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

Chaotic behavior in an algorithm to escape from poor local minima in lens design

In lens design, damped least-squares methods are typically used to find the nearest local minimum to a starting configuration in the merit function landscape. In this paper, we explore the use of such a method for a purpose that goes beyond local optimization. The merit function barrier, which separates an unsatisfactory solution from a...

Instabilities and fractal basins of attraction in optical system optimization

Many optical design programs use various forms of the damped least-squares method for local optimization. In this paper, we show that damped least-squares algorithms, with maximized computational speed, can create sensitivity with respect to changes in initial conditions. In such cases, starting points, which are very close to each other, lead...

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...

Method of designing a projection system, lithographic apparatus and device manufacturing method

Optimization of a projection system is performed to obtain a starting configuration that is at a local minimum of the merit function or simply a previously known minimum system is used as the starting configuration. A zero-thickness meniscus lens is inserted at a surface in the local minimum starting configuration with N surfaces to construct a...

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...

Looking for order in the optical design landscape

Poster presentation Optics Research Group TU Delft in cooperation with STW The presence of multiple local minima in the merit function landscape is one of the main difficulties in optical system design, especially for systems with many variables. By considering saddle points, we find a certain degree of order in the design landscape that...

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...

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...