Finding starting points analytically for optical system optimization

Understanding the structure of the design space in optical system optimization is difficult, because common human intuition fails when it encounters the challenge of high dimensionality, resulting from the many optimization parameters of lens systems. However, a deep mathematical idea, that critical points structure the properties of the space...

Systematics of the design shapes in the optical merit function landscape

In this paper we describe new properties of the design landscape that could lead in the future to a new way to determine good starting points for subsequent local optimization. While in optimization the focus is usually only on local minima, here we show that points selected in the vicinity of other types of critical points (i.e. points where...

Systematics of the design shapes in the optical merit function landscape

In this paper we describe new properties of the design landscape that could lead in the future to a new way to determine good starting points for subsequent local optimization. While in optimization the focus is usually only on local minima, here we show that points selected in the vicinity of other types of critical points (i.e. points where...

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,...

Finding new local minima in lens design landscapes by constructing saddle points

Topography of the merit function landscape in optical system design

We have shown recently that, when certain quite general conditions are satisfied, the set of local minima in the optical merit function space forms a network where they are all connected through optimization paths generated from saddle points having a Morse index of 1. A new global optimization method, that makes use of this linking network to...