基于改进Goldstein枝切法的傅里叶变换轮廓术  

Fourier Transform Profilometry Based on Improved Goldstein Branch-Cut Algorithm

作　　者：游前 翁慧 赵江 李岳彬[1] 王文峰[1] 卢仕 彭旷 You Qian;Weng Hui;Zhao Jiang;Li Yuebin;Wang Wenfeng;Lu Shi;Peng Kuang(Hubei Key Laboratory of Ferro&Piezoelectric Materials and Devices,School of Microelectronics,Hubei University,Wuhan 430062,Hubei,China)

机构地区：[1]湖北大学微电子学院,铁电压电材料与器件湖北省重点实验室,湖北武汉430062

出　　处：《光学学报》2023年第5期70-79,共10页Acta Optica Sinica

基　　金：湖北省教育厅科学技术研究计划青年人才项目(Q20201006);湖北省自然科学基金面上类青年项目(2020CFB266)。

摘　　要：Goldstein枝切法通过连接残差点生成枝切线以优化相位展开路径,枝切线的总长度越短,相位展开的结果越好。然而,该方法构造的枝切线无法确保总长度最短且容易闭合,造成部分区域相位未能正确展开,从而影响重构精度。因此,提出一种基于改进Goldstein枝切法的傅里叶变换轮廓术。通过构建加权二分图,将构造总长度最短的枝切线问题转化为最大权匹配问题。采用Kuhn-Munkres算法求解最大权匹配问题,得到最短的枝切线,提升重构精度。仿真和实验结果证明了所提方法的有效性。Objective Fringe projection profilometry is a representative method for optical three-dimensional measurement and is widely applied in intelligent manufacturing,virtual reality,cultural heritage protection,biomedicine,and industrial inspection.Fringe projection profilometry mainly includes Moiréprofilometry,Fourier transform profilometry,and phase measurement profilometry.Fourier transform profilometry can recover the three-dimensional surface information of the measured object through phase calculation,phase unwrapping,and phase-height mapping.It has the advantages of less data processing and a fast measurement speed,thus being widely used in three-dimensional reconstruction.The phase value obtained by phase calculation will be wrapped at(−π,π].It is necessary to convert the wrapped phase into a continuous phase through phase unwrapping,and then the height distribution of the measured object can be determined by phase-height mapping.Therefore,the quality of phase unwrapping directly influences the reconstructed accuracy of the measured object.Among many phase unwrapping algorithms,Goldstein branch-cut algorithm is widely used because of its noise-immune ability and high efficiency.After identifying all residues in the wrapped phase map,the Goldstein branch-cut algorithm generates branch cuts by connecting the residues to optimize the phase unwrapping path.The shorter the total length of the branch cuts is,the better the result of phase unwrapping will be.However,the branch cuts constructed by Goldstein branch-cut algorithm cannot ensure the shortest total length and are easy to close,which causes incorrect phase unwrapping in some regions and finally affects the reconstructed accuracy.Therefore,Fourier transform profilometry based on an improved Goldstein branch-cut algorithm is proposed to ensure the accuracy of three-dimensional measurement.Methods The computer-generated grating fringes are projected onto the surface of the measured object by digital light processing,and the grating fringes are modulated

关 键 词：傅里叶光学 三维测量 傅里叶变换轮廓术 相位展开 Goldstein枝切法 Kuhn-Munkres算法 

分 类 号：TN247[电子电信—物理电子学]