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In this family, most of the processing is done on the interferometric data
alone. Indeed, the interferometric data is deconvolved and corrected for
the primary beam contribution to obtain

(5.8) 
where
is a Gaussian of FWHM equal to the interferometer
resolution and is some thermal noise corrected for the primary beam
contribution. Two main facts are hidden in this formulation: 1) the
fieldofview of the observation is obviously limited to the observed
portion of the sky and 2) more importantly, the lack of shortspacings has
not yet been overcome and a better formulation would be

(5.9) 
The simplicity of equation is thus slightly misleading but
we will keep it for the sake of simplicity. The hybridization method
consists in combining two images (
and
) in the plane.
 Both images are first spatially regridded on the same fine grid.
 The FFT of those two images are computed, and linearly combined by
selecting the low spatial frequencies from FFT(
)
and the high spatial frequencies from FFT(
).
The transition between low and high spatial frequency
 The result is FFTed back to the image plane to produce a final,unique
image, which takes into account both singledish and interferometric
information.
The method has the following free parameters: the transition radius and the
detailed shape of that transition. To avoid discontinuity, the transition
shape is chosen to be reasonably smooth. The spatial frequency of
transition is generally chosen to the smallest spatial frequency reliably
measured by the interferometer (e.g. about 20 m for PdBI).
Next: Pseudovisibility technique
Up: Algorithms to merge singledish
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20180319