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Imaging and Image Velocity Definitions - INVERT and VELSW

A few comments are in order when using the imaging task, invert, to create spectral cubes (more information on invert can be found in Chapter 13):

• To conserve space, invert produces a single beam dataset for all planes of a cube. For it to do this, the cell size of each plane is scaled with frequency. For the small fractional bandwidths typical in spectral-line experiments, this affect is small. Additionally the coordinate-handling software accounts for this scaling when converting between pixel and celestial coordinates.

  For one beam to be valid for all planes, invert usually insists that the u-v coverage for all planes is the same. That is, invert usually insists that no channels of a spectrum are flagged before that spectrum can be used for imaging. This is required to ensure each image plane has the same point-spread function.

  This rule can be too restrictive for some uses. For example if deconvolution is not envisaged or if one channel (the birdie channel?) is always bad. invert's slop keyword allows the rule to be relaxed. The slop keyword takes two values. The first is the fraction of channels that invert will tolerate as being bad before a spectrum is rejected. The default is 0 (i.e. the entire spectrum is rejected if even a single channel is bad). A value of 1 indicates that invert will accept a spectrum provided at least one channel is good. The second value dictates the `replacement' method, i.e. what value to assign for the flagged channel, when imaging with flagged channels. Possible values are `interpolate' and `zero'.

  Interpolation replacement would be appropriate if there are a small number of channels that are always bad, and that you wish to replace them with something for, essentially, aesthetic reasons. Note that the interpolation is simple-minded linear interpolation.

  Surprisingly zeroing the flagged correlation also has its advantages. When zeroing, the true beam (point-spread function) will be channel dependent and will differ from the computed beam. Consequently deconvolution should not be attempted. invert attempts to scale each plane so that the true beam has a peak value of 1. This scaling is correct only for natural weighting when no tapering is used (i.e. sup=0 and fwhm unset). If this is the case, the channel images can be astrophysically useful. For other weightings and taperings, the peal value of the true beam will not be exactly 1 - the flux density scale will no longer be what is conventionally understood by Jy/(dirty beam). Additionally the beam peak value can vary from plane to plane, and so the flux density scale may not be comparable between planes. Be warned.

• invert checks that the velocity of visibilities gridded onto a particular plane remains constant. The velocity will not remain constant if the observatory does not Doppler track and velocity linetype is not being used. If the velocity of visibilities gridded onto a plane varies by more than 10% of the plane separation, invert gives a warning.
• Regardless of the line parameter, invert labels the velocity axis using the radio definition. However it is possible to switch the labelling of this axis to be either frequency or velocity using the optical definition, or indeed back to velocity using the radio convention. Note that for the optical velocity definition, the velocity separation between planes is not constant. The velocity increment stored in the header is that which corresponds to the reference frequency. The task velsw performs this task. Its inputs are fairly simple:

  VELSW
  in=line.map	Input image.
  axis=optical	Label as velocity using optical definition,
  axis=radio	or label as velocity using radio definition,
  axis=frequency	or label as frequency.