Signal-noise ratio in optical heterodyne detection

Signal-noise ratio (SNR) is an important parameter for the performance of a heterodyne detection system. In order to make full use of the received signal, the signal-noise ratio should be analyzed. The principle of signal-noise ratio is discussed, and general equations for a shot noise limited operation are derived in terms of the distribution functions of the local oscillator and signal fields, the size and quantum efficiency of the detector. To obtain the maximum signal-noise ratio, the phase, amplitude and polarization of the local oscillator and the signal light should be matched strictly. Finally, the signal-noise ratio is discussed for Airy function distribution fields. Numerical simulations show that when the ratio of the size for Airy disks is controlled within 0.8-1.2, the bias x₀ of Airy disk axis below 0.5, the size of detector in the range (0.6-0.8) λf/d, the signal-noise ratio is above 0.7ηP_s/(hvB).