## From the temperature power to the flux

For a point source, it is more natural to express the signal, and thus the sensitivity, in unit of flux. The flux ( ) of a point source is linked to its brightness temperature through

with | (4)

where is the Boltzman constant, and is the effective area of the antenna (eq. 3-113 in Kraus , 1982), and the conversion factor for a typical interferometer antenna. The effective area depends on the observing wavelength when the surface rms accuracy becomes a significant fraction of the wavelength. For NOEMA, the effective area is close to the antenna geometrical surface at 3 mm but significantly lower than it at 1 mm. Using the same conversion factor for the sensitivity, we yield

| (5)

We have the same subtlety for as for , ie, here characterizes one baseline between, eg., antennas and . Instead of just , we should write in all generality with

| (6)

where and are the single dish conversion factors for antenna and . For simplicity, we will also keep the notation hereafter.