The propagation of light through complex structures, such as biological tissue, is a poorly understood phenomenon. Current practice typically ignores the coherence of the optical field. Propagation is treated by Monte Carlo implementation of the radiative transport equation, in which the field is taken to be incoherent and is described solely by the first-order statistical moment of the intensity. Although recent Monte Carlo studies have explored the evolution of polarization using a Stokes vector description, these efforts, too are single-point statistical characterizations and thus ignore the wave nature of light. As a result, the manner in which propagation affects coherence and polarization cannot be predicted. In this paper, we demonstrate a Monte Carlo approach for propagating partially coherent fields through complicated deterministic optical systems. Random sources with arbitrary spatial coherence properties are generated using a Gaussian copula. Physical optics and Monte Carlo predictions of the first and second order statistics of the field are shown for coherent and partially coherent sources for a variety of imaging and non-imaging configurations. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. Finally, we discuss convergence criteria for judging the quality of the Monte Carlo predictions. Ultimately, this formalism will be utilized to determine certain properties of a given optical system from measurements of the spatial coherence of the field at an output plane. Although our specific interests lie in biomedical imaging applications, it is expected that this work will find application to important radiometric problems as well.
