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. We use a novel 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 has been demonstrated in all cases.

We have developed a Monte Carlo-derived Green's function for the propagation of partially coherent fields. This Green's function, which is derived by sampling Huygens-Fresnel wavelets, can be used to propagate fields through an optical system and to compute first and second order field statistics directly. The concept is illustrated for a cylindrical f/1 imaging system. A Gaussian copula is used to synthesize realizations of a Gaussian-Schell model field in the pupil plane. The animated GIF shows the ensemble intensity for different cross-sections near the focus.

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.

2012S. A. Prahl, A. Dayton, K. Juedes, E. J. Sánchez, R. López Páez, D. D. Duncan, "Experimental validation of phase using Nomarski microscopy with an extended Fried algorithm," *J. Opt. Soc. Am. A*, **29**, 2104-2109 (2012).

D. D. Duncan, D. G. Fischer, A. Dayton, S. A. Prahl, "Quantitative Carré Differential Interference Contrast Microscopy to Assess Phase and Amplitude," *J. Opt. Soc. Am. A*, **28**, 1297-1306 (2011).

D. D. Duncan, D. G. Fischer, M. Daneshbod, S. A. Prahl, "Tissue structural organization: measurement, interpretation, and modeling," *SPIE Proceedings on Dynamics and Fluctuations in Biomedical Photonics VII*, **7563**, (2010).

D. D. Duncan, D. G. Fischer, M. Daneshbod, S. A. Prahl, "Differential interference contrast microscopy for the quantitative assessment of tissue organization," *SPIE Proceedings on Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII*, (2010).

D. D. Duncan, S. A. Prahl, A. Dayton, D. G. Fischer, "Quantification of tissue organizational structure using DIC microscopy," *Saratov Fall Meeting, Joint Workshop on Microscopic and Low-Coherence Methods in Biomedical and Non-Biomedical Applications III*, (2010).

S. A. Prahl, D. D. Duncan, D. G. Fischer, "Monte Carlo Propagation of Spatial Coherence," *SPIE Proceedings on Biomedical Applications of Light Scattering IV*, **7187**, 75730D-1-6 (2010).

D. Duncan, S. Prahl, D. Fischer, "Predicting partial coherence effects with stochastic ray tracing," *Biomedical Optics & Medical Imaging*, (2009).

S. A. Prahl, D. D. Duncan, D. G. Fischer, "Monte Carlo Propagation of Spatial Coherence," *SPIE Proceedings on Biomedical Applications of Light Scattering III*, **7187**, 71870G-1-71870G-8 (2009).

S. A. Prahl, D. D. Duncan, D. G. Fischer, "Monte Carlo Sampling of Huygens-Fresnel Fields," *Proceedings of the Oregon Academy of Science*, **45**, (2009 abstract only).

S. A. Prahl, D. G. Fischer, D. D. Duncan, "A Monte Carlo Green's Function for the propagation of partially coherent light," *J. Opt. Soc. Am. A*, **26**, 1533-1543 (2009).

D. G. Fischer, S. A. Prahl, D. D. Duncan, "Monte Carlo modeling of spatial coherence: free-space diffraction," *J. Opt. Soc. Am. A*, **25**, 2571-2581 (2008).