Mutual coherence function of a finite optical beam and application to coherent detection

The mutual coherence function of a finite laser beam propagating through a random medium is calculated from the extended Huygens principle. Formulas are presented for the transverse coherence from an arbitrarily truncated focused Gaussian beam. Expressions are derived for a modified Kolmogorov spectrum for the refractive index fluctuations and for the case of nonuniform turbulence. The formalism is used to derive the conditions under which instantaneous reciprocity exists between a transmitter and receiver in a coherent detection system. It is also shown that a maximum useful transmitter (as well as receiver) diameter exists for computing the average normalized signal-to-noise ratio of this system. This maximum dimension is the smaller of the turbulence-induced coherence length and a Fresnel zone.