PSRCHIVE user documentation: pcm

Modeling variations of instrumental response across the beam

Important Note: Currently (July 2023) the pcm functionality described on this page is available only in a development version of PSRCHIVE on the npsr-pcm branch of the git repository.

By default, pcm uses a single Jones matrices to model the linear transformation of the electric field vector along the boresight of a steerable dish. For antennas that are not fully steerable (like a dipole array), or for which the response likely varies with pointing due to geometry (e.g. Kraus-type transit telescope) or gravitational deformation, it may be necessary to model the variation of the instrumental response as some two-dimensional function of sky coordinates. A two-dimensional model of the beam can also be useful when interested in the off-axis polarization of a fully-steerable dish (e.g. Liao et al 2016).

For a steerable antenna, a single pulsar can be observed at multiple offsets within the primary beam. If the antenna is not fully steerable, modelling the variability of the instrumental response requires observations of multiple pulsars that span a variety of declinations and hour angles. Therefore, the version of pcm on the npsr-pcm branch can simultaneously model observations of more than one pulsar. This is enabled by specifying multiple files from which to choose phase bins as constraints. For example, 

pcm -c 0742-2822.DFT -c 2111+46.DFT -c 0450+55.DFT [...]

A generic model of the various possible kinds of beam variability requires a flexible model, and pcm uses a YAML-formatted file to configure such a model. The YAML file is provided on the command line using the (overloaded) -P option; for example 

pcm -c 0742-2822.DFT -c 2111+46.DFT -c 0450+55.DFT -P beam.yaml [...]

Example beam configuration

Consider a model in which both the differential gain (gamma) and the differential phase (phi) of a single-axis transformation (SingleAxis) each vary as a two-dimensional polynomial function (Polynomial2D) of hour angle (ha) and declination (dec), as configured by the following YAML file 
model:
  name: SingleAxis
  G:fit: 0
chain:
  param: gamma
  model:
    name: Polynomial2D
    ncoef: 4:3
    fit[0]: 0
  args: [ha, dec]
chain:
  param: phi
  model:
    name: Polynomial2D
    ncoef: 4:3
    fit[0]: 0
  args: [ha, dec]
Both polynomials have four coefficients (polynomial order = 3; i.e. cubic) in the hour-angle dimension and three coefficients (order = 2; i.e. quadratic) in the declination dimension. They are configured to disable fitting the constant term (the zeroth coefficient) to avoid covariance/degeneracy with the differential gain and phase of the bore-sight differential gain and phase.