Reducible complexity in lens design

A major challenge in lens design is the presence of many local minima in the optimization landscape. However, unlike other global optimization problems, the lens design landscape has an additional structure, that can facilitate the design process: many local minima are closely related to minima of simpler problems. For discussing this property,...

Predictability and unpredictability in optical system optimization

Local optimization algorithms, when they are optimized only for speed, have in certain situations an unpredictable behavior: starting points very close to each other lead after optimization to different minima. In these cases, the sets of points, which, when chosen as starting points for local optimization, lead to the same minimum (the so...

Practical guide to saddle-point construction in lens design

Saddle-point construction (SPC) is a new method to insert lenses into an existing design. With SPC, by inserting and extracting lenses new system shapes can be obtained very rapidly, and we believe that, if added to the optical designer’s arsenal, this new tool can significantly increase design productivity in certain situations. Despite the...

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...