Saddle points in the merit function landscape of systems of thin lenses in contact

The merit function landscape of systems of thin lenses in contact, which are perhaps the simplest possible types of optical systems, shows remarkable regularities. It is easier to understand how the optimization parameter space of these simple systems is divided into basins of attraction for the various local minima if one focuses on the (Morse index 1) saddle points in the landscape rather than on the local minima themselves. The existence and the basic properties of these saddle points can be predicted by thin-lens theory, which is applied on a simplified model of the merit function containing only third-order spherical aberration. The predictions of this simplified model are confirmed by numerical results obtained with a typical merit function based on ray tracing.