| Optical wave propagation and imaging in discrete random media are significant problems in several practical applications, such as, biomedical diagnosis, remote sensing, and atmospheric imaging. In all of these examples, the phenomena of an optical wave propagating through a medium with discrete scatterers are of interest. The complete solution to the problem can be obtained by Maxwell's equations. However, this is mathematically rigorous; thus, it is impractical to use. In contrast, the radiative transfer theory, which is based on the power conservation statement, offers a simpler solution.; In the past, the radiative transfer equation has been solved only in limited cases because it requires a tremendous amount of computational resources. Recently, with the increase of computational power, we are able to consider problems that were previously too complicated. In this study, we develop a modified pulse vector radiative transfer equation that provides more stable solutions. We obtain the solutions using the discrete ordinates method. The first-order and the second-order scattering approximations are studied and compared with the complete radiative transfer equation. In addition, we investigate the photon density wave, which is the amplitude modulation wave. We derive the photon-density radiative transfer equation and analyze its solutions. In order to approach a real imaging scenario, the point-source approximation of the radiative transfer equation is derived to account for the distance-dependence on imaging. Finally, we consider the imaging problem and several techniques to improve imaging through discrete random media. We consider the Off-Axis Intensity Subtraction, Cross-Polarization Intensity Subtraction, and Photon Density Wave techniques, which are all based on reducing the scattering effects from the medium. We also consider the shower curtain effect phenomenon. |
