On the Mutual Coherence Function in an Inhomogeneous Medium

The paper is concerned primarily with determining the mutual coherence function of the field produced by a plane quasi-monochromatic source in a region of variable refractive index. A scalar theory is used throughout. Section I presents a brief review of the conceptual background of coherence theory. Section II contains an outline of the mathematical formalism of coherence theory and shows that in a region of variable refractive index the mutual coherence function is propagated according to a pair of inhomogeneous scalar wave equations. In Sec. III, the pair of wave equations are solved using appropriate Green's functions to derive an expression for the mutual coherence function of a field produced by a plane quasi-monochromatic source. In Sec. IV the case of a statistically homogeneous medium is treated and an expression for the ensemble average of the mutual coherence function is obtained in terms of integrals of the two-point correlation function characterizing the medium.