中文摘要：

在理论分析伽马非线性引起相位误差的基础上,本文提出一种新的反相条纹投影形貌测量方法,能补偿条纹投影法中非线性误差的影响。若相机和投影仪存在二阶和三阶伽马非线性残余,会造成四步相移法产生四倍频的非线性相位误差。通过预先引入偏移相位π/4到四步相移法中,使其对应的非线性相位误差发生变号,这样偏移前后的测量相位相加即可补偿非线性误差的影响。针对四步相移法,仿真模拟和实验结果显示出非线性相位误差的频率始终是条纹频率四倍,验证了反相条纹投影方法的可行性和适用性,与常规方法相比,具有更高的测量精度。

英文摘要：

A new inverse phase fringe projection profilometry method is proposed in this paper to compensate the nonlinear phase errors in fringe projection based on theoretical analysis of the phase error caused by gamma nonlinearity.The second-order and third-order gamma nonlinear residues existing in camera and projector system may cause nonlinear phase error with four times of fringe frequency in four-step phase shifting method.Through pre-introducing phase-offset π /4 into four-step phase shifting method,the corresponding nonlinear phase error inverses its sign,so that the nonlinear errors can be compensated by addition operation of the unwrapped phases before and after the phase-offset.For four-step phase shifting method,the simulation and experimental results show that nonlinear phase error frequency is always 4 times the fringe frequency,which verifies the feasibility and applicability of inverse phase fringe projection method.Comparing with conventional method,inverse phase method has higher measuring accuracy.