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

A systematic analysis of the optical merit function landscape: Towards improved optimization methods in optical design

A major problem in optical system design is that the optical merit function landscape is usually very complicated, especially for complex design problems where many minima are present. Finding good new local minima is then a difficult task. We show however that a certain degree of order is present in the optical design space, which is best...

Saddle-point construction in the design of lithographic objectives, part 1: Method

Saddle-point construction in the design of lithographic objectives, part 2: Application

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 landscapewithout relationships between them. We will show however that there is a certain degree of order in the design landscapeand that this order is best observed when we change the dimensionality of the optimization problem and when...

Designing lithographic objectives by constructing saddle points

Optical designers often insert or split lenses in existing designs. Here, we present, with examples from Deep and Extreme UV lithography, an alternative method that consists of constructing saddle points and obtaining new local minima from them. The method is remarkable simple and can therefore be easily integrated with the traditional design...

Saddle points in the merit function landscape of lithographic objectives

The multidimensional merit function space of complex optical systems contains a large number of local minima that are connected via links that contain saddle points. In this work, we illustrate a method to construct such saddle points with examples of deep UV objectives and extreme UV mirror systems for lithography. The central idea of our...

Generating saddle points in the merit function landscape of optical systems

Finding multiple local minima in the merit function landscape of optical system optimization is a difficult task, especially for complex designs that have a large number of variables. We discuss here a method that enables a rapid generation of new local minima for optical systems of arbitrary complexity. We have recently shown that saddle points...

The network structure of the merit function space of EUV mirror systems

The merit function space of mirror systems for EUV lithography is studied. Local minima situated in a multidimensional merit function space are connected via links that contain saddle points and form a network. In this work we present the first networks for EUV lithographic objectives and discuss how these networks change when control parameters...

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...