Finding order in the design landscape of simple optical systems

Contrary to the frequent tacit assumption that the local minima of a merit function are points scattered more or less randomly over the design landscape, we have found that, at least for simple imaging systems (doublets with three and triplets with five variables) all design shapes we have observed thus far form a strictly ordered set of points, the "fundamental network". The design shapes obtained for practical specifications with global optimization algorithms are a subset of the set of local minima in the fundamental network and are organized in a way that can be understood on the basis of the fundamental network.