Chinese Optics, Volume. 18, Issue 2, 245(2025)

Optimal fringe frequency allocation for non-standard phase-shifting profilometry

Yi-xin JI, Long-xiang ZHANG, Wei WU, and Jian-hua WANG*
Author Affiliations
  • School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China
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    Figures & Tables(9)
    Comparison of reconstruction results of dual-frequency and triple-frequency TPU algorithms. (a) 3-step and {fh=64, fm=8, fl=1}; (b) 3-step and {fh=64, fl=1}; (c) 3fh+2fm+2fl and {fh=64, fm=8, fl=1}; (d) 3fh+2fl and {fh=64, fl=1}
    Wrapped phase error variances for 3fh1+2fh2+2fh3 algorithm
    3D reconstruction results of the simulated surface. (a) Simulated surface (with magnified view); frequency combination (b) { fh=169, fm=13, fl=1}; (c) { fh=169, fm=5, fl=1}; (d) { fh=169, fm=20, fl=1}
    Comparison of reconstruction results based on 3fh1+2fh2+2fh3 heterodyne TPU. (a) 3fh1+2fh2+2fh3 and {fh1=153, fh2=148, fh3=144}; (b) 3fh1+2fh2+2fh3 and {fh1=153, fh2=143, fh3=134}; (c) 3fh1+2fh2+2fh3 and {fh1=153, fh2=133, fh3=114}; (d) 12-step and {fh1=153, fh2=148, fh3=144}; (e) 12-step and {fh1=153, fh2=143, fh3=134}; (f) 12-step and {fh1=153, fh2=133, fh3=114}; (g) cross-sectional comparison (line 600); (h) an enlarged view of (g)
    Comparison of reconstruction results based on 2fh+2fm+3fl hierarchical TPU. (a) 2fh+2fm+3fland {fh=181, fm=6, fl=1}; (b) 2fh+2fm+3fl and {fh=181, fm=16, fl=1}; (c) 2fh+2fm+3fl and {fh=181, fm=30, fl=1}; (d) 12-step and {fh=181, fm=6, fl=1}; (e)12-step and {fh=181, fm=16, fl=1}; (f) 12-step and {fh=181, fm=30, fl=1}; (g) cross-sectional comparison (line 170); (h) an enlarged view of (g)
    • Table 1. Optimal frequency combinations for non-standard triple-frequency heterodyne TPU

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      Table 1. Optimal frequency combinations for non-standard triple-frequency heterodyne TPU

      fh1fh2fh3
      3fh1+2fh2+2fh3153143134
      2fh1+2fh2+3fh3160149139
    • Table 2. Optimal frequency combinations for non-standard triple-frequency hierarchical TPU

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      Table 2. Optimal frequency combinations for non-standard triple-frequency hierarchical TPU

      fhfmfl
      3fh+2fm+2fl169131
      2fh+2fm+3fl181161
    • Table 3. Quantitative comparison based on 3fh1+2fh2+2fh3 heterodyne TPU

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      Table 3. Quantitative comparison based on 3fh1+2fh2+2fh3 heterodyne TPU

      {fh1, fh2, fh3}Error rateRMSE/rad
      {153, 143, 134}11.76%10.4789
      {153, 148, 144}30.41%11.3039
      {153, 133, 114}33.18%24.6249
    • Table 4. Quantitative comparison based on 2fh+2fm+3fl hierarchical TPU

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      Table 4. Quantitative comparison based on 2fh+2fm+3fl hierarchical TPU

      {fh, fm, fl}Error rateRMSE/rad
      {181, 16, 1}4.56%1.5398
      {181, 6, 1}15.41%3.9469
      {181, 30, 1}6.33%4.5043
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    Yi-xin JI, Long-xiang ZHANG, Wei WU, Jian-hua WANG. Optimal fringe frequency allocation for non-standard phase-shifting profilometry[J]. Chinese Optics, 2025, 18(2): 245

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    Paper Information

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    Received: Sep. 19, 2024

    Accepted: Nov. 7, 2024

    Published Online: May. 19, 2025

    The Author Email:

    DOI:10.37188/CO.2024-0163

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