The On-The-Fly (OTF) observing mode is used to map a given region of the
sky. The time/sensitivity estimator will have to link the elapsed telescope
time to cover the whole mapped region to the sensitivity in each
independent resolution element. To do this, we need to introduce
-
and
, which are respectively the area of the map and
the area of the resolution element. The map area is a user input while
the resolution area is linked to the telescope full width at half maximum
(
) by
(12)
where
comes from the fact that the OTF data is gridded by
convolution. When the convolution kernel is a Gaussian of FWHM equal to
(the default inside the GILDAS/CLASS software), it is
easy to show that
(13)
- The number of independent measurement (
) in the final map
which is given by
(14)
- The on and off time spent per independent measurement,
and
. The associated
can then be written
(15)
- The on and off time spent to map the whole map,
and
.
is deduced from
and
in a way which depends on the switching scheme.
In addition, we must ensure that the user does not try to scan faster than
the telescope can slew. To do this, we need to introduce
- The linear scanning speed,
, and its maximum value,
.
- The area scanning speed,
, and its maximum value,
. When the scanning pattern is linear, then
and
are linked through
(16)
where
is the separation between consecutive rows. To
avoid nasty signal and noise aliasing problems, we must ensure a Nyquist
sampling, i.e.
(17)