基于进化算法的光学元件琼斯矩阵表征
Jones Matrix Characterization of Optical Elements via Evolutionary Algorithms
摘要：
琼斯演算提供了一种鲁棒的和直接的方法来表征偏振光和偏振光学系统使用两个元素的矢量（琼斯矢量）和$2 \times 2$矩阵（琼斯矩阵）。琼斯矩阵用于确定由光学元件或元件序列引入的延迟和二向衰减。此外，它们是研究光学几何相位的首选工具。然而，当前用于表征光学元件的琼斯矩阵的采样方法是低效的，因为问题的搜索空间在实数的范围内，因此应用一般的采样方法是耗时的。在这项研究中，我们提出了一个初始的方法来解决的问题，找到表征琼斯矩阵的均匀光学元件通过进化算法（EA）的特征向量。我们评估分析性能的EA与多项式突变算子和遗传算法（GA）与模拟二进制交叉算子和多项式突变算子，并比较结果与通过一般的抽样方法得到的。结果表明，EA和GA都优于6,000个测量的一般采样方法，分别需要平均103和188个适应度函数测量，同时具有完美的收敛速度。
英文摘要：
Jones calculus provides a robust and straightforward method to characterize polarized light and polarizing optical systems using two-element vectors (Jones vectors) and $2 \times 2$ matrices (Jones matrices). Jones matrices are used to determine the retardance and diattenuation introduced by an optical element or a sequence of elements. Moreover, they are the tool of choice to study optical geometric phases. However, the current sampling method for characterizing the Jones matrix of an optical element is inefficient, since the search space of the problem is in the realm of the real numbers and so applying a general sampling method is time-consuming. In this study, we present an initial approach for solving the problem of finding the eigenvectors that characterize the Jones matrix of a homogeneous optical element through Evolutionary Algorithms (EAs). We evaluate the analytical performance of an EA with a Polynomial Mutation operator and a Genetic Algorithm (GA) with a Simulated Binary crossover operator and a Polynomial Mutation operator, and compare the results with those obtained through a general sampling method. The results show that both the EA and the GA out-performed a general sampling method of 6,000 measurements, by requiring in average 103 and 188 fitness functions measurements respectively, while having a perfect rate of convergence.
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