  A consistent and explicit spectral comparison between heterodyne (HD) and
direct detection (DD) derived from first principles including the atmospheric
transmission and low beam-filling factors could not be found yet in literature
but is needed for decisions in technology planification for future infrared
interferometry facilities which are e.g. focused on planet formation. This task
requires both, high sensitivity continuum and Doppler-resolved emission and
absorption line detection in the mid-IR range (N- and Q-bands) at lower source
temperatures (300-1000 K). The signal-to-noise ratios (SNRs) are derived for
both schemes within the same semi-classical theory, which consists of classical
mode theory for coupling to an antenna and occupation of these modes by quanta
of three radiation fields, the thermal signal, the thermal background, and for
HD also the coherent local oscillator (LO). The effects of very small beam
filling factors (interferometry) and atmospheric absorption/emission could be
consistently incorporated this way, as well as quantum-noise propagation which
allows in HD the consideration of balanced mixers with cross-correlation (CC).
Especially, the transition from pre- to post-detection SNRs was considered
meticulously. We do this all because the usually cited SNR-expressions were
derived for a too simple and unrealistic case, and moreover contain some wrong
assumptions. We introduce a novel HD scheme for astronomical interferometry
gaining an order of magnitude in sensitivity against conventional HD and
calculate that it should trespass the sensitivity of DD interferometry in the
N- and Q-bands for a spectral resolution of R=10000, and should do also for
R=300 with doable technical improvements. This result encourages to develop
broad-band heterodyne technologies for future mid-infrared interferometry
facilities and for new instruments at existing facilities.
