A phase-quadrature (p-q) description of a random optical field is suggested as an attractive alternative to the usual logamplitude-phase representation for the purpose of investigating the behavior of the optical heterodyne. Using the p-q representation, an expression is developed for the average signal-to-noise ratio at the heterodyne’s output when both the signal and local oscillator (LO) fields are inhomogeneous and partially coherent. An examination of the expression for the signal-to-noise ratio indicates the general nature of the previously observed saturation effect. A coherence suppression phenomenon is also apparent. It is shown that the heterodyne’s field of view may be drastically broadened (relative to that of a system which processes ideal plane waves) as a result of weak spatial coherence in either the signal or LO field. Recently published experimental data are examined in light of the results obtained i this paper, and good agreement between theory and experiment is observed.
J. N. Lahti, "Mixing Inhomogeneous, Partially Coherent Optical Fields," Appl. Opt. 8, 1815-1820 (1969)