离轴反射式头戴显示光学系统的自由曲面设计方法

为克服现有离轴头戴显示光学系统设计方法不能直接设计全视场全孔径自由曲面反射镜的问题，提出了基于马吕斯定律的自由曲面三维直接设计方法。首先根据马吕斯定律求解自由曲面在全视场和全孔径范围内的所有特征数据点，然后将特征数据点拟合成用多项式表征的自由曲面，直接获得成像质量良好的自由曲面离轴系统初始结构，最后利用评价函数对拟合的多项式系数进行优化，确定最佳拟合系数，生成所需的自由曲面反射镜，得到离轴头戴显示光学系统最终结构。该方法简化了设计流程，计算效率高。基于提出的方法分别设计了单反射面和双反射面的头戴显示光学系统，单反射面系统的出瞳直径为3 mm，视场角19.12°×14.4°；双反射面系统的出瞳直径为8 mm，视场角23°×16°。设计结果表明，用该方法设计的单/双反射面头戴显示系统，其成像质量良好，系统结构紧凑。公差分析表明，引入公差后单/双反射面头戴显示系统最终可实现全视场调制传递函数(MTF)大于0.3 lp/mm和0.35 lp/mm。

Design method of freeform surface for off-axis reflective head-mounted display optical system

In order to overcome the shortcomings of the existing direct design method of freeform surface and the large amount of calculation, according to the structural characteristics of the off-axis display system, a three-dimensional direct design method of freeform surface based on Marius's law is proposed. First, according to Marius's law, all the characteristic data points of the freeform surface are solved in the full field of view and the full aperture. Then the characteristic data points are fitted into a freeform surface characterized by polynomials, and the initial structure of freeform off-axis system with good imaging quality is obtained directly. Finally, the polynomial coefficient is optimized with the merit function and the best fitting coefficient is determined. The required freeform surface mirror is generated and the final structure of the off-axis head-mounted display optical system is obtained. This method simplifies the design process and has high calculation efficiency. Based on the proposed method, a single-mirror head-mounted display optical system and a two-mirror head-mounted display optical system are designed with an entrance pupil diameter of 3 mm, a field angle of 19.12°×14.4° and an entrance pupil diameter of 8 mm, a field angle of 23°×16°, respectively. The design results show that single/two-mirror head-mounted display system designed by proposed method has good imaging quality and compact system structure. Tolerance analysis shows that the single/two head-mounted display system can finally achieve MTF greater than 0.3 lp/mm and 0.35 lp/mm in full field of view after introducing tolerances.