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The radiometer equation for a total power measurement reads

(1) 
where
is the rms noise obtained by integration during
in a
frequency resolution
with a system whose system temperature is given
by
and spectrometer efficiency is
. However, total power
measurement includes other contributions (e.g. the atmosphere emission) in
addition to the astronomical signal. The usual way to remove most of the
unwanted contributions is to switch, i.e. to measure alternatively
onsource and offsource and then to subtract the offsource from the
onsource measurements. It is easy to show that the rms noise of the
obtained measurement is

(2) 
where
and
are the noise of the on and off
measurement observed respectively during the
and
integration
time.
is just a useful intermediate quantity.
Gildas manager
20140701