Wigner function-based modeling and propagation of partially coherent light in optical systems with scattering surfaces

Light scattering from residual manufacturing errors of optical surfaces has a large impact on the image quality of optical systems. Classical ray-based methods to simulate surface scattering in optical systems depend on statistical models of surface errors and neglect the wave properties of light, which prohibit the integration of statistical surface error models with beam propagation methods. Additionally, the impact of multiple scattering from different frequency components of surface errors cannot be easily modelled by existing methods. Here we analyze the impact of different frequency components of surface errors induced by diamond-turned surface grinding on image quality, and we propose a Wigner function-based approach in which light is modelled as partially coherent. In this unified model, by selecting the proper definition of light coherence, we can combine the statistical and deterministic models of surface errors, enabling efficient, simultaneous simulation of multiple scattering from high- and mid-spatial frequency (HSF and MSF, respectively) surface errors, as well as the interference and edge diffraction of light.