Li Fuqian, Chen Wenjing
Department of Opto-Electronics, Sichuan University, Chengdu 610065, China.
Sensors (Basel). 2021 Sep 28;21(19):6475. doi: 10.3390/s21196475.
Crossed-grating phase-shifting profilometry (CGPSP) has great utility in three-dimensional shape measurement due to its ability to acquire horizontal and vertical phase maps in a single measurement. However, CGPSP is extremely sensitive to the non-linearity effect of a digital fringe projection system, which is not studied in depth yet. In this paper, a mathematical model is established to analyze the phase error caused by the non-linearity effect. Subsequently, two methods used to eliminate the non-linearity error are discussed in detail. To be specific, a double five-step algorithm based on the mathematical model is proposed to passively suppress the second non-linearity. Furthermore, a precoding gamma correction method based on probability distribution function is introduced to actively attenuate the non-linearity of the captured crossed fringe. The comparison results show that the active gamma correction method requires less fringe patterns and can more effectively reduce the non-linearity error compared with the passive method. Finally, employing CGPSP with gamma correction, a faster and reliable inverse pattern projection is realized with less fringe patterns.
交叉光栅相移轮廓术（CGPSP）由于能够在单次测量中获取水平和垂直相位图，在三维形状测量中具有很大的实用性。然而，CGPSP对数字条纹投影系统的非线性效应极为敏感，目前对此尚未进行深入研究。本文建立了一个数学模型来分析由非线性效应引起的相位误差。随后，详细讨论了两种用于消除非线性误差的方法。具体而言，基于该数学模型提出了一种双五步算法来被动抑制二次非线性。此外，引入了一种基于概率分布函数的预编码伽马校正方法来主动减弱所捕获交叉条纹的非线性。比较结果表明，与被动方法相比，主动伽马校正方法所需的条纹图案更少，并且能够更有效地降低非线性误差。最后，通过采用具有伽马校正的CGPSP，用更少的条纹图案实现了更快且可靠的逆图案投影。
