Optical antenna gain. 2: receiving antennas.

Expressions are derived for the gain of a centrally obscured, circular optical antenna when used as the collecting and focusing optics in a laser receiver which include losses due to (1) blockage of the incoming light by the central obscuration, (2) the spillover of energy at the detector, and (3) the effect of local oscillator distribution in the case of heterodyne or homodyne detection. Numerical results are presented for direct detection and for three types of local oscillator distributions (uniform, Gaussian, and matched) in the case of heterodyne or homodyne detection. The results are presented in several graphs that allow the rapid evaluation of receiver gain for an arbitrary set of telescope and detector parameters. It is found that, for uniform illumination by the LO, the optimum SNR is obtained when the detector radius is approximately 0.74 times the Airy disk radius. The use of an optimized Gaussian (spot size = 0.46 times the Airy disk radius) improves the receiver gain by less than 1 dB. Theuse results are insensitive to the size of the central obscuration.