We made a brief summary of the development and application of free-form surface, introduced the research status of free-form surface in space optical system abroad, described the characteristics of three kinds of free surface mathematical models and the aberration balancing ability, focused on the aberration characteristics of free-form surface optical system compared with the axisymmetric system and plane-symmetric system. In addition, we presented the aberration controlling and evaluation method of the free-form space optical system. Finally, we gave the design results of the free-form surface multi-spectral camera adopting Zernike polynomial representations. The results show that the imaging field of view is 76° it adopts telecentric optical path design ; the wide field of view MTF is superior to 0. 56, and it is applicable for space multispectral imaging.%对自由曲面的发展及应用做简要梳理,介绍国外自由曲面空间光学系统的研究现状,讨论3种自由曲面数理模型的特点和像差平衡能力,阐述自由曲面光学系统相对轴对称系统和平面对称系统的像差特点以及自由曲面空间光学系统的像差控制与评价方法,给出采用泽尼克多项式表述的自由曲面多光谱相机的设计结果,成像视场76°,为远心光路设计,全视场调制传递函数(MTF)优于0.56,适用于空间多光谱成像.
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