Leveraging off genetic algorithms for optimizing AGRIN lenses

Abstract

While researching various gradient index glass families for superb color correction using ZEMAX<SUP>1</SUP> optical design program, the authors found that certain solutions could only be found using the Hammer routine<SUP>2</SUP>. Hammer is a genetic algorithm that breeds a particular lens configuration with variations of itself<SUP>3</SUP>. It is not intended to be a global search routine. Hammer is typically used after the best performance is obtained using the standard damped least squares (DLS) algorithm with the default merit function (MF) based on minimizing root mean square (RMS) spot size. Upon this discovery, the authors proceeded to explore the benefit of using the genetic Hammer algorithm on three different lens systems. To make the solution space more complicated, two axial gradient index (AGRIN) elements were used in each lens type; a bi- AGRIN cemented doublet; a bi-AGRIN air spaced triplet with CaF2 as the center element, and a double Gauss with four AGRIN elements and two CaF2 elements. AGRIN elements were used in each lens to provide a more complex solution space and to make optimization more difficult. After optimization, the performance of each lens was compared wiht the conventionally optimized counterpart using the default MF with a DLS algorithm. After this comparison was made, another trade study was done between the Hammer and DLS algorithms, but in this case, the optimization used a custom MF instead of the default MF. The authors believe this study shows the importance of MF construction over that of using the default RMS spot size metric. A significant improvement was obtained for all lenses with the default MF using the Hammer over the DLS technique, but that improvement was less obvious when a custom MF was used.