Quantum Noise & Effective Noise Temperature

9006-005

9006-005a

Due to the particulate nature of electromagnetic radiation, photons of increasing frequency carry more energy, so that for a given flux intensity (W/m²), 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 front-end is given by:

        h.f
Teff = ------  K
       eta.k

where:

h = Planck's constant (6.63 x 10^-34 J.s),
f = frequency (4.57 x 10¹⁴ Hz),
eta = quantum efficiency (0.5),
k = Boltzmann's constant (1.38 x 10^-23 J/K).

9006-005b

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 signal-to-noise 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 noise-equivalent bandwidth B (without further integration), the energy collected by the receiving telescope in that bandwidth must be greater than kT_effB. 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/m².Hz.

The Columbus Optical SETI Observatory
Copyright (c), 1990