Paraxial design of four-component zoom lens system with fixed distance between focal points by matrix optics

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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 to achieve a relatively high zoom ratio. In the method, the zoom trajectory under each chosen paraxial design is determined through matrix method, which is challenging but meaningful to achieve a globally optimized design for the complex zoom system. 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 specific examples under different configurations, both of which have acquired a final zoom ratio of 8X. 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.