Quantum Noise & Effective Noise Temperature
9006005
9006005a
Due to the particulate nature of electromagnetic radiation, photons of increasing
frequency carry more energy, so that for a given flux intensity (W/m^{2}), less
optical photons arrive per second than microwave photons. This means that in the optical
regime, there is more noise associated with the statistics of the arrival of a given flux
of optical photons. In microwave communication systems, it is the thermal kT noise of the
receiver and sky temperature that limits the detection sensitivity. In optical systems, it
is usually (ideally) the case that it is the basic quantum shot noise that limits the
detection sensitivity.
The effective system temperature of an optical frontend is given by:
h.f
T_{eff} =  K
eta.k
where:
h = Planck's constant (6.63 x 10^{34} J.s),
f = frequency (4.57 x 10^{14} Hz),
eta = quantum efficiency (0.5),
k = Boltzmann's constant (1.38 x 10^{23} J/K).
9006005b
If we assume that the heterodyning efficiency is unity, i.e., perfect optical mixing
efficiency, the overall receiver quantum/heterodyning efficiency is then 50%. Substituting
into the above equation the values in parentheses, we find that the effective system
temperature at 656 nm:
T_{eff} = 43,912 K
The signaltonoise ratio (SNR) or sensitivity penalty is 36.4 dB as compared to a 10
K microwave system. This sensitivity penalty is often given as one of the major reasons
for preferring the Microwave SETI approach. However, the very high gain of optical
antennas more than makes up for this penalty.
In order that we can detect a signal in a noiseequivalent bandwidth B (without
further integration), the energy collected by the receiving telescope in that bandwidth
must be greater than kT_{eff}B. To detect an optical signal confined to a 1 Hz
bandwidth (without signal integration), the received signal power P_{r} > 6.06
x 10^{19} W. Alternatively, this may be expressed for a 10 meter diameter
telescope, in the form of intensity spectral density I_{r}(f) >7.72 x 10^{21}
W/m^{2}.Hz.
The Columbus Optical SETI Observatory
Copyright (c), 1990
