Heterodyne receivers mix a local oscillator frequency,
, to the
astronomical signal to transfer the frequency axis from high radio
frequencies,
, to low intermediate frequencies,
, which
are then suitable for easy electronic processing. A consequence is that two
bands of radio frequencies, namely the lower side band (LSB) and the upper
side band (USB) are mixed in the observed spectrum, i.e., the set of
brightnesses,
, are associated to one IF frequency axis and two RF
frequency axes linked through
must be modified as
with