Wide-Field Imaging. Michael Bietenholz. Based on a lecture by Rick Perley (NRAO) at the NRAO Synthesis Imaging Workshop. Field-of-View Limited by Antenna Primary Beam. Simplest wide-field problem: source is larger than primary beam
Based on a lecture by Rick Perley (NRAO) at the NRAO Synthesis Imaging Workshop
ATCA observations of HI in the SMC. Dirty mosaic, interferometer only.
Deconvolved mosaic, interferometer only. Stanimirovic et al. (1999).
Total power image from Parkes.
Interferometer plus single dish feathered together (immerge). Stanimirovic et al. (1999).
The unit direction vectors
is defined by its projections
on the (u,v,w) axes. These
components are called the
Direction Cosines, (l,m,n)
The baseline vector b is specified by its coordinates (u,v,w) (measured in wavelengths).
The (u,v,w) axes are oriented so that:
w points to the source center
u points to the East
v points to the North
When N2D > 1,
2-dimensional imaging is in trouble.
Table showing the VLA’s and MeerKAT’s distortion free imaging range (green), marginal zone (yellow), and danger zone (red)
Where we define a modified visbility:
2-D Cuts through our 3-D (l,m,n) space
Upper Left: True Image. Upper right: Dirty Image.
Lower Left: After deconvolution. Lower right: After projection
To phase center
Dirty ‘beam ball’
2-d ‘flat’ map
where Z = the zenith distance, YP= parallactic angle,
and (l,m) are the correct coordinates of the source.
H = hour angle
d = declination
f = array latitude
d = 90
e ~ lcm (tan Z)/20 (inbeamwidths)
B = maximum baseline
D = antenna diameter
Z = zenith distance
l = wavelength
N2D ~ Bq2/l ~ lB/D2
For each facet,
the entire dataset must be
phase-shifted for the facet center,
and the (u,v,w) coordinates
recomputed for the new orientation.
Nf ~ 2lB/D2
or twice the number of planes needed for 3-D imaging.
Total Number of Facets/w-planes
Cornwell, Golap, Bhatnagar