Looking for order in the optical design landscape

In present-day optical system design, it is tacitly assumed that local minima are points in the merit function landscape without relationships between them. We will show however that there is a certain degree of order in the design landscape and that this order is best observed when we change the dimensionality of the optimization problem and when we consider not only local minima, but saddle points as well. We have developed earlier a computational method for detecting saddle points numerically, and a method, then applicable only in a special case, for constructing saddle points by adding lenses to systems that are local minima. The saddle point construction method will be generalized here and we will show how, by performing a succession of one-dimensional calculations, many local minima of a given global search can be systematically obtained from the set of local minima corresponding to systems with fewer lenses. As a simple example, the results of the Cooke triplet global search will be analyzed. In this case, the vast majority of the saddle points found by our saddle point detection software can in fact be obtained in a much simpler way by saddle point construction, starting from doublet local minima.