光学自由曲面是一种面形没有旋转对称轴的曲面，为光学设计提供了非常高的自由度，有利于实现具有高、新性能的光学系统设计。在成像光谱仪系统中，空间维和光谱维两个维度都有独立的设计要求；而在具有特定局域光学特性的成像光学系统中，各个视场具有随视场变化的光学性质。本论文将自由曲面应用于上述两种光学系统的设计，对相应的设计方法和设计策略展开了研究，提出了一种多解的自动设计方法，能够求解具有不同光焦度分配形式和结构形式的自由曲面系统。本论文提出了带有色散器件的光学系统设计中的“视场-孔径-波长”问题，并提出了一种具有衍射光栅的自由曲面成像光谱仪设计方法，能够从无光焦度平面结构或球面结构出发，计算得到高质量的自由曲面成像光谱仪系统。提出了一种具有单个元件的自由曲面成像光谱仪设计，该系统中只具有一个自由曲面凹面光栅，并利用上述设计方法探究了该类系统的性能参数。提出了视场焦距、视场入瞳与视场F数三个局域光学特性参数的描述方法，讨论了它们的意义以及视场焦距的性质。提出了一种具有类人眼功能的成像光学系统，该系统中间视场分辨率高、边缘视场分辨率低，能够兼顾成像系统中的视场与分辨率。对这类系统的设计策略与方法展开了研究。提出了一种自由曲面光学系统的自动多解设计方法，只需输入系统性能参数，就能够得到多种具有不同光焦度分配形式和结构形式的光学系统。基于该方法设计了自由曲面成像光学系统，输出结果的像质达到衍射极限（波像差<0.075λ）。基于自动多解设计方法和具有衍射光栅的自由曲面光学系统设计方法，实现了自由曲面成像光谱仪初始解求解；系统最终具有高像质（达到衍射极限）、低畸变（畸变<20%像元大小）。基于该自动多解设计方法，提出了一种在视场焦距和视场入瞳设计要求约束下，逐步扩大视场并循环计算各镜面面形的计算策略，实现了具有特定局域光学特性的自由曲面光学系统初始解的求解。

Optical freeform surfaces are defined as surfaces that have no axis of rotational invariance, which provide high degrees of freedom for optical design and are beneficial to realizing optical systems with high or novel performances. In imaging spectrometers, the spectral and spatial dimensions have independent design requirements; while in imaging optical systems having field-dependent characteristics, each field-of-view position have various optical properties. In this dissertation, freeform surfaces are applied to the design of the above two types of optical systems. The corresponding design methods and strategies are studied and a result-diversified automatic design method is proposed, which can solve for freeform systems that have various optical power distributions and structures. In this dissertation, the problem of “field-pupil-wavelength” in the design of optical systems containing diffractive element is proposed. A design method for freeform imaging spectrometers containing diffraction grating is proposed, which can obtain a good initial design of freeform imaging spectrometers starting from a planar or spherical initial structure. The design of imaging spectrometer that has single component of freeform concave grating is proposed and the peak specifications are explored by using the method proposed above. A description method of three field-dependent characteristic parameters are proposed, which includes the field focal length, the field entrance pupil and the field F-number. The meanings and properties of the three parameters are discussed. An imaging optical system with a human-like function is proposed, which has a higher resolution in the central part of the field and lower resolution in the marginal part. The field-of-view and resolution can be improved simultaneously in this type of system, and the relevant design method and strategy are studied. A result-diversified automatic design method for freeform imaging systems are proposed, which requires the system specifications as the only input and a lot of systems that has various structures and various optical power distributions can be obtained. By using the proposed method, freeform imaging systems with imaging quality as higher as diffraction-limited （wavefront error ＜ 0.075λ） can be obtained. Based on this automatic design method and the design method for freeform imaging spectrometers containing diffraction gratings, the initial solution of the freeform surface imaging spectrometer with high imaging quality （diffraction-limited） and low distortion （distortion ＜ 20% pixel-pitch） can be realized. Based on this automatic design method, a design method is proposed to solve for the initial solution that has the given field-dependent characteristic specifications, which gradually expand the field-of-view while calculating the freeform figure of each mirror iteratively under the constraints field focal length and field entrance pupil.