Keywords: astro-30m-emir-time-estimator

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## The radiometer equation

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 on-source and off-source and then to subtract the off-source from the on-source 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.