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Mutual Coherence Function of a Finite Optical Beam and Application to Coherent Detection

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Abstract

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.

© 1973 Optical Society of America

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Equations (71)

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