Obtaining Different Lens System Shapes by using Saddle-Point Construction

Saddle points in the merit function landscape of optical systems can be used to find new local minima in a systematic way [1,2]. In this paper, the goal is to show the potential of the so called Saddle-Point Construction (SPC) method in the global coverage of design shapes. This will be illustrated by describing how all triplet lens system shapes can be obtained from a singlet.When applied in a structured way, the SPC algorithm is able to find all typical doublet system shapes from a singlet. In a similar way all triplets can be found from the doublets. The system shapes found with the SPC algorithm are typically identified as local minima defined in the idealized networks [3], including the well-known Cooke triplet.