Principle

Let us note D the diameter of the single-dish antenna (D = 30m for the IRAM-30m telescope) used to produce the short-spacing information and $d$ the diameter of the interferometer antennas (d = 15m for NOEMA). We already mentioned that a multiplicative interferometer filters out all the spatial frequencies smaller than $\sim d$ meters. When this information is needed to get reliable results, the source should also be observed with a single-dish antenna to produce the missing information. The single-dish antenna furnishes information about all spatial frequencies up to $\sim D$ meters (but this information is weighted by the single-dish beam shape, i.e. high frequencies are measured with a worse signal-to-noise ratio than low frequencies). To recover all the information at spatial frequencies smaller than d meters, the diameter of single-dish antenna must be larger or equal to the diameter of the interferometer antennae: D$\ge$d.