Abstract: Phase unwrapping is a key step in fringe projection profilometry. The theory of weighted least squares is introduced and Picard iterative algorithm is improved by using wavelet multi-resolution analysis. The errors are decomposed into low-frequency components and high-frequency components. Both of them use Picard iteration to speed up the convergence. The experimental results indicate that it can suppress more noise with less iteration.

Key words: fringe projection profilometry, phase unwrapping, weighted least squares, Picard iteration, wavelet multi-resolution analysis

摘要： 相位展开是光栅投影廓术中的一个关键步骤。对加权最小二乘相位展开算法的原理进行了介绍，利用小波多分辨率特性对Picard迭代算法进行了改进。改进的算法将误差分解为低频和高频成分，对它们分别进行Picard迭代来提高收敛速度。实验结果证明：改进后的算法具有收敛速度快，抗噪能力强等优点。

关键词: 光栅投影轮廓术, 相位展开, 加权最小二乘, Picard迭代, 小波多分辨率分析