  Imaging systems are inherently prone to aberrations. We present an
optimization method to design two-dimensional freeform reflectors that minimize
aberrations for various parallel ray beams incident on the optical system. We
iteratively design reflectors using inverse methods from non-imaging optics and
optimize them to obtain a system that produces minimal aberrations. This is
done by minimizing a merit function that quantifies aberrations and is
dependent on the energy distributions at the source and target of an optical
system, which are input parameters essential for inverse freeform design. The
proposed method is tested for two configurations: a single-reflector system and
a double-reflector system. Classical designs consisting of aspheric elements
are well-known for their ability to minimize aberrations. We compare the
performance of our freeform optical elements with classical designs. The
optimized freeform designs outperform the classical designs in both
configurations.
