设计了一种自由曲面车载抬头显示器（Head-up Display，HUD）光学系统.在HUD光学系统初始结构设计中，基于种子曲线扩展算法，对HUD中两个自由曲面上的采样数据点进行计算，并拟合成扩展多项式.将设计的HUD光学系统初始结构进行光线追迹，验证了设计结果.结果表明，在0.5 mm光线采样间隔下，初始光学系统的性能达到了衍射极限，可作为进一步全视场优化的起点.对系统进行优化，利用多重结构模拟人眼在孔径光阑移动范围（眼动范围）内的观察情况，对于不同的孔径光阑位置，光学系统的调制传递函数在6 lp/mm下均大于0.5，接近衍射极限，并且系统畸变小于2%.最后对系统中的自由曲面反射镜进行面形公差分析，两个曲面在其各自面形公差峰谷值分别为0.42 μm和0.62 μm下的调制传递函数均高于0.3，完全满足现在自由曲面加工精度.

A freeform optical system of automotive Head-Up Display (HUD) was designed. In the initial layout design of the HUD optical system, the sample points on two optical freeform surfaces of the HUD optical system are calculated by the seed curve extension algorithm. And the two freeform surfaces are expressed by the extended polynomials. Then the ray tracing is performed for the initial layout of the HUD optical system at center field of view with 0.5 mm ray sampling interval. The results show that the performance of the initial layout of the HUD optical system is the diffraction-limited, which can be used as the starting point for further optimization at full field of view. After optimization, the final HUD optical system is obtained. In order to simulate the observation of human eyes, several test points in the Eyebox are taken as object points, which are imaged on the image plane by the HUD optical system. The modulation transfer function plots of the several test points are greater than 0.5 at 6 lp/mm, which are close to diffraction limit. And the distortions of the final HUD system are less than 2%. Finally, the manufacture tolerances of two optical freeform surfaces are analyzed. The results show that the modulation transfer function plots of the HUD optical system are higher than 0.3 with the tolerance PV values of 0.42 μm and 0.62 μm of the two optical freeform surfaces respectively. For the current machining capacity, the tolerance requirements are reasonable.