基于改进希尔伯特-黄变换的单帧相位解调技术

王少强; 刘春兵; 高楠; 倪育博; 孟召宗; 张宗华

您当前的位置：

首页 >

文章列表页 >

基于改进希尔伯特-黄变换的单帧相位解调技术

光学传感与测量 | 更新时间：2026-05-20

- 基于改进希尔伯特-黄变换的单帧相位解调技术
- Single-frame phase demodulation technique based on the improved Hilbert–Huang transform
- 光学技术 2026年52卷第3期页码：279-287
- 作者机构：
  
  1.河北工业大学机械工程学院，天津 300401
  2.河北工业大学创新研究院（石家庄），河北石家庄 050299
- 作者简介：
  
  王少强（2000— ），男，硕士研究生，从事光学三维形貌测量研究。wangsq3245@163.com
  高楠（1982— ），男，副教授，博士，从事光学三维形貌测量研究。ngao@hebut.edu.cn
- 基金信息：
  
  国家自然科学基金(U2341275);河北省自然科学基金(E2024202121)
- DOI：
  中图分类号： TH741
- 收稿：2026-01-19，
  
  修回：2026-03-10，
  
  录用：2026-03-30，
  
  纸质出版：2026-05-20
- 稿件说明：
移动端阅览
王少强,刘春兵,高楠等.基于改进希尔伯特-黄变换的单帧相位解调技术[J].光学技术,2026,52(03):279-287.

WANG Shaoqiang,LIU Chunbing,GAO Nan,et al.Single-frame phase demodulation technique based on the improved Hilbert–Huang transform[J].OPTICAL TECHNIQUE,2026,52(03):279-287.
王少强,刘春兵,高楠等.基于改进希尔伯特-黄变换的单帧相位解调技术[J].光学技术,2026,52(03):279-287. DOI：

WANG Shaoqiang,LIU Chunbing,GAO Nan,et al.Single-frame phase demodulation technique based on the improved Hilbert–Huang transform[J].OPTICAL TECHNIQUE,2026,52(03):279-287. DOI：

摘要

单帧条纹投影技术可用于测量动态连续目标的三维形貌，希尔伯特-黄变换因具有自适应局部分析能力被广泛应用于单帧相位解调过程，方法中的经验模态分解阶段存在条纹分量难以集中提取的问题，影响相位解调精度。为此，提出一种基于改进希尔伯特-黄变换的单帧相位解调方法。首先对去噪条纹图执行小波变换以估计条纹局部周期；然后将局部周期作为经验模态分解的自适应滤波器尺寸，使条纹分量集中在单一本征模函数中；最后对条纹分量执行希尔伯特变换完成相位解调。仿真及实验结果表明，相比于已有方法，相位解调精度提高约3倍。所提方法为单帧条纹投影技术提供了一个有效的相位解调方法。

Abstract

Single-frame fringe projection techniques can be used to measure the three-dimensional shape of dynamic and continuous objects. The Hilbert–Huang transform is widely applied to single-frame phase demodulation due to its adaptive local analysis capability; however

the empirical mode decomposition suffers from difficulty in concentrating the extraction of fringe components

which degrades phase demodulation accuracy. To address this issue

a single-frame phase demodulation method based on an improved Hilbert–Huang transform is proposed. First

the wavelet transform is applied to the denoised fringe pattern to estimate the local fringe period. Then

the local period is used as the adaptive filter size in empirical mode decomposition

enabling the fringe component to be concentrated into a single intrinsic mode function. Finally

the Hilbert transform is applied to the extracted fringe component to complete phase demodulation. Simulation and experimental results demonstrate that

compared with existing method

the phase demodulation accuracy is improved by approximately three times. The proposed method provides an effective phase demodulation method for single-frame fringe projection techniques.

关键词

Keywords

references

王晨 , 张宗华 , 丁宇航 , 等 . 基于立体标靶的双目系统标定研究 [J ] . 光学技术 , 2020 , 46 （ 3 ）: 322 — 329 .

Wang Chen , Zhang Zonghua , Ding Yuhang , et al . Research on the calibration of binocular system based on stereoscopic target [J ] . Optical Technique , 2020 , 46 （ 3 ）: 322 — 329 .

王永红 , 张倩 , 胡寅 , 等 . 显微条纹投影小视场三维表面成像技术综述 [J ] . 中国光学 , 2021 , 14 （ 03 ）: 447 — 457 .

Wang Yonghong , Zhang Qian , Hu Yan , et al . 3D small-field surface imaging based on microscopic fringe projection profilometry： a review [J ] . Chinese Optics , 2021 , 14 （ 03 ）: 447 — 457 .

Wang J H , Yang Y X . Phase extraction accuracy comparison based on multi-frequency phase-shifting method in fringe projection profilometry [J ] . Measurement , 2022 , 199 : 111525 .

王邺 , 陈文静 , 韩梦奇 . 基于傅里叶变换的改进圆形条纹投影轮廓术 [J ] . 光学学报 , 2022 , 42 （ 13 ）: 89 — 99 .

Wang Ye , Chen Wenjing , Han Mengqi . Improved circular fringe projection profilometry based on Fourier transform [J ] . Acta Optica Sinica , 2022 , 42 （ 13 ）: 89 — 99 .

邓烨欢 , 陈文静 , 张启灿 . 基于窗口傅里叶变换的圆形条纹投影轮廓术 [J ] . 光学与光电技术 , 2025 , 23 （ 01 ）: 67 — 78 .

Deng Yehuan , Chen Wenjing , Zhang Qican . Circular fringe projection profilometry based on windowed Fourier transform [J ] . Optics & Optoelectronic Technology , 2025 , 23 （ 01 ）: 67 — 78 .

Han M Q , Chen W J . Dual-angle rotation two-dimensional wavelet transform profilometry [J ] . Optics Letters , 2022 , 47 （ 6 ）: 1395 — 1398 .

Huang N E , Shen Z , Long S R , et al . The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis [J ] . Proceedings Mathematical Physical & Engineering Sciences , 1998 , 454 （ 1971 ）: 903 — 995 .

Zhao Q , Tang C , Min X , et al . Dynamic shape measurement for objects with patterns by Fourier fringe projection profilometry based on variational decomposition and multi-scale Retinex [J ] . Applied Optics , 2021 , 60 （ 33 ）: 10322 — 10331 .

黄宇 , 钟金钢 . 窗口傅里叶变换轮廓术中窗口尺度选取的改进 [J ] . 光学技术 , 2010 , 36 （ 3 ）: 378 — 385 .

Huang Yu , Zhong Jingang . Improved algorithm to choose the window scale for windowed Fourier transform profilometry [J ] . Optical Technique , 2010 , 36 （ 3 ）: 378 — 385 .

Han M Q , Chen W J . Two-dimensional complex wavelet with directional selectivity used in fringe projection profilometry [J ] . Optics Letters , 2021 , 46 （ 15 ）: 3653 — 3656 .

高楠 , 张璨 , 孟召宗 , 等 . 频域分析的条纹投影技术相位解调方法研究进展 [J ] . 光学技术 , 2023 , 49 （ 04 ）: 436 — 445 .

Gao Nan , Zhang Can , Meng Zhaozong , et al . Review on phase demodulation methods of fringe projection based on frequency domain analysis [J ] . Optical Technique , 2023 , 49 （ 04 ）: 436 — 445 .

王辰星 , 达飞鹏 . 基于经验模态分解法的光学条纹图像处理研究进展 [J ] . 红外与激光工程 , 2020 , 49 （ 3 ）: 0303013-0303013-11 .

Wang Chenxing , Da Feipeng . Researches of optical fringe pattern analysis based on EMD algorithms [J ] . Infrared and Laser Engineering , 2020 , 49 （ 3 ）: 0303013-0303013-11 .

Nunes J C , Bouaoune Y , Delechelle E , et al . Image analysis by bidimensional empirical mode decomposition [J ] . Image and Vision Computing , 2003 , 21 （ 12 ）: 1019 — 1026 .

Bhuiyan S M A , Adhami R R , Khan J F . Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation [J ] . EURASIP Journal on Advances in Signal Processing , 2008 , 2008 : 1 — 18 .

Trusiak M , Wielgus M , Patorski K . Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition [J ] . Optics and Lasers in Engineering , 2014 , 52 : 230 — 240 .

Cywińska M , Trusiak M , Patorski K . Automatized fringe pattern preprocessing using unsupervised variational image decomposition [J ] . Optics Express , 2019 , 27 （ 16 ）: 22542 — 22562 .

Guo W B , Wu Z J , Zhang Q C , et al . Real-time motion-induced error compensation for 4-step phase-shifting profilometry [J ] . Optics Express , 2021 , 29 （ 15 ）: 23822 — 23834 .

Zhang Z H , Towers C E , Towers D P . Time efficient color fringe projection system for 3D shape and color using optimum 3-frequency selection [J ] . Optics Express , 2006 , 14 （ 14 ）: 6444 — 6455 .

张宗华 , 李雁玲 , 高峰 , 等 . 面向结构光三维测量的相位展开技术综述（特邀） [J ] . 红外与激光工程 , 2023 , 52 （ 08 ）: 23 — 45 .

Zhang Zonghua , Li Yanling , Gao Feng , et al . Phase unwrapping technology for structured light three-dimensional measurement: a review （invited） [J ] . Infrared and Laser Engineering , 2023 , 52 （ 08 ）: 23 — 45 .

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

基于斐索干涉仪的红外光学材料折射率测量方法

基于分组多线编码与特征增强的口内三维测量技术

基于近红外光谱辐照度和卷积神经网络的积冰分类方法

基于混合互相关光流算法的背景定向纹影温度场测量研究

显微光谱拟合法在微区薄膜表征中的优化与应用