Global map of possible lens design shapes for simple optical systems.

The choice of a starting system is one of the main difficulties in optical system optimization due to the presence of multiple local minima in the merit function landscape. During the design process an optical designer often does not have a global overview of which stable local minima are present in the merit function landscape. At least for relatively simple systems we found a robust network structure that contains all lens design shapes (i.e. types of local minima) that can exist in the merit function landscape, including their connections with respect to each other. We will present the so-called ideal network for doublets and triplets which contains the general design shapes, individually separated by saddle points. In practical problems, some minima disappear and the set of existing local minima appears to be a subset of the maximum set present in the ideal network. Remarkably, the network of the remaining solutions is closely related to the ideal network. Therefore, knowledge about the structure of the merit function landscape can help the designer to navigate through the design space for improving the design.