Since the signals3.15 in
a radio telescope are random in nature, the output of a total power
detector attached to a radio telescope too will show random fluctuations.
Supposing a telescope with system temperature T, gain G,
and bandwidth is used to try and detect some astrophysical
source. The strategy one could follow is to first look at a `blank'
part of the sky, and then switch to a region containing the source.
Clearly if the received power increases, then one has detected
radio waves from this source3.16. But
given that the output even on a blank region of sky is fluctuating,
how can one be sure that the increase in antenna temperature is not
a random fluctuation but is indeed due to the astrophysical source?
In order to make this decision, one needs to know what the rms is
in the fluctuations. It will be shown later3.17,
that for a total power detector with instantaneous rms T, the rms
after integrating a signal of bandwidth Hz for
seconds is3.18 T
The increase in system temperature is just GS, where S is the
flux density of the source. The signal to noise ratio is hence
The signal to noise ratio here considers only the `thermal noise', i.e. the noise from the receivers, spillover, sky temperature etc. In addition there will be random fluctuations from position to position as discussed below because of confusion. For most single dish radio telescopes, especially at low frequencies, the thermal noise reaches the confusion limit (see Section 3.4) in fairly short integration times. To detect even fainter sources, it becomes necessary then to go for higher resolution, usually attainable only through interferometry.