传统球面以及非球面可供光学系统设计使用的自由度较少。自由曲面打破了旋转对称以及平移对称的几何约束,特别适用于校正非旋转对称系统的像差,同时可以减少系统中元件的数量,减小系统的体积与质量,实现传统光学系统难以实现的系统参数、结构与功能。自由曲面为光学设计的发展注入了巨大潜力,但同时也带来了全新的困难与挑战。概括性地总结了自由曲面成像系统设计的研究现状。简要介绍了自由曲面的常用数学描述与自由曲面成像系统的像差理论,总结了自由曲面成像系统的设计方法,并对自由曲面在各类成像系统中的应用进行概述。最后,对自由曲面成像光学设计的未来发展方向进行了讨论与展望。

Traditional spherical and aspherical surfaces offer limited degrees of freedom for optical system design. Freeform surface breaks the geometric constraints of rotational or translational symmetry. It can correct the aberrations in non-rotationally symmetric systems while decreasing the system size, mass, and number of elements in optical design. The system specifications, configurations, and functions which are difficult to be realized by traditional spherical or aspherical systems can be achieved by using freeform surfaces. The use of freeform surfaces not only offers great potential in the development of the optical design field, but also introduces new difficulties and challenges. This review briefly summarizes the current status of research on the freeform imaging system design. The commonly used types of freeform surface mathematical expression and the aberration theory of freeform imaging systems are demonstrated. The design methods of freeform imaging systems and the applications of freeform surface in various imaging systems are summarized. Finally, the future research directions of the freeform imaging system design are discussed and analyzed.