Abstract

Camera calibration is an important part of high-precision optical measurement, which is especially difficult in the micro-nano field. Based on the integrated correlation calculation and CCD moiré method, this paper describes the development of a lens calibration technique called the Integrated Colour CCD Moiré Method (ICCM). The CCD moiré fringes, formed by superimposing a periodic optical signal of a specimen grating with a CCD target array or a Bayer filter array, significantly enlarges the deformation modulated by lens distortion and the calibration plate attitude (i.e. the rotation angle relative to the camera coordinate system). To measure lens distortion using CCD moiré, the deformation pattern that is governed by the lens distortion, specimen grating attitude and carrier was used to construct a CCD fringe image. If the constructed CCD fringe image based on the trial lens distortion and rotation angles have a maximum similarity to the captured CCD moiré image, the lens distortion and rotation angles are correctly inversed. Particle swarm optimisation algorithm was selected to search for the true value so that the accuracy and robustness could be improved. Numerical experiments verified that the ICCM method developed in this work can simultaneously inverse the lens distortion, rotation angle and the grating pitch with high precision. The lens distortion of the metallographic microscope has been successfully characterised by the developed method with an 833 nm pitch grating. Simulations and experiments showed that ICCM is an intuitive, accurate, anti-noise and robust distortion calibration method.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  2. B. Pan, L. Yu, J. Yuan, Z. Shen, and G. Tang, “Determination of Viscoelastic Poisson’s Ratio of Solid Propellants using an Accuracy-enhanced 2D Digital Image Correlation Technique,” Propellants, Explos., Pyrotech. 40(6), 821–830 (2015).
    [Crossref]
  3. B. Pan, “Digital image correlation for surface deformation measurement: historical developments, recent advances and future goals,” Meas. Sci. Technol. 29(8), 082001 (2018).
    [Crossref]
  4. N. T. Vo, R. C. Atwood, and M. Drakopoulos, “Radial lens distortion correction with sub-pixel accuracy for X-ray micro-tomography,” Opt. Express 23(25), 32859–32868 (2015).
    [Crossref]
  5. J. Zhao, Z. Liu, and B. Guo, “Three-dimensional digital image correlation method based on a light field camera,” Opt. Lasers Eng. 116, 19–25 (2019).
    [Crossref]
  6. Z. Gao, Q. Zhang, Y. Su, and S. Wu, “Accuracy evaluation of optical distortion calibration by digital image correlation,” Opt. Lasers Eng. 98, 143–152 (2017).
    [Crossref]
  7. A. Gonzalez and J. Meneses, “Accurate calibration method for a fringe projection system by projecting an adaptive fringe pattern,” Appl. Opt. 58(17), 4610–4615 (2019).
    [Crossref]
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    [Crossref]
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    [Crossref]
  10. Q. Dai, R. Xiong, and S. Li, “An Optimization Based Vision Calibration Method for PTZ Camera's Errors in Model and Execution,” Procedia Eng. 15, 585–593 (2011).
    [Crossref]
  11. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
    [Crossref]
  12. P. Jin and X. Li, “Correction of image drift and distortion in a scanning electron microscopy,” J. Microsc. 260(3), 268–280 (2015).
    [Crossref]
  13. Y. Hou, H. Zhang, J. Zhao, J. He, H. Qi, Z. Liu, and B. Guo, “Camera lens distortion evaluation and correction technique based on a colour CCD moiré method,” Opt. Lasers Eng. 110, 211–219 (2018).
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  17. L. Zhanwei and G. Jianxin, “Deformation-pattern-based digital speckle correlation for coefficient of thermal expansion evaluation of film,” Opt. Express 19(18), 17469–17479 (2011).
    [Crossref]
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    [Crossref]
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  22. M. M. Noel, “A new gradient based particle swarm optimization algorithm for accurate computation of global minimum,” Appl. Soft. Comput. 12(1), 353–359 (2012).
    [Crossref]
  23. M. Jenkinson and S. Smith, “A global optimisation method for robust affine registration of brain images,” Med. Image Anal. 5(2), 143–156 (2001).
    [Crossref]
  24. E. Ergun, S. Tasgetiren, and M. Topcu, “Determination of SIF for patched crack in aluminum plates by the combined finite element and genetic algorithm approach,” Fatigue Fract. Eng. Mater. Struct. 31(11), 929–936 (2008).
    [Crossref]
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  26. X. Dai and H. Xie, “A simple and residual-layer-free solute–solvent separation soft lithography method,” J. Micromech. Microeng. 25(9), 095013 (2015).
    [Crossref]
  27. X. Dai and H. Xie, “Versatile specimen-grating fabrication technique for moiré method based on solute-solvent separation soft lithography,” Opt. Mater. Express 6(5), 1530–1544 (2016).
    [Crossref]

2019 (2)

J. Zhao, Z. Liu, and B. Guo, “Three-dimensional digital image correlation method based on a light field camera,” Opt. Lasers Eng. 116, 19–25 (2019).
[Crossref]

A. Gonzalez and J. Meneses, “Accurate calibration method for a fringe projection system by projecting an adaptive fringe pattern,” Appl. Opt. 58(17), 4610–4615 (2019).
[Crossref]

2018 (2)

B. Pan, “Digital image correlation for surface deformation measurement: historical developments, recent advances and future goals,” Meas. Sci. Technol. 29(8), 082001 (2018).
[Crossref]

Y. Hou, H. Zhang, J. Zhao, J. He, H. Qi, Z. Liu, and B. Guo, “Camera lens distortion evaluation and correction technique based on a colour CCD moiré method,” Opt. Lasers Eng. 110, 211–219 (2018).
[Crossref]

2017 (2)

Z. Gao, Q. Zhang, Y. Su, and S. Wu, “Accuracy evaluation of optical distortion calibration by digital image correlation,” Opt. Lasers Eng. 98, 143–152 (2017).
[Crossref]

J. Dong, Z. Liu, and J. Gao, “Multi-Parameter Inversion and Thermo-Mechanical Deformation Decoupling using I-DIC,” Exp. Mech. 57(1), 31–39 (2017).
[Crossref]

2016 (1)

2015 (4)

X. Dai and H. Xie, “A simple and residual-layer-free solute–solvent separation soft lithography method,” J. Micromech. Microeng. 25(9), 095013 (2015).
[Crossref]

N. T. Vo, R. C. Atwood, and M. Drakopoulos, “Radial lens distortion correction with sub-pixel accuracy for X-ray micro-tomography,” Opt. Express 23(25), 32859–32868 (2015).
[Crossref]

B. Pan, L. Yu, J. Yuan, Z. Shen, and G. Tang, “Determination of Viscoelastic Poisson’s Ratio of Solid Propellants using an Accuracy-enhanced 2D Digital Image Correlation Technique,” Propellants, Explos., Pyrotech. 40(6), 821–830 (2015).
[Crossref]

P. Jin and X. Li, “Correction of image drift and distortion in a scanning electron microscopy,” J. Microsc. 260(3), 268–280 (2015).
[Crossref]

2014 (3)

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

J.-E. Dufour, F. Hild, and S. Roux, “Integrated digital image correlation for the evaluation and correction of optical distortions,” Opt. Lasers Eng. 56, 121–133 (2014).
[Crossref]

L. Junfei, Z. Youqi, W. Jianglong, X. Yang, W. Zhipei, M. Qinwei, and M. Shaopeng, “Formation mechanism and a universal period formula for the CCD moiré,” Opt. Express 22(17), 20914–20923 (2014).
[Crossref]

2012 (2)

V. Saveljev and S.-K. Kim, “Simulation and measurement of moiré patterns at finite distance,” Opt. Express 20(3), 2163–2177 (2012).
[Crossref]

M. M. Noel, “A new gradient based particle swarm optimization algorithm for accurate computation of global minimum,” Appl. Soft. Comput. 12(1), 353–359 (2012).
[Crossref]

2011 (2)

L. Zhanwei and G. Jianxin, “Deformation-pattern-based digital speckle correlation for coefficient of thermal expansion evaluation of film,” Opt. Express 19(18), 17469–17479 (2011).
[Crossref]

Q. Dai, R. Xiong, and S. Li, “An Optimization Based Vision Calibration Method for PTZ Camera's Errors in Model and Execution,” Procedia Eng. 15, 585–593 (2011).
[Crossref]

2009 (1)

2008 (1)

E. Ergun, S. Tasgetiren, and M. Topcu, “Determination of SIF for patched crack in aluminum plates by the combined finite element and genetic algorithm approach,” Fatigue Fract. Eng. Mater. Struct. 31(11), 929–936 (2008).
[Crossref]

2006 (1)

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

2004 (1)

E. Verhulp, B. van Rietbergen, and R. Huiskes, “A three-dimensional digital image correlation technique for strain measurements in microstructures,” J. Biomech. 37(9), 1313–1320 (2004).
[Crossref]

2002 (1)

T. S. Smith, B. K. Bay, and M. M. Rashid, “Digital volume correlation including rotational degrees of freedom during minimization,” Exp. Mech. 42(3), 272–278 (2002).
[Crossref]

2001 (1)

M. Jenkinson and S. Smith, “A global optimisation method for robust affine registration of brain images,” Med. Image Anal. 5(2), 143–156 (2001).
[Crossref]

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

1999 (1)

R. I. Hartley, “Theory and practice of projective rectification,” Int. J. Comput. Vis. 35(2), 115–127 (1999).
[Crossref]

1997 (1)

C. S. Fraser, “Digital camera self-calibration,” ISPRS J. Photogramm. Remote Sens. 52(4), 149–159 (1997).
[Crossref]

Atwood, R. C.

Bay, B. K.

T. S. Smith, B. K. Bay, and M. M. Rashid, “Digital volume correlation including rotational degrees of freedom during minimization,” Exp. Mech. 42(3), 272–278 (2002).
[Crossref]

Dai, Q.

Q. Dai, R. Xiong, and S. Li, “An Optimization Based Vision Calibration Method for PTZ Camera's Errors in Model and Execution,” Procedia Eng. 15, 585–593 (2011).
[Crossref]

Dai, X.

X. Dai and H. Xie, “Versatile specimen-grating fabrication technique for moiré method based on solute-solvent separation soft lithography,” Opt. Mater. Express 6(5), 1530–1544 (2016).
[Crossref]

X. Dai and H. Xie, “A simple and residual-layer-free solute–solvent separation soft lithography method,” J. Micromech. Microeng. 25(9), 095013 (2015).
[Crossref]

Dong, J.

J. Dong, Z. Liu, and J. Gao, “Multi-Parameter Inversion and Thermo-Mechanical Deformation Decoupling using I-DIC,” Exp. Mech. 57(1), 31–39 (2017).
[Crossref]

Drakopoulos, M.

Dufour, J.-E.

J.-E. Dufour, F. Hild, and S. Roux, “Integrated digital image correlation for the evaluation and correction of optical distortions,” Opt. Lasers Eng. 56, 121–133 (2014).
[Crossref]

Ergun, E.

E. Ergun, S. Tasgetiren, and M. Topcu, “Determination of SIF for patched crack in aluminum plates by the combined finite element and genetic algorithm approach,” Fatigue Fract. Eng. Mater. Struct. 31(11), 929–936 (2008).
[Crossref]

Fraser, C. S.

C. S. Fraser, “Digital camera self-calibration,” ISPRS J. Photogramm. Remote Sens. 52(4), 149–159 (1997).
[Crossref]

Gao, J.

J. Dong, Z. Liu, and J. Gao, “Multi-Parameter Inversion and Thermo-Mechanical Deformation Decoupling using I-DIC,” Exp. Mech. 57(1), 31–39 (2017).
[Crossref]

Gao, Z.

Z. Gao, Q. Zhang, Y. Su, and S. Wu, “Accuracy evaluation of optical distortion calibration by digital image correlation,” Opt. Lasers Eng. 98, 143–152 (2017).
[Crossref]

Gonzalez, A.

Guo, B.

J. Zhao, Z. Liu, and B. Guo, “Three-dimensional digital image correlation method based on a light field camera,” Opt. Lasers Eng. 116, 19–25 (2019).
[Crossref]

Y. Hou, H. Zhang, J. Zhao, J. He, H. Qi, Z. Liu, and B. Guo, “Camera lens distortion evaluation and correction technique based on a colour CCD moiré method,” Opt. Lasers Eng. 110, 211–219 (2018).
[Crossref]

Hartley, R. I.

R. I. Hartley, “Theory and practice of projective rectification,” Int. J. Comput. Vis. 35(2), 115–127 (1999).
[Crossref]

He, J.

Y. Hou, H. Zhang, J. Zhao, J. He, H. Qi, Z. Liu, and B. Guo, “Camera lens distortion evaluation and correction technique based on a colour CCD moiré method,” Opt. Lasers Eng. 110, 211–219 (2018).
[Crossref]

Hild, F.

J.-E. Dufour, F. Hild, and S. Roux, “Integrated digital image correlation for the evaluation and correction of optical distortions,” Opt. Lasers Eng. 56, 121–133 (2014).
[Crossref]

Hou, Y.

Y. Hou, H. Zhang, J. Zhao, J. He, H. Qi, Z. Liu, and B. Guo, “Camera lens distortion evaluation and correction technique based on a colour CCD moiré method,” Opt. Lasers Eng. 110, 211–219 (2018).
[Crossref]

Huiskes, R.

E. Verhulp, B. van Rietbergen, and R. Huiskes, “A three-dimensional digital image correlation technique for strain measurements in microstructures,” J. Biomech. 37(9), 1313–1320 (2004).
[Crossref]

Jenkinson, M.

M. Jenkinson and S. Smith, “A global optimisation method for robust affine registration of brain images,” Med. Image Anal. 5(2), 143–156 (2001).
[Crossref]

Jianglong, W.

Jianxin, G.

Jin, P.

P. Jin and X. Li, “Correction of image drift and distortion in a scanning electron microscopy,” J. Microsc. 260(3), 268–280 (2015).
[Crossref]

Junfei, L.

Jung, J.-H.

Kikuta, H.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

Kim, J.

Kim, S.-K.

Kim, Y.

Kitagawa, A.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

Kitamura, K.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

Lee, B.

Li, S.

Q. Dai, R. Xiong, and S. Li, “An Optimization Based Vision Calibration Method for PTZ Camera's Errors in Model and Execution,” Procedia Eng. 15, 585–593 (2011).
[Crossref]

Li, X.

P. Jin and X. Li, “Correction of image drift and distortion in a scanning electron microscopy,” J. Microsc. 260(3), 268–280 (2015).
[Crossref]

Liu, Z.

J. Zhao, Z. Liu, and B. Guo, “Three-dimensional digital image correlation method based on a light field camera,” Opt. Lasers Eng. 116, 19–25 (2019).
[Crossref]

Y. Hou, H. Zhang, J. Zhao, J. He, H. Qi, Z. Liu, and B. Guo, “Camera lens distortion evaluation and correction technique based on a colour CCD moiré method,” Opt. Lasers Eng. 110, 211–219 (2018).
[Crossref]

J. Dong, Z. Liu, and J. Gao, “Multi-Parameter Inversion and Thermo-Mechanical Deformation Decoupling using I-DIC,” Exp. Mech. 57(1), 31–39 (2017).
[Crossref]

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

Meneses, J.

Noel, M. M.

M. M. Noel, “A new gradient based particle swarm optimization algorithm for accurate computation of global minimum,” Appl. Soft. Comput. 12(1), 353–359 (2012).
[Crossref]

Pan, B.

B. Pan, “Digital image correlation for surface deformation measurement: historical developments, recent advances and future goals,” Meas. Sci. Technol. 29(8), 082001 (2018).
[Crossref]

B. Pan, L. Yu, J. Yuan, Z. Shen, and G. Tang, “Determination of Viscoelastic Poisson’s Ratio of Solid Propellants using an Accuracy-enhanced 2D Digital Image Correlation Technique,” Propellants, Explos., Pyrotech. 40(6), 821–830 (2015).
[Crossref]

Park, G.

Qi, H.

Y. Hou, H. Zhang, J. Zhao, J. He, H. Qi, Z. Liu, and B. Guo, “Camera lens distortion evaluation and correction technique based on a colour CCD moiré method,” Opt. Lasers Eng. 110, 211–219 (2018).
[Crossref]

Qinwei, M.

Rashid, M. M.

T. S. Smith, B. K. Bay, and M. M. Rashid, “Digital volume correlation including rotational degrees of freedom during minimization,” Exp. Mech. 42(3), 272–278 (2002).
[Crossref]

Roux, S.

J.-E. Dufour, F. Hild, and S. Roux, “Integrated digital image correlation for the evaluation and correction of optical distortions,” Opt. Lasers Eng. 56, 121–133 (2014).
[Crossref]

Saveljev, V.

Shaopeng, M.

Shen, Z.

B. Pan, L. Yu, J. Yuan, Z. Shen, and G. Tang, “Determination of Viscoelastic Poisson’s Ratio of Solid Propellants using an Accuracy-enhanced 2D Digital Image Correlation Technique,” Propellants, Explos., Pyrotech. 40(6), 821–830 (2015).
[Crossref]

Smith, S.

M. Jenkinson and S. Smith, “A global optimisation method for robust affine registration of brain images,” Med. Image Anal. 5(2), 143–156 (2001).
[Crossref]

Smith, T. S.

T. S. Smith, B. K. Bay, and M. M. Rashid, “Digital volume correlation including rotational degrees of freedom during minimization,” Exp. Mech. 42(3), 272–278 (2002).
[Crossref]

Su, Y.

Z. Gao, Q. Zhang, Y. Su, and S. Wu, “Accuracy evaluation of optical distortion calibration by digital image correlation,” Opt. Lasers Eng. 98, 143–152 (2017).
[Crossref]

Tang, G.

B. Pan, L. Yu, J. Yuan, Z. Shen, and G. Tang, “Determination of Viscoelastic Poisson’s Ratio of Solid Propellants using an Accuracy-enhanced 2D Digital Image Correlation Technique,” Propellants, Explos., Pyrotech. 40(6), 821–830 (2015).
[Crossref]

Tasgetiren, S.

E. Ergun, S. Tasgetiren, and M. Topcu, “Determination of SIF for patched crack in aluminum plates by the combined finite element and genetic algorithm approach,” Fatigue Fract. Eng. Mater. Struct. 31(11), 929–936 (2008).
[Crossref]

Topcu, M.

E. Ergun, S. Tasgetiren, and M. Topcu, “Determination of SIF for patched crack in aluminum plates by the combined finite element and genetic algorithm approach,” Fatigue Fract. Eng. Mater. Struct. 31(11), 929–936 (2008).
[Crossref]

van Rietbergen, B.

E. Verhulp, B. van Rietbergen, and R. Huiskes, “A three-dimensional digital image correlation technique for strain measurements in microstructures,” J. Biomech. 37(9), 1313–1320 (2004).
[Crossref]

Verhulp, E.

E. Verhulp, B. van Rietbergen, and R. Huiskes, “A three-dimensional digital image correlation technique for strain measurements in microstructures,” J. Biomech. 37(9), 1313–1320 (2004).
[Crossref]

Vo, N. T.

Wu, C.

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

Wu, S.

Z. Gao, Q. Zhang, Y. Su, and S. Wu, “Accuracy evaluation of optical distortion calibration by digital image correlation,” Opt. Lasers Eng. 98, 143–152 (2017).
[Crossref]

Xie, H.

X. Dai and H. Xie, “Versatile specimen-grating fabrication technique for moiré method based on solute-solvent separation soft lithography,” Opt. Mater. Express 6(5), 1530–1544 (2016).
[Crossref]

X. Dai and H. Xie, “A simple and residual-layer-free solute–solvent separation soft lithography method,” J. Micromech. Microeng. 25(9), 095013 (2015).
[Crossref]

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

Xiong, R.

Q. Dai, R. Xiong, and S. Li, “An Optimization Based Vision Calibration Method for PTZ Camera's Errors in Model and Execution,” Procedia Eng. 15, 585–593 (2011).
[Crossref]

Yang, X.

Yoneyama, S.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

Youqi, Z.

Yu, L.

B. Pan, L. Yu, J. Yuan, Z. Shen, and G. Tang, “Determination of Viscoelastic Poisson’s Ratio of Solid Propellants using an Accuracy-enhanced 2D Digital Image Correlation Technique,” Propellants, Explos., Pyrotech. 40(6), 821–830 (2015).
[Crossref]

Yuan, J.

B. Pan, L. Yu, J. Yuan, Z. Shen, and G. Tang, “Determination of Viscoelastic Poisson’s Ratio of Solid Propellants using an Accuracy-enhanced 2D Digital Image Correlation Technique,” Propellants, Explos., Pyrotech. 40(6), 821–830 (2015).
[Crossref]

Zhang, H.

Y. Hou, H. Zhang, J. Zhao, J. He, H. Qi, Z. Liu, and B. Guo, “Camera lens distortion evaluation and correction technique based on a colour CCD moiré method,” Opt. Lasers Eng. 110, 211–219 (2018).
[Crossref]

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

Zhang, Q.

Z. Gao, Q. Zhang, Y. Su, and S. Wu, “Accuracy evaluation of optical distortion calibration by digital image correlation,” Opt. Lasers Eng. 98, 143–152 (2017).
[Crossref]

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Zhanwei, L.

Zhao, J.

J. Zhao, Z. Liu, and B. Guo, “Three-dimensional digital image correlation method based on a light field camera,” Opt. Lasers Eng. 116, 19–25 (2019).
[Crossref]

Y. Hou, H. Zhang, J. Zhao, J. He, H. Qi, Z. Liu, and B. Guo, “Camera lens distortion evaluation and correction technique based on a colour CCD moiré method,” Opt. Lasers Eng. 110, 211–219 (2018).
[Crossref]

Zhipei, W.

Appl. Opt. (2)

Appl. Soft. Comput. (1)

M. M. Noel, “A new gradient based particle swarm optimization algorithm for accurate computation of global minimum,” Appl. Soft. Comput. 12(1), 353–359 (2012).
[Crossref]

Exp. Mech. (2)

J. Dong, Z. Liu, and J. Gao, “Multi-Parameter Inversion and Thermo-Mechanical Deformation Decoupling using I-DIC,” Exp. Mech. 57(1), 31–39 (2017).
[Crossref]

T. S. Smith, B. K. Bay, and M. M. Rashid, “Digital volume correlation including rotational degrees of freedom during minimization,” Exp. Mech. 42(3), 272–278 (2002).
[Crossref]

Fatigue Fract. Eng. Mater. Struct. (1)

E. Ergun, S. Tasgetiren, and M. Topcu, “Determination of SIF for patched crack in aluminum plates by the combined finite element and genetic algorithm approach,” Fatigue Fract. Eng. Mater. Struct. 31(11), 929–936 (2008).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Int. J. Comput. Vis. (1)

R. I. Hartley, “Theory and practice of projective rectification,” Int. J. Comput. Vis. 35(2), 115–127 (1999).
[Crossref]

ISPRS J. Photogramm. Remote Sens. (1)

C. S. Fraser, “Digital camera self-calibration,” ISPRS J. Photogramm. Remote Sens. 52(4), 149–159 (1997).
[Crossref]

J. Biomech. (1)

E. Verhulp, B. van Rietbergen, and R. Huiskes, “A three-dimensional digital image correlation technique for strain measurements in microstructures,” J. Biomech. 37(9), 1313–1320 (2004).
[Crossref]

J. Micromech. Microeng. (1)

X. Dai and H. Xie, “A simple and residual-layer-free solute–solvent separation soft lithography method,” J. Micromech. Microeng. 25(9), 095013 (2015).
[Crossref]

J. Microsc. (1)

P. Jin and X. Li, “Correction of image drift and distortion in a scanning electron microscopy,” J. Microsc. 260(3), 268–280 (2015).
[Crossref]

Meas. Sci. Technol. (2)

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

B. Pan, “Digital image correlation for surface deformation measurement: historical developments, recent advances and future goals,” Meas. Sci. Technol. 29(8), 082001 (2018).
[Crossref]

Med. Image Anal. (1)

M. Jenkinson and S. Smith, “A global optimisation method for robust affine registration of brain images,” Med. Image Anal. 5(2), 143–156 (2001).
[Crossref]

Opt. Eng. (1)

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (4)

Y. Hou, H. Zhang, J. Zhao, J. He, H. Qi, Z. Liu, and B. Guo, “Camera lens distortion evaluation and correction technique based on a colour CCD moiré method,” Opt. Lasers Eng. 110, 211–219 (2018).
[Crossref]

J. Zhao, Z. Liu, and B. Guo, “Three-dimensional digital image correlation method based on a light field camera,” Opt. Lasers Eng. 116, 19–25 (2019).
[Crossref]

Z. Gao, Q. Zhang, Y. Su, and S. Wu, “Accuracy evaluation of optical distortion calibration by digital image correlation,” Opt. Lasers Eng. 98, 143–152 (2017).
[Crossref]

J.-E. Dufour, F. Hild, and S. Roux, “Integrated digital image correlation for the evaluation and correction of optical distortions,” Opt. Lasers Eng. 56, 121–133 (2014).
[Crossref]

Opt. Mater. Express (1)

Procedia Eng. (1)

Q. Dai, R. Xiong, and S. Li, “An Optimization Based Vision Calibration Method for PTZ Camera's Errors in Model and Execution,” Procedia Eng. 15, 585–593 (2011).
[Crossref]

Propellants, Explos., Pyrotech. (1)

B. Pan, L. Yu, J. Yuan, Z. Shen, and G. Tang, “Determination of Viscoelastic Poisson’s Ratio of Solid Propellants using an Accuracy-enhanced 2D Digital Image Correlation Technique,” Propellants, Explos., Pyrotech. 40(6), 821–830 (2015).
[Crossref]

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Figures (10)

Fig. 1.
Fig. 1. A schematic showing a colour CCD moiré forming process.
Fig. 2.
Fig. 2. An illustration of virtual displacement caused by rotation.
Fig. 3.
Fig. 3. Flow chart.
Fig. 4.
Fig. 4. A graph showing the correlation coefficient varying with the specimen grating pitch.
Fig. 5.
Fig. 5. Anti-noise performance analysis showing (a) a simulated moiré with noise, (b) the image optimised by PSO, and (c), (d) and (e) the brightness distribution taken at the lines marked (1), (2), and (3). The blue plots in (c), (d), and (e) show the greyscale of the lines (${l_{a1}},{l_{a2}},{l_{a3}}$) shown in (a) whereas the red plots are the greyscale of the lines (${l_{b1}},{l_{b2}},{l_{b3}}$) shown in (b).
Fig. 6.
Fig. 6. A photograph of the experimental setup.
Fig. 7.
Fig. 7. Four-step phase shift images, (a) x direction and (b) y direction.
Fig. 8.
Fig. 8. Decoupled displacement, (a) carrier, (b) rotation and (c) distortion.
Fig. 9.
Fig. 9. Relative errors of the displacement between the phase analyzing results and inversion results.
Fig. 10.
Fig. 10. A photograph showing the metallographic microscope special ruler.

Tables (4)

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Table 1. The internal and external parameters of the microscope lens

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Table 2. Numerical simulation experimental results for different values of P s

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Table 3. Numerical simulation experimental results for different values of α i

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Table 4. Numerical simulation experimental results for different values of k 1

Equations (20)

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U d ( x , y ) = [ k 1 y ( x 2 + y 2 ) + k 2 y ( x 2 + y 2 ) 2 ] + [ 2 p 2 x y + p 1 ( 2 x 2 + 3 y 2 ) ]  +  s 1 ( x 2 + y 2 )
V d ( x , y ) = [ k 1 x ( x 2 + y 2 ) + k 2 x ( x 2 + y 2 ) 2 ] + [ 2 p 1 x y + p 2 ( 3 x 2 + 2 y 2 ) ] + s 2 ( x 2 + y 2 )
{ U ( x , y ) = f i ( cos α y cos α z sin α x sin α y sin α z ) x + f i cos α x sin α z y f cos α x sin α y x sin α x y x V ( X P , Y P ) = f i ( cos α y sin α z + sin α x sin α y cos α z ) x + f i cos α x cos α z y P f i cos α x sin α y x sin α x y y
U c ( x , y ) = sgn ( P s P r ) P s P r P r x
V c ( x , y ) = sgn ( P s P r ) P s P r P r y
U ( x , y ) = U d ( x , y , K ) + U r ( x , y , R ) + U c ( x , y , P s )
V ( x , y ) = V d ( x , y , K ) + V r ( x , y , R ) + V c ( x , y , P s )
K = [ k 1 k 2 p 1 p 2 ]
R = [ α x α y α z ]
[ J ( x , y ) ] image = M ( x , y ) = Re ( e i 2 π U ( x , y ) / i 2 π U ( x , y ) P r P r )
C ( P ) = x , y ROI [ I ( x , y ) I m ] [ J ( x , y ) J m ] x , y ROI [ I ( x , y ) I m ] 2 x , y ROI [ J ( x , y ) J m ] 2
V d t + 1 = ω V d t + c 1 R 1 ( X d p b X d t ) + c 2 R 2 ( X d g b X d t )
X d t + 1 = X d t + V d t + 1
{ I 1 ( x , y ) = B ( x , y ) + n ( x , y ) [ 1 + sin ( 2 π f x + Φ ( x , y ) ) ] I 2 ( x , y ) = B ( x , y ) + n ( x , y ) [ 1 + sin ( 2 π f x + Φ ( x , y ) + π 2 ) ] I 3 ( x , y ) = B ( x , y ) + n ( x , y ) [ 1 + sin ( 2 π f x + Φ ( x , y ) + π ) ] I 4 ( x , y ) = B ( x , y ) + n ( x , y ) [ 1 + sin ( 2 π f x + Φ ( x , y ) + 3 π 2 ) ]
[ 2 π f x + Φ ( x , y ) ] = tan 1 I 1 ( x , y ) I 3 ( x , y ) I 2 ( x , y ) I 4 ( x , y )
I ( x , y ) C sin ( tan 1 I 1 ( x , y ) I 3 ( x , y ) I 2 ( x , y ) I 4 ( x , y ) ) + D
P s = P r N L = ( 1 / 1200 ) × 518 12 × 0.01 = 3.597 p i x e l s
Z C [ x y 1 ] = [ f d x 0 u 0 0 0 f d y v 0 0 0 0 1 0 ] [ 1 0 0 T x 0 1 0 T y 0 0 1 T z 0 0 0 1 ] [ X W Y W 0 1 ]
Z C [ x y 1 ] = [ f d x 0 u 0 0 0 f d y v 0 0 0 0 1 0 ] [ R 11 R 12 R 13 T x R 21 R 22 R 23 T y R 31 R 32 R 33 T z 0 0 0 1 ] [ X W Y W 0 1 ]
{ U ( x , y ) = x x = f i ( cos α y cos α z sin α x sin α y sin α z ) x + f i cos α x sin α z y f i cos α x sin α y x sin α x y x V ( x , y ) = y y = f i ( cos α y sin α z + sin α x sin α y cos α z ) x + f i cos α x cos α z y f i cos α x sin α y x sin α x y y

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