• Laser & Optoelectronics Progress
  • Vol. 55, Issue 6, 061204 (2018)
Xiaoting Deng, Nan Gao, and Zonghua Zhang*
Author Affiliations
  • School of Mechanical Engineering, Heibei University of Technology, Tianjin 300130, China
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    DOI: 10.3788/LOP55.061204 Cite this Article Set citation alerts
    Xiaoting Deng, Nan Gao, Zonghua Zhang. Calibration of System Parameters Based on Direct Phase Measuring Deflectometry[J]. Laser & Optoelectronics Progress, 2018, 55(6): 061204 Copy Citation Text show less
    Schematic of the measuring system
    Fig. 1. Schematic of the measuring system
    Images of hollow ring marker matrix captured by the camera. (a) Texture image; (b) red dots representing the center of each hollow ring marker
    Fig. 2. Images of hollow ring marker matrix captured by the camera. (a) Texture image; (b) red dots representing the center of each hollow ring marker
    Fringe patterns displayed on the screen. (a) Horizontal fringe; (b) vertical fringe
    Fig. 3. Fringe patterns displayed on the screen. (a) Horizontal fringe; (b) vertical fringe
    Feature points matching using absolute phase image
    Fig. 4. Feature points matching using absolute phase image
    Calibration of parameters d1 and d2
    Fig. 5. Calibration of parameters d1 and d2
    Experimental system
    Fig. 6. Experimental system
    Reprojection error of the calibrated camera (pixel)
    Fig. 7. Reprojection error of the calibrated camera (pixel)
    Error of the calibrated extrinsic parameters
    Fig. 8. Error of the calibrated extrinsic parameters
    Photos of (a) concave mirror and (b) manufactured artificial step
    Fig. 9. Photos of (a) concave mirror and (b) manufactured artificial step
    Measured 3D shapes. (a) Concave mirror; (b) artificial specular step
    Fig. 10. Measured 3D shapes. (a) Concave mirror; (b) artificial specular step
    Focal length /pixelRadial distortion/pixelTangential distortion
    FuFvPuPvK1K2K3K4
    10137.45210137.8111204.7831011.174-0.2712-1.8758-0.00020.0003
    Table 1. Calibrated internal parameters of the camera
    Step distanceCalculated distance 1Calculated distance 2
    1010.0589.915
    2019.92319.880
    3030.12230.172
    4040.15440.194
    5049.78949.758
    6060.29460.246
    7070.31470.288
    8080.46880.327
    9089.45489.606
    10099.34299.558
    Table 2. Results of LCD's extrinsic parameters using checkerboard and fringe patternsmm
    ActualdistanceMeasureddistanceAbsoluteerrorRoot meansquare error
    3.9873.9690.0180.022
    7.0257.0100.0150.019
    5.0065.0280.0220.024
    6.0996.1200.0210.020
    Table 3. True and measured distances of the artificial specular step and their errorsmm
    Xiaoting Deng, Nan Gao, Zonghua Zhang. Calibration of System Parameters Based on Direct Phase Measuring Deflectometry[J]. Laser & Optoelectronics Progress, 2018, 55(6): 061204
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