The Mechanism

• The amplitude and phase
• the location of a point source with the same phase,
• the flux of the equivalent point source with the same amplitude.

• the equivalent source location is the centroid of the source object itself;
• The flux of the equivalent source is independent of roll angle for:
  • circular Gaussian,
  • 360-degree arc,
  • any circularly-symmetric source;
• The flux of the equivalent source is roll dependent for:
  • orthogonal Gaussians
  • elliptical Gaussians
  • segments
  • arcs
  • almost anything else

For arcs and other such asymmetric shapes,

• the location of the equivalent point source is a function of roll angle;
• but this is not a complication, because so is the flux.
• The trick is to substitute a polygonal arc, and add up the contribution from segments;
• so the output of all the equivalent-source routines contains (at least) these vectors:
  • equivalent_flux
  • equivalent source_location
  • roll angle

Convolved Sources

• Any Equivalent Point Source (EPS) may be convolved with a Gaussian, producing another Equivalent Point Source .
• This is found very simply by a multiplication, angle bin by angle bin, of the equivalent flux for the input source and the Fourier amplitude of the convolving Gausssian.
• Any EPS can be convolved with a radially-symmetric source this way (e.g. an arc with a segment)
• An EPS can also be convolved with a non-radially-symmetric source (such as an arc), but
  • the phases must be included
  • why bother?

IDL programs for Equivalent Point Sources