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Mosaicking
Mosaicking is a particular case of wide-field imaging: The user wishes to
observe a given field of view larger than the primary beam size with a
sensitivity as uniform as possible.
The targeted field (which area is
, define by the user) can be
divided in a number of independent resolution elements or independent
(primary) beams
. We have:
 |
(25) |
where
is the area of the primary beam. It is linked to the telescope
full width at half maximum (
) by
 |
(26) |
The 0.8 factor represents the truncation of the beam at 20% of its
maximum, which is performed during the imaging process.
Note that
is not the number of pointed positions that are observed
for the mosaic (
, see below).
For the sensitivity estimation we assume a standard sampling of targeted
field and the on-source time is equally divided between the independent
primary beams
in the targeted field of view. To first order, we
thus yield:
 |
(27) |
 |
(28) |
There are several subtleties in this computation.
-
must be larger than 2 times
(below this we advise to
use the track sharing mode with two independent fields).
- The processing (imaging and deconvolution) of a mosaic implies a
division by the primary beam of the interferometer. As the primary beam
is to first order a Gaussian decreasing to zero, this implies that the
noise of the mosaic will vary over the field of view. In particular it
increases sharply at the edges of the field of view. In other words,
Eq. 27 does not apply to the mosaic edges!
- The cycling of the pointings of the mosaic should ensure Nyquist
sampling of the observed field of view. This implies that there is an
important redundancy between the pointings, contrary to track sharing
where the sources are supposed to be fully independent on the sky. For
instance, when mosaicking with a hexagonal compact pattern, each line of
sight will be observed by 7 contiguous pointings, except at the mosaic
edges. It can thus been shown that the number of mosaic pointings,
, is related to the number of independent elements through
 |
(29) |
for a correctly sampled mosaic. Equation 27 is only valid
inside a correctly sampled mosaic.
- The pointings of a mosaic must be observed in short time cycles to
ensure that all pointings are observed with similar weather conditions
and that they share similar
coverage. This minimizes the
shift-variant part of the interferometer wide-field imaging
response. This calls for the shortest possible integration time per
pointing. However, the interferometer takes time to slew from one
pointing to the next one without integrating. As a result, the observing
efficiency
is degraded in the cases of mosaics and we have
another relationship between the elapsed telescope time and the on-source
time as:
 |
(30) |
where
is the integration time per pointing and
is the
time to slew between two consecutive pointings. Having a large
integration time per pointing compared to
will decrease the
mosaicking overhead. This requirement is in sharp contrast with the
previous one, namely the need to homogenize the interferometer wide-field
response. The best compromise comes from two different considerations.
- The smallest integration time is set by the acquisition system (for
instance, the maximum achievable data rate). In pratice, we enforce
that
 |
(31) |
- The distance covered by a visibility in the
-plane during an
integration should always smaller than the distance associated to
tolerable aliasing (see Pety and Rodríguez-Fernández 2010 for more
details). This can be written as the following condition (Eq. C.3 in
this article)
 |
(32) |
where
is the map angular size, and
the
angular resolution. For a given angular resolution, the interferometer
minimum integration time corresponds to
 |
(33) |
where
is a ad-hoc integer set to 5 to ensure the condition
defined in Eq. 32.
As the typical slew time between two pointings is
sec, we
yield that
 |
(34) |
- If the time to cycle all the pointings,
, is set to 45
minutes, we yield that the maximum number of pointing per track is
 |
(35) |
- Finally, if the PI wishes to observe an area that will require more
that 130 pointings per independent track, the estimator will ask to
either increase the requested elapsed telescope time or to decrease the
requested field-of-view area. The computation is done as follows.
- The number of tracks is then computed as described in
section 4.1.
- The number of point per track is then
This value must be lower than
.
In summary, the sensitivity of a Nyquist sampled mosaic is
 |
(36) |
 |
(37) |
Next: Bibliography
Up: Observing mode and elapsed
Previous: Track-sharing, single-field observations
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Gildas manager
2023-06-01