Path sampling and integration method to calculate speckle patterns

A stable speckle pattern is generated when a coherent beam illuminates a stationary scattering medium that contains numerous scatterers with fixed positions. To date, there has been no valid method to the best of our knowledge for calculating the speckle pattern of a macro medium with a large number of scatterers. Here, a new method based on possible path sampling with corresponding weights and coherent superposition is presented for the simulation of optical field propagation in a scattering medium and output speckle patterns. In this method, a photon is launched onto a medium with fixed scatterers. It propagates in one direction; upon collision with a scatterer, its direction is updated. The procedure is repeated until it exits the medium. A sampled path is obtained in this manner. By repeatedly launching photons, numerous independent optical paths can be sampled. A speckle pattern, corresponding to the probability density of the photon, is formed by the coherent superposition of sufficiently sampled path lengths ending on a receiving screen. This method can be used in sophisticated studies of the influences of medium parameters, motion of scatterers, sample distortions on speckle distributions, and morphological appearances. It can be used for micro-examination of optical fields in scattering media and may inspire new methods and techniques for non-invasive precision detection and diagnosis of scattering media.