为了使投影设备具有超短投影距离, 实现大尺寸高清显示画面, 设计了一款采用折反式成像光路的具有大相对孔径和小投射比的超短焦距投影物镜。系统使用12mm(0.47in)DMD微显示芯片, 在450mm距离处实现了2032mm(80in)的投影画面, 采用远心光路提高像面照度均匀性。基于微分几何原理和斯涅尔反射定律, 建立自由曲面方程计算自由曲面轮廓线的离散点坐标, 运用最小二乘法进行偶次非球面拟合得到非球面反射面, 对大视场像差和畸变进行校正。物镜焦距为2.64mm、光学总长193mm、投射比0.25、F数1.83、视场角150°作为参数; 各视场MTF值在单个像素对应的奈奎斯特频率处达到0.3以上, 水平、垂直TV畸变小于0.5%, 投影像面相对照度大于90%。各项指标满足系统设计要求, 结构简单, 易于加工和生产。

A refractive-reflective ultra-short focus projection lens is designed to make projection equipment get ultra short projection distance and large size high-definition display screen. The system uses 12mm(0.47 in) DMD micro display chip and achieves a 2032mm(80 in) projection screen at 450mm distance. Telecentric optical path is adopted to improve illumination uniformity of image plane. According to differential geometry theory and the law of reflection, freeform surface equation is established and discrete point coordinate of the contour line is computed. Then aspheric reflector is solved by least square method and even aspheric fitting method. The lens has a focal length of 2.64mm, a total length of 193mm, a projection ratio of 0.25, a F-number of 1.83 and a wide field of view ( FOV) of 150°. Its MTF is higher than 0.3 in all fields at the Nyquist frequency corresponding to a single pixel, its horizontal and vertical TV distortion is below 0.5%. The projected image plane relative illumination of the lens is above 90%. Each index meet the design requirements of the system. The structure is simple and easy to process and produce.