Antenna design for Ka-band SAR systems used in earth observation missions is demanding for two reasons. A narrow beamshape results in a large aperture, and the frequency band dictates a short spacing between neighboring radiating elements. In our case, this leads to a requirement of more than a million radiating elements. In this thesis it is assessed how such a challenge can be solved, yielding a solution that is compliant with the specifications and industrially feasible. In particular, it is recognized that the distribution of radiating elements is more important than the placement of individual elements, and the synthesis and analysis methods explored in this work build on this principle.