Single-frame phase demodulation technique based on the improved Hilbert–Huang transform

WANG Shaoqiang; LIU Chunbing; GAO Nan; NI Yubo; MENG Zhaozong; ZHANG Zonghua

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Single-frame phase demodulation technique based on the improved Hilbert–Huang transform

Optical Sensing and Measurement | 更新时间：2026-05-20

- Single-frame phase demodulation technique based on the improved Hilbert–Huang transform
- OPTICAL TECHNIQUE Vol. 52, Issue 3, Pages: 279-287(2026)
- 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：
- 基金信息：
- DOI：
  CLC： TH741
- Received：19 January 2026，
  
  Revised：2026-03-10，
  
  Accepted：30 March 2026，
  
  Published：20 May 2026
- 稿件说明：
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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.

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references

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