)) Note that these are the instantaneous calibration errors in a target source; for a synthesis observation, where \chi varies, the resultant error in the Stokes V image will be more complicated. GPDoF estimates the std and standard error in the dofs. These parameters be combined with the above equation for Stokes V Error to estimate the likely level of leakage errors in a target observation. If you are just using the solution from a single calibrator, calculate using the std. If you are going to use the average calibration solution (using GPComb), then calculate using the standard error. For each dof, GPDoF has an "error" estimate, which measures the variations in the calibration solutions which are NOT attributable to a dof. The physical significance of these quantities isn't even clear to the author. In general, however, if the "error" term is dominant, then un-dof-like errors are dominating the calibration eg. pure random errors, or bizzarro systematic errors. In this situation, the relationship between the dofs and the error in the target observation may break down. Um, I did mention that there are actually seven dofs? GPDoF only computes the three which affect calibration of circular polarization. There are some good reasons for this (some of the others can't easily be computed, or are time-variable), besides the obvious one that I'm too lazy. Note that GPDoF is entirely ATCAcentric. Note that the leakage errors derived from GPDoF are not the only errors in a circular polarization observation! See Equation 1 of Rayner et al, 2000. A task to estimate the effect of the dofs on a synthesis observation will hopefully become available soon. Actually, forget the "soon"... And finally, if you have consistent systematic errors in your solutions (eg. you haven't used xyref,polref in gpcal), then GPDoF will severely underestimate the leakage errors. References: For an explanation of degrees of freedom, see: Sault, R J, "The Hamaker-Bregman-Sault Measurement Equation", pp 657--699, in Syhthesis Imaging in Radio Astronomy II, 1999, eds. Taylor, Carilli,and Perley. or Sault, Hamaker and Bregman, "Understanding radio polarimetry II. Instrumental calibration of an interferometer array", 1996 A&AS, v117, pp149-159. ftp://ftp.atnf.csiro.au/pub/people/rsault/papers/polar2.ps.gz For an overview of high-precision circular polarization calibration with the ATCA, see Rayner, "Circular Polarization User's Guide", ATNF Technical Document Series, 2000, 39.3/102, http://www.atnf.csiro.au/people/drayner/Publications/ index.html#Circular_Polarization_Users_Guide For a summary of the ATCA circular polarization error budget, see Equation 1 of Rayner, Norris, Sault, "Radio circular polarization of active galaxies", 2000, v319, pp484-496 http://www.atnf.csiro.au/people/drayner/Publications/mnr3854.pdf Key: cal The data-sets containing the nominally correct polarization calibration. No default. Key: select Normal uv selection. Only antenna-based selection is supported.

Generated by miriad@atnf.csiro.au on 21 Jun 2016