Fast phase unwrapping algorithm based on region segmenting with mathematical morphology

Meng-xia LI; Bo CAO; Jia-wei LU; Kai-Hua CUI; Qian LIU

doi:10.37188/OPE.20212911.2724

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Fast phase unwrapping algorithm based on region segmenting with mathematical morphology

Information Sciences | 更新时间：2022-01-25

- Fast phase unwrapping algorithm based on region segmenting with mathematical morphology
- Optics and Precision Engineering Vol. 29, Issue 11, Pages: 2724-2733(2021)
- 作者机构：
  
  1.中国工程物理研究院机械制造工艺研究所，四川绵阳 621000
  2.清华大学精密仪器系，北京 100084
- 作者简介：
- 基金信息：
- DOI：10.37188/OPE.20212911.2724
  CLC： O436.1;TH744
- Received：28 April 2021，
  
  Revised：28 May 2021，
  
  Published：15 November 2021
- 稿件说明：
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李梦霞,曹博,卢佳玮等.数学形态学区域分割的快速相位解包裹算法[J].光学精密工程,2021,29(11):2724-2733.

LI Meng-xia,CAO Bo,LU Jia-wei,et al.Fast phase unwrapping algorithm based on region segmenting with mathematical morphology[J].Optics and Precision Engineering,2021,29(11):2724-2733.
李梦霞,曹博,卢佳玮等.数学形态学区域分割的快速相位解包裹算法[J].光学精密工程,2021,29(11):2724-2733. DOI： 10.37188/OPE.20212911.2724.

LI Meng-xia,CAO Bo,LU Jia-wei,et al.Fast phase unwrapping algorithm based on region segmenting with mathematical morphology[J].Optics and Precision Engineering,2021,29(11):2724-2733. DOI： 10.37188/OPE.20212911.2724.

摘要

相位解包裹是光学干涉测量的关键环节，要求计算速度快、精度高、适应性强。根据包裹相位不同级次间存在明显边界的特点，本文提出数学形态学区域分割的快速相位解包裹算法。首先，采用数学形态学提取边界并分割相位区域。然后，计算区域之间的相位差异以确定各区域的相位级次和抬升值，判断边界点归属以确定边界各点抬升值。最后，根据抬升值对各区域相位进行整体抬升，最终获得空间上连续分布的相位。仿真和实验表明：基于数学形态学的解包裹算法对于1 000×1 000 pixels像素的相位处理时间在1 s以内，仅为经典的最小二乘算法用时的1/4，且相位自身边界、无效区域、噪声等因素对解包裹效果并无影响。该算法具有速度快、适用性强、精度较高等优点，在动态光干涉、光全息、光栅条纹投影轮廓测量等对运算速度要求较高的测量场景中有广泛的应用前景。

Abstract

The key step of optical interferometry is phase unwrapping， which is expected to be computationally fast， highly precise， and widely applicable. According to the feature of wrapped phase that between different order fringes there are significant edges

a fast unwrapping algorithm based on region segmenting with mathematical morphology(RSMM) is proposed. First， mathematical morphology is applied to extract the boundaries and segment regions from the phase map. Then

phase differences between adjacent regions are calculated in order to determine the phase order and elevated quantity of each region

and so are phases of the pixels on boundaries. Finally， wrapped phases in regions and boundaries are elevated individually according to the quantified elevation to obtain the unwrapped phase map. Simulations and experiments indicate that RSMM requires less than 1 second to unwrap and generate a phase map for 1 000×1 000 pixels， and this required time is less than a quarter of the computation time of conventional least-square algorithms. In addition， the phase unwrapping performance is not influenced by phase boundary， data dropout， and noise. The RSMM algorithm has the advantages of high speed， broad adaptability， and high accuracy and is promising for measurement applications with a commanding requirement for computation speed， such as dynamic interferometry， optical holography， and fringe projecting profilometry.

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