用矩阵光学设计定焦点距四组元变焦镜头系统的近轴
Paraxial design of four-component zoom lens system with fixed distance between focal points by matrix optics
摘要：
本文提出了一种基于矩阵光学的固定焦点间距四分量变焦系统的设计方法。由于模型越复杂，其自由度越高，因此确定变焦轨迹的任务是有意义且具有挑战性的。系统矩阵的元素反映了光学系统的工作状态，通过限制特定的矩阵元素，推导出了所需变焦系统的轴向位移方程。适当地选择由参数函数描述的特定部件的轨迹可以使模型变得显式可解。然后将傍轴设计问题转化为这些参数的优化问题，这些参数是关于包含初级像差项、紧凑性、轨迹光滑性的价值函数的。我们采用粒子群优化算法（PSO）的全局优化参数，检索在特定的设计标准的最佳变焦轨迹。通过两个不同构型下的数值算例，验证了该方法的有效性.仿真结果表明，该方法可以为复杂多组变焦光学系统的傍轴设计提供一种实用而有力的工具。
英文摘要：
In this paper, we propose a systematic approach to design a four-component zoom system with fixed spacing between focal points based on matrix optics. Since the more complex model the higher degree of freedom it has, the task of determining the zoom trajectory is meaningful and challenging. The elements of the system matrix imply the working state of the optical system, and axial displacement equation for the desired zoom system are derived by restricting specific matrix elements. Properly selected trajectory of the particular component described by means of a parametric function can make the model become solvable explicitly. Then the paraxial design problem is transformed into the optimization of these parameters with regard to the merit functions encompassing the primary aberration terms, compactness, smoothness of the trajectories. We adopt Particle Swarm Optimization (PSO) algorithm to globally optimize the parameters to retrieve the optimum zoom trajectory in specific design criteria. The proposed method is demonstrated through two numerical examples under different configurations. The simulation results demonstrate that our proposed method can be a practical and powerful tool for paraxial design of complex multi-group zoom optical systems.
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