光束整形技术能够实现激光光束能量分布的良好控制，在激光加工、医疗、激光核聚变等方面具有广泛的应用前景。光束整形方法主要分为几何光学方法和物理光学方法两大类，其中几何光学方法由于忽略了衍射效应，导致一些情形下的光束整形效果不够精细，但却能为物理光学方法提供良好的优化起点。结合几何光学方法和物理光学方法的复合设计方法能够设计出易于加工的自由曲面衍射光学元件，同时能抑制杂散光和散斑噪声。首先回顾了物理光学方法，然后综述了几何光学-物理光学复合设计方法的研究进展，最后对衍射光学元件设计方法的未来发展方向进行了一定的展望。

We implement Monte Carlo-based parallel ray tracing to achieve quick irradiance evaluation for freeform lenses with non-uniform rational B-splines (NURBS) surfaces. We employ the inverse transform sampling method to sample rays uniformly from the Lambertian light source and adopt the analytical form of the B-spline basis function to achieve fast surface interpolation. When performing parallel calculations for the intersections between the rays and the NURBS surfaces, we propose a parameter transformation method to avoid the parameters escaping from the defined range in the iteration process. Simulation results of two complex picture-generating freeform lenses show that our method is fast and effective.

It is still very challenging to determine a freeform lens for converting a given input beam into a prescribed output beam where not only the irradiance distribution but also the phase distribution hardly can be expressed analytically. Difficulties arise because the ray mapping from the input beam to the output beam is not only intertwined with the required double freeform surfaces but also intertwined with the output phase distribution, whose gradient represents the directions of the output rays. Direct determination of such a problem is very difficult. Here, we develop a special iterative wavefront tailoring (IWT) method to tackle this problem. In a certain iteration, the current calculation data of the double freeform surfaces and the output phase gradient are used to update the coefficients of a Monge–Ampère equation describing an intermediate wavefront next to the entrance freeform surface. The solution to the wavefront equation could lead to an improved ray mapping to be used to update the corresponding phase gradient data and reconstruct the double freeform surfaces. In a demonstrative example that deviates much from the paraxial or small-angle approximation, the new IWT method can generate a freeform lens that performs much better than that designed by a conventional ray mapping method for producing two irradiance distributions in the forms of numerals “1” and “2” on two successive targets, respectively.

Current freeform illumination optical designs are mostly focused on producing prescribed irradiance distributions on planar targets. Here, we aim to design freeform optics that could generate a desired illumination on a curved target from a point source, which is still a challenge. We reduce the difficulties that arise from the curved target by involving its varying z-coordinates in the iterative wavefront tailoring (IWT) procedure. The new IWT-based method is developed under the stereographic coordinate system with a special mesh transformation of the source domain, which is suitable for light sources with light emissions in semi space such as LED sources. The first example demonstrates that a rectangular flat-top illumination can be generated on an undulating surface by a spherical-freeform lens for a Lambertian source. The second example shows that our method is also applicable for producing a non-uniform irradiance distribution in a circular region of the undulating surface.