In modern laser-based ion acceleration systems, the field distribution of the focused laser beam at the position of the target strongly influences the overall characteristics of the resulting ion beam. To obtain an unidirectional and quasi mono-energetic ion beam, a flat-top field distribution of the focused laser beam is optimal. This can only be achieved, by using a beam-profiling system that reshapes the incident laser beam into an Airy-shaped field distribution in the far field. Here, we present an extensive design study of such a beam-profiling system based on two free-form mirrors. In order to realize the rings of zero intensity, corresponding to the roots of the Airy-function, strong curvature peaks on the first mirror are necessary. Additionally, the alternating phase in between these rings can only be achieved with grooves on the second mirror. These aspects actually raise the question, if the used purely geometric optical modeling approach is still valid. Therefore, our design study is entirely accompanied with wave-optical simulations to identify influences of diffraction within the beam profiling system. We find that especially the grooves on the second mirror are mandatory, not only to ensure the alternating phase, but also to realize the roots of zero intensity of the Airy-function. On the other hand, these grooves cause diffraction effects in the beam-profiling system that slightly degrade the at-top focal field. These influences are in the range of a few percent and cannot be further avoided.