<title>Optimization of the Cooke triplet with various evolution strategies and damped least squares</title>

Abstract

Optimization ofthe Cooke triplet with various evolution strategies and the damped least squares is presented. All algorithms are described and their advantages and shortcomings are presented. After detailed presentation of the evolution strategies their adaptation to the optimization of optical systems are discussed. Analysis of the Cooke triplet optimizations is given and optimum optimized optical system is chosen.

Suppression of Petzval Aberration in a Projector Lens by Using Genetic Algorithm

“…Noting that in (6) the value of the objective functions is expressed as the smaller or the closer to zero, the better. Therefore we need to transform the target values to their corresponding adaptability value, according to the following equation, also called the fit function: for (7) From (7) the probability that each lens will be selected for the crossover operation is for (8) According to the roulette rule, the area (probability) of the whole dish is 1 and the area (probability) occupied by each lens system is calculated from (8). The cumulative probability of each lens system in terms of the roulette dish area is obtained from the following:…”

“…Some writers suggest optimization by means of a varying radius of the curvature of the image plane [5] to alleviate the Petzval FCA; however, it has been found impracticable to vary the radius of the curvature of the screen for the purpose of eliminating Petzval FCA in the projector system. Most commercial software programs employ the Damped Least Square (DLS) method [6], [7] to go through optimizations, but we propose an alternative solution, which implements the global searching capacity of genetic algorithm (GA) [8]- [12] to accomplish both optimization and efficiency at the same time. Although most commercial softwave programs also offer some global optimizations, they are not flexible for the specific aberration optimization such as the Petzval FCA or chromatic aberration improvement [1].…”

Taguchi Method Optimization for PCB Lamination Process

“…Thus Taguchi experiment method provides orthogonal arrays to reduce the experiment number. In the Taguchi experiment method, let board temperature be A = {A1, A2} = { 20°C, 40°C}, lamination temperature be B = {B 1 The objective of Taguchi experiments is to find maximum successful ratio. Higher successful ratio owns better the performance.…”

Suppression of primary chromatic aberration by genetic algorithm in an advanced telephoto lens

“…Since 1960 advances in computing have been developed step by step and optical designers can now optimize the system and then reach optimal system performance efficiently and precisely, even in extremely difficult cases. The currently employed method, damped least squares (DLS) [1][2][3], a raytracing-based method, is, however, limited as a technique, owing to its inability to identify an enhanced optical system configuration, especially in chromatic aberrations in very complicated cases.…”