为了求得未知椭球曲面的曲线方程,模拟曲面的几何结构,以数字投影系统中椭球反光镜为例,介绍了大口径非球面反光镜数据采集及拟合方法。利用三坐标测量机(CMM)对椭球反光镜面型进行精密测量,根据测试数据,采用数学拟合方法获得椭球反光镜的曲线方程。并对测试模型与拟合曲面进行了光线追迹和误差分析,拟合曲面与测试曲面符合较好。因此,采用三坐标测量机进行曲面数据采集及数学方法拟合,能够得到较理想的拟合曲面方程。

In order to obtain the unknown curve equation of the ellipsoid surface, the geometrical structure of the ellipsoid surface is simulated, and, with the combination of ellipsoid reflector used in digital projection, the data acquisition and fitting method of aspheric reflector is introduced. The reflector is measured with coordinate measuring machining (CMM), according to the results of the test data, to obtain the theory curve equation of ellipsoid reflector with Mathematical methods. Model and ray tracing results are analysed. Fitting surface is consistent with the test surface. By coordinating the data acquisition with CMM and surface fitting with mathematical methods, an ideal fit surface equation is obtained.