Basic Information on gpdof

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.