Practical guide to saddle-point construction in lens design

Abstract

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 fact that the theory behind SPC contains mathematical concepts that are still unfamiliar to many optical designers, the practical implementation of the method is actually very easy and the method can be fully integrated with all other traditional design tools. In this work we will illustrate the use of SPC with examples that are very simple and illustrate the essence of the method. The method can be used essentially in the same way even for very complex systems with a large number of variables, in situations where other methods for obtaining new system shapes do not work so well.

System design process for refractive simultaneous short and long wave infrared imaging

“…Design a doublet for both wavebands simultaneously. 4. Create a triplet using the two doublets that shared a mutual glass.…”

“…5. Utilize saddle point decomposition [4] to assemble a four element "component". Construct full optical system 6.…”

Saddle points reveal essential properties of the merit-function landscape

“…The theory behind SPC is based on mathematical concepts which are still new in optical design, but the practical implementation is very easy, and the method can be fully integrated with all other traditional design tools. 5,6 In principle, SPC will also be applicable in other optimization problems satisfying certain mathematical conditions (i.e., the existence of two independent transformations of a null element that leave the merit function unchanged 1 ), e.g., in thin-film optimization. However, in applications other than lens design more research is needed to investigate the practical use of SPC.…”

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

“…A detailed description of all necessary steps is given in an earlier publication. 19 For CODE V, 20 lens files for all examples and a macro that creates the NESP are available via our website. 21 All three examples can be executed in a very short time.…”

“…19 For CODE V, 20 lens files for all examples and a macro that creates the NESP are available via our website. 21 All three examples can be executed in a very short time. By optimizing two points at opposite sides of the saddle ͓the points given by Eq.…”