Chen Qili, Han Mengqi, Wang Ye, Chen Wenjing
Department of Opto-Electronics, Sichuan University, Chengdu 610065, China.
Sensors (Basel). 2022 Aug 12;22(16):6048. doi: 10.3390/s22166048.
Circular fringe projection profilometry (CFPP), as a branch of carrier fringe projection profilometry, has attracted research interest in recent years. Circular fringe Fourier transform profilometry (CFFTP) has been used to measure out-of-plane objects quickly because the absolute phase can be obtained by employing fewer fringes. However, the existing CFFTP method needs to solve a quadratic equation to calculate the pixel displacement amount related to the height of the object, in which the root-seeking process may get into trouble due to the phase error and the non-uniform period of reference fringe. In this paper, an improved CFFTP method based on a non-telecentric model is presented. The calculation of displacement amount is performed by solving a linear equation instead of a quadratic equation after introducing an extra projection of circular fringe with circular center translation. In addition, Gerchberg iteration is employed to eliminate phase error of the region close to the circular center, and the plane calibration technique is used to eliminate system error by establishing a displacement-to-height look-up table. The mathematical model and theoretical analysis are presented. Simulations and experiments have demonstrated the effectiveness of the proposed method.
环形条纹投影轮廓术（CFPP）作为载波条纹投影轮廓术的一个分支，近年来引起了研究兴趣。环形条纹傅里叶变换轮廓术（CFFTP）已被用于快速测量离面物体，因为通过使用较少的条纹就可以获得绝对相位。然而，现有的CFFTP方法需要求解一个二次方程来计算与物体高度相关的像素位移量，其中由于相位误差和参考条纹的非均匀周期，寻根过程可能会遇到麻烦。本文提出了一种基于非远心模型的改进CFFTP方法。在引入具有圆心平移的环形条纹的额外投影后，通过求解线性方程而不是二次方程来进行位移量的计算。此外，采用Gerchberg迭代来消除靠近圆心区域的相位误差，并使用平面校准技术通过建立位移-高度查找表来消除系统误差。给出了数学模型和理论分析。仿真和实验证明了该方法的有效性。
