中文摘要：

针对常规光栅条纹反射三维形貌测量方法中对实际参考面的需求，提出了基于虚拟参考面方法。在系统标定阶段，通过向标定用平面镜投射一幅特殊标记的棋盘格图像，将其在平面镜另一侧成的虚拟像所在的平面定义为虚拟参考面。根据虚拟参考面上各点与编码光栅条纹相位间的对应关系，经计算可直接得到测量所需的两垂直方向的参考相位分布，从而无需在工件测量前首先对实际参考面进行相位提取操作。与常规光栅条纹反射三维形貌测量方法相比，由于避免了对参考平面测量的需求，本文方法获得的参考相位分布，在保证测量精度的同时提高了测量速度，降低了测量的复杂性，有利于系统的集成化。搭建了光栅条纹反射三维形貌测量系统，采用基于虚拟参考面的光栅条纹反射方法对超精密加工平面镜和组合台阶的表面形貌进行测量，建立相位偏移与被测工件表面梯度的对应关系，由梯度恢复工件表面高度，测量精度达到50μm左右。

英文摘要：

To achieve the requirement for a real reference surface in regular three-dimensional （3D） shape measurement based on fringe reflection technique, a novel method of virtual reference surface is proposed. A marked checkerboard image is projected onto a flat mirror at the stage of system calibration and the virtual image plane on the other side of the mirror is defined as the virtual reference surface. The reference phase distribution can be calculated directly through the corresponding relationship between the points on the virtual reference surface and the phase distribution on the encoded fringe patterns. Thus the procedure of phase extraction on the real reference surface can be avoided before the measurement of the high-reflected parts. Results show that with this method,the three dimensional shape of the high-reflected surface can be obtained fast and precisely compared with regular fringe reflection method. The detection efficiency has been improved and the measurement complexity can be reduced. The measurement e- qnipment is built and fringe reflection method based on virtual reference surface is adopted to recover the three dimensional shapes of an ultra-precise mirror and a combination step. By establishing the relationship between the phase deflection and the slope distribution on the measured parts, the topography can be reconstructed by the slope information and the measurement accuracy can reach 50 μm approximately.