非垂轴观测平面上自由曲面零光展度光束调控研究

自由曲面可实现具有高性能和新功能的轻小型光束调控系统，观测平面与调控系统光轴之间的垂轴约束是制约自由曲面面形灵活优势发挥的主要因素，而非垂轴观测平面上自由曲面零光展度光束调控一直未得到有效解决。项目根据斯涅耳定律和能量守恒定律，采用微分几何理论建立非垂轴观测平面上自由曲面零光展度光束调控模型，分析观测平面的空间位姿对细光束能量传输的影响，探明非垂轴约束下零光展度光束能量传输的调控机理；研究有限差分法的精度、光学曲面初始面形以及观测平面空间位姿的演进路径对模型求解收敛性的影响，实现自由曲面的准确重构；研究多曲面光束偏折中曲面高斯曲率、能量传输效率以及光束偏折分配之间的内在关联，实现多曲面光束调控系统的合理化设计；开展光束调控理论的原理性试验验证及应用研究，形成非垂轴观测平面上自由曲面零光展度光束调控方法；为自由曲面光束调控应用提供理论基础，在高效节能照明和激光束整形等领域有着广泛应用前景。

The flexible surface geometry of freeform optical surfaces allows us to create compact yet efficient beam control systems with new functions and better performance. However, the orthogonality of observation plane with respect to the optical axis of a beam control system is the main factor which invalidates the advantages of freeform surfaces. Unfortunately, the precise propagation control of zero-étendue light beam in a tilted observation plane by freeform surfaces remains unsolved and is still a big challenge facing us. To solve this problem, according to the Snell’s law, conservation law of energy, and the differential geometric theory, this project first develops a mathematical model to represent the propagation control of zero-étendue light beam in a tilted observation plane by freeform surfaces. Base on this mathematical model, the influence of the pose of tilted observation plane on the energy transmission of an infinitely thin light beam through the optical system is then analyzed, and the regulation mechanisms of redirecting light beam to produce a prescribed irradiance distribution in a tilted observation plane is then revealed and discussed. In order to achieve an accurate reconstruction of freeform surfaces, the influence of three key factors, which are the accuracy of the finite difference method, the initial profiles of the freeform surfaces and the evolutionary path of the pose of a tilted observation plane, on the convergence of the numerical algorithm used to solve the mathematical model is analyzed. Meanwhile, the relation between the Gauss curvature, the efficiency of energy transfer, and the deflection of light by each freeform surface is also explored, which can be used to obtain a rational design when the optical system includes multiple optical surfaces. After that, the experimental verification and application research of the developed beam regulation theory are carried out. The ultimate purpose of this project is to establish an effective and complete design theory, by which the precise propagation control of zero-étendue light beam in a tilted observation plane can be achieved by use of freeform surfaces. This project not only provides the theoretical support and technical guidance for beam shaping with freeform optics, but also has great prospects and wide application possibilities in the energy-efficient lighting and laser beam shaping in the near future.