Point spread function computation in normal incidence for rough optical surfaces

TL;DR: In this paper, the point spread function (PSF) is used to specify the angular resolution of optical systems, which is a key parameter used to define the performances of most optical systems.

Abstract: The Point Spread Function (PSF) allows for specifying the angular resolution of optical systems which is a key parameter used to define the performances of most optics. A prediction of the system's PSF is therefore a powerful tool to assess the design and manufacture requirements of complex optical systems. Currently, well-established ray-tracing routines based on a geometrical optics are used for this purpose. However, those ray-tracing routines either lack real surface defect considerations (figure errors or micro-roughness) in their computation, or they include a scattering effect modeled separately that requires assumptions difficult to verify. Since there is an increasing demand for tighter angular resolution, the problem of surface finishing could drastically damage the optical performances of a system, including optical telescopes systems. A purely physical optics approach is more effective as it remains valid regardless of the shape and size of the defects appearing on the optical surface. However, a computation when performed in the two-dimensional space is time consuming since it requires processing a surface map with a few micron resolution which sometimes extends the propagation to multiple-reflections. The computation is significantly simplified in the far-field configuration as it involves only a sequence of Fourier Transforms. We show how to account for measured surface defects and roughness in order to predict the performances of the optics in single reflection, which can be applied and validated for real case studies.