为了解决传统头盔显示器大出瞳距、大视场与轻型化、小型化间的矛盾，采用径向基函数表征自由曲面设计了一款头盔显示器光学系统。详细论述了径向基函数表征自由曲面的原理，分析了光学系统像差校正方法。在设计中，尝试了一种方法来快速地确定优化起点，分析了该光学系统的成像质量。该光学系统的视场为45°×32°，出瞳大小为15 mm，出瞳距为50 mm。在奈奎斯特频率处，全视场的调制传输函数(MTF)值大于0.6。在(-22.5°,16°)视场处有最大畸变值-1.54%。系统尺寸56 mm×128 mm，重量136 g。优化设计结果表明，该全息头盔显示光学系统像差小，可以较好地为使用者提供清晰的字符信息或者视频图像。该头盔显示光学系统成像质量好，体积小重量轻，可以应用于新一代机载头盔显示技术。

In order to resolve the contradictions between large exit pupil, wide field of view (FOV) and lightweight, small size, a helmet mounted displays (HMDs) system is designed, using freeform surface described by radial basis function. The principle that radial basis function describes freeform surface is introduced, and the approaches for aberration correction are analyzed. A new way is tried to determine a starting point of optimization quickly while designing. At last, the imaging quality of the optical system is analyzed. A HMD with 45°×32°, 15 mm pupil, 50 mm eye relief is designed. The modulation transfer function (MTF) value is more than 0.6 within the entire FOV at the Nyquist frequency. The magnitude of maximum distortion occurs at (-22.5°, 16°) in the field and it is measured in simulation to be -1.54%. The size of the system is 56 mm×128 mm and the weight is 136 g. The design results show that the optical system of HMDs has low aberration, and it can provide user clear symbol or video images. This HMDs system, which has good image quality, small volume, and light weight, can be applied to the next generation avionic HMD technology.