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For OTF observations, there are several effects to take into account.
 We will use the average system temperature to take into account the
different mixer performances.
 Edges result in inhomogeneous noise, which depends on the exact
observing setup. We here try to estimate a single noise value for the
whole map. The area swept in edges are thus considered as overheads. If
the total targeted area is
, the receiver will then have to map
. As discussed above, we can write the previous sum as a
product of the targeted area times an efficiency factor, i.e.

(38) 
We thus have to remplace
by
in
Eqs and to compute
and
. Now, if edge area is considered overheads when estimating the
sensitivity, the spectra acquired in the edges will nevertheless be used
to form the final image. We must thus ensure that enough time is observed
on the off position when estimating the sensitivity in the position
switch mode. This comes naturally if we consider the edge area as part of
the submap between two off positions. This implies that the change on the
total mapped area, expressed above, is the only one needed in the
equations to take the edges into account.
 A multipixel can cover
times as fast the same area of the
sky with the same sensitivity as a singlepixel of similar
.
Another way to look at this, is to assume that each identical (average)
pixel will cover an independent part of the sky during a given observing
time (i.e.
). This implies that the area seen by each
pixel will be

(39) 
This finally gives

(40) 
where
and
are computed with

(41) 

(42) 
The times spent on and off and in the edges per pixel are then

(43) 
The algorithm to derive the time/sensitivity estimation in the case of OTF
can thus be applied with the following modifications in the input
parameters :
,
,
,
must be replaced by
,
,
,
.
Next: Bibliography
Up: Generalization to a multipixel
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20140701