• Laser & Optoelectronics Progress
  • Vol. 58, Issue 8, 0812002 (2021)
Ruifeng Zhang and Chang Liu*
Author Affiliations
  • School of Microelectronics, Tianjin University, Tianjin 300072, China
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    DOI: 10.3788/LOP202158.0812002 Cite this Article Set citation alerts
    Ruifeng Zhang, Chang Liu. Interference Fringe Center Point Extraction Method Based on Interval Curve Fitting[J]. Laser & Optoelectronics Progress, 2021, 58(8): 0812002 Copy Citation Text show less
    Grayscale distribution of interference fringe. (a) Tangential direction; (b) normal direction
    Fig. 1. Grayscale distribution of interference fringe. (a) Tangential direction; (b) normal direction
    Interference fringe patterns. (a) Original image; (b) R-value image; (c) Gaussian filter image
    Fig. 2. Interference fringe patterns. (a) Original image; (b) R-value image; (c) Gaussian filter image
    Grayscale along normal direction. (a) Original image; (b) after Gaussian filtering
    Fig. 3. Grayscale along normal direction. (a) Original image; (b) after Gaussian filtering
    Schematic of interval fitting
    Fig. 4. Schematic of interval fitting
    Results of curve fitting. (a) f1(x); (b) f2(x)
    Fig. 5. Results of curve fitting. (a) f1(x); (b) f2(x)
    Images of f1(x) and f2(x) and filtered image
    Fig. 6. Images of f1(x) and f2(x) and filtered image
    Image of f(x)=f2(x)-f1(x)
    Fig. 7. Image of f(x)=f2(x)-f1(x)
    Extraction results. (a) Interference fringe pattern; (b) centerline extraction result
    Fig. 8. Extraction results. (a) Interference fringe pattern; (b) centerline extraction result
    Interference fringe patterns. (a) Image 1; (b) image 2; (c) image 3; (d) image 4; (e) image 5
    Fig. 9. Interference fringe patterns. (a) Image 1; (b) image 2; (c) image 3; (d) image 4; (e) image 5
    Known centerline images. (a) Image 6; (b) image 7; (c) image 8; (d) image 9; (e) image 10
    Fig. 10. Known centerline images. (a) Image 6; (b) image 7; (c) image 8; (d) image 9; (e) image 10
    Fitting methodSSERMSERsquareRAdj-sq
    Gaussian curve fitting218.79853.95330.99710.9965
    Polynomial curve fitting1187.99.21120.98350.9812
    Proposed method141.4583.29700.99800.9976
    Table 1. Comparison of statistical parameters of three curve fitting methods
    AlgorithmAverage processing time /s
    Image 1Image 2Image 3Image 4Image 5
    Gray threshold algorithm[8]0.82010.95540.98410.93440.8406
    Steger algorithm[12]6.84487.78128.26628.65237.0884
    Gray-gravity algorithm[22]0.32500.43900.40060.43050.2977
    Proposed algorithm0.64150.79810.78070.83470.6306
    Table 2. Comparison of average processing time of extracting results by four methods
    AlgorithmRMSE /pixel
    Image 6Image 7Image 8Image 9Image 10
    Gray threshold algorithm[8]0.98401.67732.51751.51261.4967
    Steger algorithm[12]0.05210.06420.04890.05620.0601
    Gray-gravity algorithm[22]0.39300.55810.25890.43740.4895
    Proposed algorithm0.04240.04410.01950.04630.0449
    Table 3. RMSE comparison between the extraction results of the four methods and the standard value
    Ruifeng Zhang, Chang Liu. Interference Fringe Center Point Extraction Method Based on Interval Curve Fitting[J]. Laser & Optoelectronics Progress, 2021, 58(8): 0812002
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