Acta Optica Sinica, Volume. 44, Issue 9, 0934001(2024)

X-Ray Three-Dimensional Reconstruction Algorithm of Plate-Like Objects Based on Filter Path Transformation

Ziyang Mu, Rongsheng Lu*, Pan He, Guilin Zhang, and Mingtao Fang
Author Affiliations
  • School of Instrument Science and Opto-Electronics Engineering, Hefei University of Technology, Hefei 230009, Anhui , China
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    Figures & Tables(23)
    Schematic diagram of equally spaced fan beam rearrangement
    Schematic diagram of cone beam CT imaging
    Comparison of projection surfaces by algorithms
    Schematic diagram of reconstruction of using variable filter path algorithm. (a) Schematic of x‑y plane geometry; (b) arc curves with different parameter combinations; (c) section view of ray SβD perpendicular to x‑y plane
    Reconstruction flow of the proposed algorithm combined with CLRP approach
    Schematic diagram of projection conversion parameters. (a) Schematic diagram of CL projection transformation geometry; (b) converted equivalent CT projection
    Schematic diagram of focus coordinate conversion. (a) Before conversion; (b) after conversion
    Reconstructed images at y=-32 mm for different parameter combinations. (a) Ideal image; (b)-(d) reconstructed images when the parameter condition is k2<k1; (e) reconstructed image when the parameter condition is k2=k1; (f)-(h) reconstructed images when the parameter condition is k2>k1
    Gray scale value comparison of the center sequence of y=-32 mm reconstructed images under different parameter combinations
    Plots of mean square error surfaces reconstructed using different parameter combinations for each cone angle. (a) 15° cone angle; (b) 23° cone angle; (c) 30° cone angle; (d) 40° cone angle; (e) 50° cone angle
    Comparison of reconstructed images for each algorithm. (a) Ideal image; (b) FDK; (c) P-FDK; (d) T-FDK; (e) proposed algorithm
    Gray scale value comparison of reconstructed images at different locations for each algorithm. (a) x=32 mm; (b) y=-32 mm; (c) z=70 mm
    Comparison of reconstructed images for every algorithm at different cone angles. (a) 15° cone angle; (b) 23° cone angle; (c) 40° cone angle; (d) 50° cone angle
    Projection schematic before and after CLRP conversion and data rearrangement. (a) Multilayer PCB model; (b) CL projection; (c) CT projection after CLRP conversion; (d) projection after data rearrangement
    Comparison of reconstructed images for each layer of multilayer PCB model. (a) Layer 6; (b) layer 24; (c) layer 42; (d) layer 60; (e) layer 78; (f) layer 96
    Comparison of detailed parts of multilayer PCB model reconstruction. (a) FDK reconstruction; (b) reconstruction by proposed algorithm; (c) ROI-I comparison; (d) ROI-II comparison
    CL scanning system and sample. (a) CL scanning system; (b) sample to be reconstructed
    Comparison of actual PCB reconstruction results. (a) Component layer reconstructed by FDK algorithm; (b) component layer reconstructed by the proposed algorithm; (c) built line layer reconstructed by FDK algorithm; (d) built line layer reconstructed by the proposed algorithm
    • Table 1. 3D Shepp-Logan model simulation reconstruction parameters

      View table

      Table 1. 3D Shepp-Logan model simulation reconstruction parameters

      Parameter nameParameter value
      Distance from radiation source to center of rotation /mm478
      Cone angle of radiation beam /(°)30
      Rotary angular stepping /(°)1
      Center virtual detector size /(mm×mm)256×256
      Detector pixel size /(mm×mm)1×1

      Model reconstruction dimensions /

      (mm×mm×mm)

      256×256×256
      Reconstructed voxel size /(mm×mm×mm)1×1×1
      Recommended range for reconstructing grayscale[1.00, 1.05]
    • Table 2. Multilayer PCB model simulation reconstruction parameters

      View table

      Table 2. Multilayer PCB model simulation reconstruction parameters

      Parameter nameParameter value
      Distance from radiation source to center of rotation /mm900
      Distance from source to detector /mm1700
      Rotary axis tilt angle /(°)75
      Rotary angular stepping /(°)1
      Detector size /(mm×mm)1024×1024
      Detector pixel size /(mm×mm)2×2
      Model reconstruction dimension /(mm×mm×mm)323×378×102
      Reconstructed voxel size /(mm×mm×mm)1×1×1
    • Table 3. Quantitative analysis of reconstructed images

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      Table 3. Quantitative analysis of reconstructed images

      Evaluation indicatorFDKProposed algorithm
      ROI-ⅠROI-ⅡROI-ⅠROI-Ⅱ
      RMSE84.473176.770478.930371.3084
      PSNR9.596410.426910.185911.0680
    • Table 4. Geometric parameters of the CL system

      View table

      Table 4. Geometric parameters of the CL system

      Parameter nameParameter value

      Distance from radiation source to

      center of rotation /mm

      556.22
      Distance from source to detector /mm851.02
      Rotary axis tilt angle /(°)31
      Rotary angular stepping /(°)1
      Detector pixel size /(μm×μm)85.00×85.00

      Reconstructed voxel size /

      (μm×μm×μm)

      55.56×55.56×55.56
    • Table 5. Running time of different algorithms

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      Table 5. Running time of different algorithms

      AlgorithmCL projection conversionCone beam rearrangementWeighting, filtering and backprojectionTotal time
      FDK330268301
      Proposed algorithm99435567
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    Ziyang Mu, Rongsheng Lu, Pan He, Guilin Zhang, Mingtao Fang. X-Ray Three-Dimensional Reconstruction Algorithm of Plate-Like Objects Based on Filter Path Transformation[J]. Acta Optica Sinica, 2024, 44(9): 0934001

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    Paper Information

    Category: X-Ray Optics

    Received: Jan. 8, 2024

    Accepted: Feb. 23, 2024

    Published Online: May. 10, 2024

    The Author Email: Rongsheng Lu (rslu@hfut.edu.cn)

    DOI:10.3788/AOS240459

    CSTR:32393.14.AOS240459

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