Structural design of cemented triplets by genetic algorithm

Abstract

We present an implementation of a genetic algorithm in the structural design of cemented triplets according to a prespecified set of Gaussian characteristics and primary aberration targets. The approach is directed toward obtaining a suite of promising solutions allowing some floating of the primary aberration targets. This method obviates the need for any heuristic preselection of glasses for the three elements of the triplet. Searches for optimal solutions are conducted in the total configuration space of the degrees of freedom, consisting of continuous variables like shape factor and power distributions, and discrete variables like available glass types. The role of genetic diversity in the evolving population on convergence of the optimization runs has been investigated, and, accordingly suitable modifications are incorporated in the basic genetic algorithm to eliminate undue stagnation and premature convergence problems. Some illustrative examples are given.

Methods of solving aspheric singlets and cemented doublets with given primary aberrations

“…Chen et al [12] derived a more general algorithm to solve cemented triplets using three glass types. Chatterjee and Hazra [13] proposed a genetic algorithm to solve cemented triplets. Chen et al [14,15] also solved the triplets containing a singlet and a cemented doublet to further meet the secondary spectrum.…”

Aberration correction of zoom lenses using evolutionary programming

“…The target aberrations for each component may be realized by one or more closely placed thin lens elements in a subsequent design stage. The optimal thin lens structures for each component are determined by using methods described by Khan and Macdonald [12], Hazra and co-workers [14,15] or Chretien [16]. Thin lens components are then thickened using the method described by Hopkins and Rao [17] to get practically realizable structures of the zoom lens.…”

“…Also, the design method presented here uses a global optimization technique, GA, for the optimization of the aberration targets. Furthermore, when coupled with the design strategies presented in [1][2][3][4] for the determination of thin lens structure of the zoom lenses and in [14,15] for the determination of structures of optimal thin lens elements, this optimization strategy can be used to establish ab initio structure of zoom lenses. A search for a globally or quasi-globally optimal solution in each of these design stages is facilitated by using the global optimization technique GA.…”

Optimum Values for Genetic Operators in Evolutionary Optimization of Structural Design of Cemented Doublets

“…II). 13 Notwithstanding the successes in achieving solutions as sought for, it was noted that the procedure often suffered from slow convergence and undue stagnation problems. It was noticed that the values of the genetic operators, namely the crossover probability, the mutation probability and the threshold genetic diversity requirements for acceptable populations, affect significantly the optimization runs.…”