针对自由曲面能提升成像光学系统的性能和校正像差的特点，分析了自由曲面在离轴光学系统中的应用优势。光学系统选用视场角为30°×11°、焦距为150 mm、F数为3的Cook-TMA。本设计中，离轴三反光学系统的主反射镜采用自由曲面设计。分析了使用Zernike多项式曲面在大视场离轴反射式光学系统中对离轴光学系统性能的提升效果，并与使用常规非球面的情况进行了比较，分析了自由曲面的优缺点。结果表明，自由曲面在提高离轴光学系统的成像质量方面具有更大的优势，系统的平均传递函数比常规非球面提升了15.9%以上，系统接近衍射极限。Zernike多项式曲面在离轴三反系统中的应用效果良好，系统的成像性能得到了较大的提升。

According to the features of free-form surfaces which can improve the performance of optical systems and correct aberration, the advantages of using free-form surfaces in off-axis optical systems are analyzed. The optical system used is a Cook-TMA with a field angle of 30°×11°, a focal length of 150 mm and a F number of 3. In this design, the main reflector in the off-axis three-mirror optical system is designed by using a free-form surface. The performance improvement of using Zernike polynomial surface in a wide field off-axis reflecting optical system is analyzed and compared with that of the use of conventional aspheric surface. The advantages and disadvantages of free-form surfaces are analyzed. The results show that free-form surfaces have more advantages in the improvement of imaging quality of off-axis optical systems. The average transfer function of using free-form surface is 15.9% higher than that of using conventional aspheric surface. The system is close to diffraction limit. The use effectiveness of Zernike polynomial surface in the off-axis three-mirror optical system is good and the imaging performance of the system is improved greatly.