The paper presents a methodology of calculation of the inner structure of two- and three-component hybrid liquid-membrane lenses with variable focal length that have corrected spherical aberration and coma. Specifically, the formulas for calculation of initial-design inner parameters (radii of curvatures of individual surfaces, axial thickness, and refractive indices of a material of the lens) of a thin-lens system are derived for a hybrid two-component system (doublet) made by one glass and one liquid-membrane lens, and a hybrid three-component lens (triplet) made by one glass lens and two liquid-membrane lenses, which both have variable focal length and corrected spherical aberration and coma for an object at infinity. As optimization during the optical design process requires the starting point be very close to the optimal solution, the presented approach can be successfully used for its calculation, as it is based on fundamental proven formulas of optical aberrations.

中文翻译：

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由一个固定的光学元件和一个或两个有源的光学元件制成的混合液膜透镜

本文提出了一种计算焦距可变并校正了球差和彗差的两组分和三组分混合液膜透镜内部结构的计算方法。具体地，对于混合两成分系统（双峰），推导出用于薄透镜系统的初始设计内部参数（各个表面的曲率半径，轴向厚度和透镜的材料的折射率）的计算公式。 ）由一个玻璃和一个液膜透镜制成，以及由一个玻璃透镜和两个液膜透镜制成的混合三分量透镜（三重透镜），它们均具有可变的焦距并校正了物镜的球差和彗差无限。由于在光学设计过程中进行优化需要起点非常接近最佳解决方案，