The antenna properties of optical heterodyne receivers

An optical heterodyne receiver is, in effect, both a receiver and an antenna. As an antenna it has an effective aperture or capture cross section A
R
(Ω) for plane wave signals arriving from any direction Ω. The wavefront alignment between signal and local-oscillator (LO) beams required for effective optical heterodyning may be summarized in the "antenna theorem" ∫∫A
R
(Ω)dΩ = [η
²
/η
²
]λ
²
where the moments of the quantum efficiency η are evaluated over the photosensitive surface. Thus, an optical heterodyne having effective aperture A
R
for signals arriving within a single main antenna lobe or field of view of solid angle Ω
R
is limited by the constraint A
R
Ω
R
≈ λ
²
. Optical elements placed in the signal and/or LO beam paths can vary the trade-off between A
R
and Ω
R
but cannot change their product. It is also noted that an optical heterodyne is an insensitive detector for thermal radiation, since a thermal source filling the receiver's field of view must have a temperature T ≈ [In (1 + η)]
^-1
hf/k to be detected with S/N ≈ 1. Optical heterodyning can be useful in practical situations, however, for detecting Doppler shifts in coherent light scattered by liquids, gases, or small particles. Another antenna theorem applicable to this problem says that in a scattering experiment the received power will be ≲ Nσλ/4π times the transmitted power, where N is the density of scatterers and σ is the total scattering cross section of a single scatterer. The equality sign is obtained only when a single aperture serves as both. transmitting and receiving aperture, or when two separate apertures are optimally focused at short range onto a common volume.