Abstract

Calibration is required to maximize the sensitivity and measurement accuracy of vibration sensors. In this study, a low-frequency vibration calibration method is proposed that is based on the concept of monocular vision. In this method, we employ a high-accuracy edge extraction method to extract the edges of sequential images so as to obtain the high calibration accuracy. However, the proposed method must rely on a long-stroke shaker to provide vibration excitation to the sensor, and the bending in the guideway caused by the mechanical processing reduces the calibration accuracy, especially at very low frequencies. The proposed setting compensates for the bending using an additional monocular vision technique to significantly improve the calibration accuracy. To validate the calibration accuracy of the proposed method, a comparison was conducted between results obtained via the laser interferometry, the Earth's gravitation method, and the proposed method when applied to calibrate the sensitivity of a tri-axial acceleration sensor at frequencies between 0.04 and 8 Hz. The results of the comparison showed the proposed method calibrated the sensor sensitivity with high accuracy and was able to accurately account for the bending when the frequency was lower than 0.3 Hz. In contrast, the calibration accuracy of the laser interferometry decreased because of the bending.

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

Full Article  |  PDF Article
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References

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  1. W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
    [Crossref]
  2. C. D. Ferreira, G. P. Ripper, R. S. Dias, and D. B. Teixeira, “Primary calibration system for vibration transducers from 0.4 Hz to 160 Hz,” J. Phys. Conf. Ser. 575, 012003 (2015).
    [Crossref]
  3. W. He, Z. Wang, Y. Mei, and R. Shen, “A novel vibration-level-adjustment strategy for ultralow-frequency vibration calibration based on frequency-shifted method,” Meas. Sci. Technol. 24(2), 025007 (2013).
    [Crossref]
  4. N. Garg and M. I. Schiefer, “Low frequency accelerometer calibration using an optical encoder sensor,” Measurement 111, 226–233 (2017).
    [Crossref]
  5. R. J. Li, Y. J. Lei, L. S. Zhang, Z. X. Chang, K. C. Fan, Z. Y. Cheng, and P. H. Hu, “High-precision and low-cost vibration generator for low-frequency calibration system,” Meas. Sci. Technol. 29(3), 034008 (2018).
    [Crossref]
  6. J. Dosch, “Low frequency accelerometer calibration using Earth’s gravity,” In: IMAC XXV: Conference & Exposition on Structural Dynamics 2007.
  7. X. Diao, P. Hu, Z. Xue, and Y. Kang, “High-speed high-resolution heterodyne interferometer using a laser with low beat frequency,” Appl. Opt. 55(1), 110–116 (2016).
    [Crossref] [PubMed]
  8. H. Fu, P. Hu, J. Tan, and Z. Fan, “Simple method for reducing the first-order optical nonlinearity in a heterodyne laser interferometer,” Appl. Opt. 54(20), 6321–6326 (2015).
    [Crossref] [PubMed]
  9. ISO 16063–11, “Methods for the calibration of vibration and shock sensors-part 11: primary vibration calibration by laser interferometry,” Geneva, (1999).
  10. M. Dobosz, T. Usuda, and T. Kurosawa, “Methods for the calibration of vibration pick-ups by laser interferometry: 1. Theoretical analysis,” Meas. Sci. Technol. 9(2), 232–239 (1998).
    [Crossref]
  11. H. J. von Martens, A. Täubner, W. Wabinski, A. Link, and H. J. Schlaak, “Traceability of vibration and shock measurements by laser interferometry,” Measurement 28(1), 3–20 (2000).
    [Crossref]
  12. H. Nicklich and M. Mende, “Calibration of very-low-frequency accelerometers a challenging task,” Sound Vibrat. 45(5), 1521–1527 (2011).
    [Crossref]
  13. T. Bruns and S. Gazioch, “Correction of shaker flatness deviations in very low frequency primary accelerometer calibration,” Metrologia 53(3), 986–990 (2016).
    [Crossref]
  14. J. Jin, L. Zhao, and S. Xu, “High-precision rotation angle measurement method based on monocular vision,” J. Opt. Soc. Am. A 31(7), 1401–1407 (2014).
    [PubMed]
  15. G. A. Papakostas, Y. S. Boutalis, D. A. Karras, and B. G. Mertzios, “A new class of Zernike moments for computer vision applications,” Inf. Sci. 177(13), 2802–2819 (2007).
    [Crossref]
  16. F. Zhou, Y. Cui, B. Peng, and Y. Wang, “A novel optimization method of camera parameters used for vision measurement,” Opt. Laser Technol. 44(6), 1840–1849 (2012).
    [Crossref]
  17. K. Nishi and Y. Matsuda, “Camera vibration measurement using blinking light-emitting diode array,” Opt. Express 25(2), 1084–1105 (2017).
    [Crossref] [PubMed]
  18. L. Deng, G. Lu, Y. Shao, M. Fei, and H. Hu, “A novel camera calibration technique based on differential evolution particle swarm optimization algorithm,” Neurocomputing 174, 456–465 (2016).
    [Crossref]
  19. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE. Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
    [Crossref]
  20. D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51(5), 538–541 (2013).
    [Crossref]
  21. Z. Wang, “Removal of noise and radial lens distortion during calibration of computer vision systems,” Opt. Express 23(9), 11341–11356 (2015).
    [Crossref] [PubMed]
  22. Y. Hong, G. Ren, and E. Liu, “Non-iterative method for camera calibration,” Opt. Express 23(18), 23992–24003 (2015).
    [Crossref] [PubMed]
  23. C. Ricolfe-Viala and A. J. Sanchez-Salmeron, “Camera calibration under optimal conditions,” Opt. Express 19(11), 10769–10775 (2011).
    [Crossref] [PubMed]
  24. Y. Cui, F. Zhou, Y. Wang, L. Liu, and H. Gao, “Precise calibration of binocular vision system used for vision measurement,” Opt. Express 22(8), 9134–9149 (2014).
    [Crossref] [PubMed]
  25. Y. Liu, S. Liu, Y. Cao, and Z. Wang, “Automatic chessboard corner detection method,” IET Image Process. 10(1), 16–23 (2016).
    [Crossref]
  26. Y. Bok, H. Ha, and I. S. Kweon, “Automated checkerboard detection and indexing using circular boundaries,” Pattern Recognit. Lett. 71, 66–72 (2016).
    [Crossref]
  27. K. Wang, L. Xiao, and Z. Wei, “Motion blur kernel estimation in steerable gradient domain of decomposed image,” Multidimens. Syst. Signal Proc. 27(2), 577–596 (2016).
    [Crossref]
  28. T. Brox and J. Malik, “Large displacement optical flow: descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 33(3), 500–513 (2011).
    [Crossref] [PubMed]
  29. S. Baker, D. Scharstein, J. P. Lewis, S. Roth, M. J. Black, and R. Szeliski, “A database and evaluation methodology for optical flow,” Int. J. Comput. Vis. 92(1), 1–31 (2011).
    [Crossref]
  30. Y. Xin, S. Liao, and M. Pawlak, “Circularly orthogonal moments for geometrically robust image watermarking,” Pattern Recognit. 40(12), 3740–3752 (2007).
    [Crossref]
  31. C. Singh and E. Walia, “Fast and numerically stable methods for the computation of Zernike moments,” Pattern Recognit. 43(7), 2497–2506 (2010).
    [Crossref]
  32. Q. Sun, T. Bruns, A. Täubner, L. Yang, A. Liu, and A. Zuo, “Modifications of the sine-approximation method for primary vibration calibration by heterodyne interferometry,” Metrologia 46(6), 646–654 (2009).
    [Crossref]
  33. C. S. Veldman, “A novel implementation of an ISO standard method for primary vibration calibration by laser interferometry,” Metrologia 40(2), 1–8 (2003).
    [Crossref]

2018 (1)

R. J. Li, Y. J. Lei, L. S. Zhang, Z. X. Chang, K. C. Fan, Z. Y. Cheng, and P. H. Hu, “High-precision and low-cost vibration generator for low-frequency calibration system,” Meas. Sci. Technol. 29(3), 034008 (2018).
[Crossref]

2017 (2)

N. Garg and M. I. Schiefer, “Low frequency accelerometer calibration using an optical encoder sensor,” Measurement 111, 226–233 (2017).
[Crossref]

K. Nishi and Y. Matsuda, “Camera vibration measurement using blinking light-emitting diode array,” Opt. Express 25(2), 1084–1105 (2017).
[Crossref] [PubMed]

2016 (6)

X. Diao, P. Hu, Z. Xue, and Y. Kang, “High-speed high-resolution heterodyne interferometer using a laser with low beat frequency,” Appl. Opt. 55(1), 110–116 (2016).
[Crossref] [PubMed]

T. Bruns and S. Gazioch, “Correction of shaker flatness deviations in very low frequency primary accelerometer calibration,” Metrologia 53(3), 986–990 (2016).
[Crossref]

L. Deng, G. Lu, Y. Shao, M. Fei, and H. Hu, “A novel camera calibration technique based on differential evolution particle swarm optimization algorithm,” Neurocomputing 174, 456–465 (2016).
[Crossref]

Y. Liu, S. Liu, Y. Cao, and Z. Wang, “Automatic chessboard corner detection method,” IET Image Process. 10(1), 16–23 (2016).
[Crossref]

Y. Bok, H. Ha, and I. S. Kweon, “Automated checkerboard detection and indexing using circular boundaries,” Pattern Recognit. Lett. 71, 66–72 (2016).
[Crossref]

K. Wang, L. Xiao, and Z. Wei, “Motion blur kernel estimation in steerable gradient domain of decomposed image,” Multidimens. Syst. Signal Proc. 27(2), 577–596 (2016).
[Crossref]

2015 (4)

2014 (3)

2013 (2)

W. He, Z. Wang, Y. Mei, and R. Shen, “A novel vibration-level-adjustment strategy for ultralow-frequency vibration calibration based on frequency-shifted method,” Meas. Sci. Technol. 24(2), 025007 (2013).
[Crossref]

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51(5), 538–541 (2013).
[Crossref]

2012 (1)

F. Zhou, Y. Cui, B. Peng, and Y. Wang, “A novel optimization method of camera parameters used for vision measurement,” Opt. Laser Technol. 44(6), 1840–1849 (2012).
[Crossref]

2011 (4)

C. Ricolfe-Viala and A. J. Sanchez-Salmeron, “Camera calibration under optimal conditions,” Opt. Express 19(11), 10769–10775 (2011).
[Crossref] [PubMed]

T. Brox and J. Malik, “Large displacement optical flow: descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 33(3), 500–513 (2011).
[Crossref] [PubMed]

S. Baker, D. Scharstein, J. P. Lewis, S. Roth, M. J. Black, and R. Szeliski, “A database and evaluation methodology for optical flow,” Int. J. Comput. Vis. 92(1), 1–31 (2011).
[Crossref]

H. Nicklich and M. Mende, “Calibration of very-low-frequency accelerometers a challenging task,” Sound Vibrat. 45(5), 1521–1527 (2011).
[Crossref]

2010 (1)

C. Singh and E. Walia, “Fast and numerically stable methods for the computation of Zernike moments,” Pattern Recognit. 43(7), 2497–2506 (2010).
[Crossref]

2009 (1)

Q. Sun, T. Bruns, A. Täubner, L. Yang, A. Liu, and A. Zuo, “Modifications of the sine-approximation method for primary vibration calibration by heterodyne interferometry,” Metrologia 46(6), 646–654 (2009).
[Crossref]

2007 (2)

Y. Xin, S. Liao, and M. Pawlak, “Circularly orthogonal moments for geometrically robust image watermarking,” Pattern Recognit. 40(12), 3740–3752 (2007).
[Crossref]

G. A. Papakostas, Y. S. Boutalis, D. A. Karras, and B. G. Mertzios, “A new class of Zernike moments for computer vision applications,” Inf. Sci. 177(13), 2802–2819 (2007).
[Crossref]

2003 (1)

C. S. Veldman, “A novel implementation of an ISO standard method for primary vibration calibration by laser interferometry,” Metrologia 40(2), 1–8 (2003).
[Crossref]

2000 (2)

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

H. J. von Martens, A. Täubner, W. Wabinski, A. Link, and H. J. Schlaak, “Traceability of vibration and shock measurements by laser interferometry,” Measurement 28(1), 3–20 (2000).
[Crossref]

1998 (1)

M. Dobosz, T. Usuda, and T. Kurosawa, “Methods for the calibration of vibration pick-ups by laser interferometry: 1. Theoretical analysis,” Meas. Sci. Technol. 9(2), 232–239 (1998).
[Crossref]

Baker, S.

S. Baker, D. Scharstein, J. P. Lewis, S. Roth, M. J. Black, and R. Szeliski, “A database and evaluation methodology for optical flow,” Int. J. Comput. Vis. 92(1), 1–31 (2011).
[Crossref]

Black, M. J.

S. Baker, D. Scharstein, J. P. Lewis, S. Roth, M. J. Black, and R. Szeliski, “A database and evaluation methodology for optical flow,” Int. J. Comput. Vis. 92(1), 1–31 (2011).
[Crossref]

Bok, Y.

Y. Bok, H. Ha, and I. S. Kweon, “Automated checkerboard detection and indexing using circular boundaries,” Pattern Recognit. Lett. 71, 66–72 (2016).
[Crossref]

Boutalis, Y. S.

G. A. Papakostas, Y. S. Boutalis, D. A. Karras, and B. G. Mertzios, “A new class of Zernike moments for computer vision applications,” Inf. Sci. 177(13), 2802–2819 (2007).
[Crossref]

Brox, T.

T. Brox and J. Malik, “Large displacement optical flow: descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 33(3), 500–513 (2011).
[Crossref] [PubMed]

Bruns, T.

T. Bruns and S. Gazioch, “Correction of shaker flatness deviations in very low frequency primary accelerometer calibration,” Metrologia 53(3), 986–990 (2016).
[Crossref]

Q. Sun, T. Bruns, A. Täubner, L. Yang, A. Liu, and A. Zuo, “Modifications of the sine-approximation method for primary vibration calibration by heterodyne interferometry,” Metrologia 46(6), 646–654 (2009).
[Crossref]

Cao, Y.

Y. Liu, S. Liu, Y. Cao, and Z. Wang, “Automatic chessboard corner detection method,” IET Image Process. 10(1), 16–23 (2016).
[Crossref]

Chang, Z. X.

R. J. Li, Y. J. Lei, L. S. Zhang, Z. X. Chang, K. C. Fan, Z. Y. Cheng, and P. H. Hu, “High-precision and low-cost vibration generator for low-frequency calibration system,” Meas. Sci. Technol. 29(3), 034008 (2018).
[Crossref]

Cheng, Z. Y.

R. J. Li, Y. J. Lei, L. S. Zhang, Z. X. Chang, K. C. Fan, Z. Y. Cheng, and P. H. Hu, “High-precision and low-cost vibration generator for low-frequency calibration system,” Meas. Sci. Technol. 29(3), 034008 (2018).
[Crossref]

Cui, Y.

Y. Cui, F. Zhou, Y. Wang, L. Liu, and H. Gao, “Precise calibration of binocular vision system used for vision measurement,” Opt. Express 22(8), 9134–9149 (2014).
[Crossref] [PubMed]

F. Zhou, Y. Cui, B. Peng, and Y. Wang, “A novel optimization method of camera parameters used for vision measurement,” Opt. Laser Technol. 44(6), 1840–1849 (2012).
[Crossref]

Deng, L.

L. Deng, G. Lu, Y. Shao, M. Fei, and H. Hu, “A novel camera calibration technique based on differential evolution particle swarm optimization algorithm,” Neurocomputing 174, 456–465 (2016).
[Crossref]

Diao, X.

Dias, R. S.

C. D. Ferreira, G. P. Ripper, R. S. Dias, and D. B. Teixeira, “Primary calibration system for vibration transducers from 0.4 Hz to 160 Hz,” J. Phys. Conf. Ser. 575, 012003 (2015).
[Crossref]

Dobosz, M.

M. Dobosz, T. Usuda, and T. Kurosawa, “Methods for the calibration of vibration pick-ups by laser interferometry: 1. Theoretical analysis,” Meas. Sci. Technol. 9(2), 232–239 (1998).
[Crossref]

Fan, K. C.

R. J. Li, Y. J. Lei, L. S. Zhang, Z. X. Chang, K. C. Fan, Z. Y. Cheng, and P. H. Hu, “High-precision and low-cost vibration generator for low-frequency calibration system,” Meas. Sci. Technol. 29(3), 034008 (2018).
[Crossref]

Fan, Z.

Fei, M.

L. Deng, G. Lu, Y. Shao, M. Fei, and H. Hu, “A novel camera calibration technique based on differential evolution particle swarm optimization algorithm,” Neurocomputing 174, 456–465 (2016).
[Crossref]

Ferreira, C. D.

C. D. Ferreira, G. P. Ripper, R. S. Dias, and D. B. Teixeira, “Primary calibration system for vibration transducers from 0.4 Hz to 160 Hz,” J. Phys. Conf. Ser. 575, 012003 (2015).
[Crossref]

Fu, H.

Gao, H.

Garg, N.

N. Garg and M. I. Schiefer, “Low frequency accelerometer calibration using an optical encoder sensor,” Measurement 111, 226–233 (2017).
[Crossref]

Gazioch, S.

T. Bruns and S. Gazioch, “Correction of shaker flatness deviations in very low frequency primary accelerometer calibration,” Metrologia 53(3), 986–990 (2016).
[Crossref]

Ha, H.

Y. Bok, H. Ha, and I. S. Kweon, “Automated checkerboard detection and indexing using circular boundaries,” Pattern Recognit. Lett. 71, 66–72 (2016).
[Crossref]

He, W.

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

W. He, Z. Wang, Y. Mei, and R. Shen, “A novel vibration-level-adjustment strategy for ultralow-frequency vibration calibration based on frequency-shifted method,” Meas. Sci. Technol. 24(2), 025007 (2013).
[Crossref]

Hong, Y.

Hu, H.

L. Deng, G. Lu, Y. Shao, M. Fei, and H. Hu, “A novel camera calibration technique based on differential evolution particle swarm optimization algorithm,” Neurocomputing 174, 456–465 (2016).
[Crossref]

Hu, P.

Hu, P. H.

R. J. Li, Y. J. Lei, L. S. Zhang, Z. X. Chang, K. C. Fan, Z. Y. Cheng, and P. H. Hu, “High-precision and low-cost vibration generator for low-frequency calibration system,” Meas. Sci. Technol. 29(3), 034008 (2018).
[Crossref]

Jin, J.

Kang, Y.

Karras, D. A.

G. A. Papakostas, Y. S. Boutalis, D. A. Karras, and B. G. Mertzios, “A new class of Zernike moments for computer vision applications,” Inf. Sci. 177(13), 2802–2819 (2007).
[Crossref]

Kurosawa, T.

M. Dobosz, T. Usuda, and T. Kurosawa, “Methods for the calibration of vibration pick-ups by laser interferometry: 1. Theoretical analysis,” Meas. Sci. Technol. 9(2), 232–239 (1998).
[Crossref]

Kweon, I. S.

Y. Bok, H. Ha, and I. S. Kweon, “Automated checkerboard detection and indexing using circular boundaries,” Pattern Recognit. Lett. 71, 66–72 (2016).
[Crossref]

Lei, Y. J.

R. J. Li, Y. J. Lei, L. S. Zhang, Z. X. Chang, K. C. Fan, Z. Y. Cheng, and P. H. Hu, “High-precision and low-cost vibration generator for low-frequency calibration system,” Meas. Sci. Technol. 29(3), 034008 (2018).
[Crossref]

Lewis, J. P.

S. Baker, D. Scharstein, J. P. Lewis, S. Roth, M. J. Black, and R. Szeliski, “A database and evaluation methodology for optical flow,” Int. J. Comput. Vis. 92(1), 1–31 (2011).
[Crossref]

Li, D.

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51(5), 538–541 (2013).
[Crossref]

Li, R. J.

R. J. Li, Y. J. Lei, L. S. Zhang, Z. X. Chang, K. C. Fan, Z. Y. Cheng, and P. H. Hu, “High-precision and low-cost vibration generator for low-frequency calibration system,” Meas. Sci. Technol. 29(3), 034008 (2018).
[Crossref]

Liao, S.

Y. Xin, S. Liao, and M. Pawlak, “Circularly orthogonal moments for geometrically robust image watermarking,” Pattern Recognit. 40(12), 3740–3752 (2007).
[Crossref]

Link, A.

H. J. von Martens, A. Täubner, W. Wabinski, A. Link, and H. J. Schlaak, “Traceability of vibration and shock measurements by laser interferometry,” Measurement 28(1), 3–20 (2000).
[Crossref]

Liu, A.

Q. Sun, T. Bruns, A. Täubner, L. Yang, A. Liu, and A. Zuo, “Modifications of the sine-approximation method for primary vibration calibration by heterodyne interferometry,” Metrologia 46(6), 646–654 (2009).
[Crossref]

Liu, E.

Liu, L.

Liu, S.

Y. Liu, S. Liu, Y. Cao, and Z. Wang, “Automatic chessboard corner detection method,” IET Image Process. 10(1), 16–23 (2016).
[Crossref]

Liu, Y.

Y. Liu, S. Liu, Y. Cao, and Z. Wang, “Automatic chessboard corner detection method,” IET Image Process. 10(1), 16–23 (2016).
[Crossref]

Lu, G.

L. Deng, G. Lu, Y. Shao, M. Fei, and H. Hu, “A novel camera calibration technique based on differential evolution particle swarm optimization algorithm,” Neurocomputing 174, 456–465 (2016).
[Crossref]

Malik, J.

T. Brox and J. Malik, “Large displacement optical flow: descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 33(3), 500–513 (2011).
[Crossref] [PubMed]

Matsuda, Y.

Mei, Y.

W. He, Z. Wang, Y. Mei, and R. Shen, “A novel vibration-level-adjustment strategy for ultralow-frequency vibration calibration based on frequency-shifted method,” Meas. Sci. Technol. 24(2), 025007 (2013).
[Crossref]

Mende, M.

H. Nicklich and M. Mende, “Calibration of very-low-frequency accelerometers a challenging task,” Sound Vibrat. 45(5), 1521–1527 (2011).
[Crossref]

Mertzios, B. G.

G. A. Papakostas, Y. S. Boutalis, D. A. Karras, and B. G. Mertzios, “A new class of Zernike moments for computer vision applications,” Inf. Sci. 177(13), 2802–2819 (2007).
[Crossref]

Nicklich, H.

H. Nicklich and M. Mende, “Calibration of very-low-frequency accelerometers a challenging task,” Sound Vibrat. 45(5), 1521–1527 (2011).
[Crossref]

Nishi, K.

Papakostas, G. A.

G. A. Papakostas, Y. S. Boutalis, D. A. Karras, and B. G. Mertzios, “A new class of Zernike moments for computer vision applications,” Inf. Sci. 177(13), 2802–2819 (2007).
[Crossref]

Pawlak, M.

Y. Xin, S. Liao, and M. Pawlak, “Circularly orthogonal moments for geometrically robust image watermarking,” Pattern Recognit. 40(12), 3740–3752 (2007).
[Crossref]

Peng, B.

F. Zhou, Y. Cui, B. Peng, and Y. Wang, “A novel optimization method of camera parameters used for vision measurement,” Opt. Laser Technol. 44(6), 1840–1849 (2012).
[Crossref]

Ren, G.

Ricolfe-Viala, C.

Ripper, G. P.

C. D. Ferreira, G. P. Ripper, R. S. Dias, and D. B. Teixeira, “Primary calibration system for vibration transducers from 0.4 Hz to 160 Hz,” J. Phys. Conf. Ser. 575, 012003 (2015).
[Crossref]

Roth, S.

S. Baker, D. Scharstein, J. P. Lewis, S. Roth, M. J. Black, and R. Szeliski, “A database and evaluation methodology for optical flow,” Int. J. Comput. Vis. 92(1), 1–31 (2011).
[Crossref]

Sanchez-Salmeron, A. J.

Scharstein, D.

S. Baker, D. Scharstein, J. P. Lewis, S. Roth, M. J. Black, and R. Szeliski, “A database and evaluation methodology for optical flow,” Int. J. Comput. Vis. 92(1), 1–31 (2011).
[Crossref]

Schiefer, M. I.

N. Garg and M. I. Schiefer, “Low frequency accelerometer calibration using an optical encoder sensor,” Measurement 111, 226–233 (2017).
[Crossref]

Schlaak, H. J.

H. J. von Martens, A. Täubner, W. Wabinski, A. Link, and H. J. Schlaak, “Traceability of vibration and shock measurements by laser interferometry,” Measurement 28(1), 3–20 (2000).
[Crossref]

Shao, Y.

L. Deng, G. Lu, Y. Shao, M. Fei, and H. Hu, “A novel camera calibration technique based on differential evolution particle swarm optimization algorithm,” Neurocomputing 174, 456–465 (2016).
[Crossref]

Shen, R.

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

W. He, Z. Wang, Y. Mei, and R. Shen, “A novel vibration-level-adjustment strategy for ultralow-frequency vibration calibration based on frequency-shifted method,” Meas. Sci. Technol. 24(2), 025007 (2013).
[Crossref]

Singh, C.

C. Singh and E. Walia, “Fast and numerically stable methods for the computation of Zernike moments,” Pattern Recognit. 43(7), 2497–2506 (2010).
[Crossref]

Sun, Q.

Q. Sun, T. Bruns, A. Täubner, L. Yang, A. Liu, and A. Zuo, “Modifications of the sine-approximation method for primary vibration calibration by heterodyne interferometry,” Metrologia 46(6), 646–654 (2009).
[Crossref]

Szeliski, R.

S. Baker, D. Scharstein, J. P. Lewis, S. Roth, M. J. Black, and R. Szeliski, “A database and evaluation methodology for optical flow,” Int. J. Comput. Vis. 92(1), 1–31 (2011).
[Crossref]

Tan, J.

Täubner, A.

Q. Sun, T. Bruns, A. Täubner, L. Yang, A. Liu, and A. Zuo, “Modifications of the sine-approximation method for primary vibration calibration by heterodyne interferometry,” Metrologia 46(6), 646–654 (2009).
[Crossref]

H. J. von Martens, A. Täubner, W. Wabinski, A. Link, and H. J. Schlaak, “Traceability of vibration and shock measurements by laser interferometry,” Measurement 28(1), 3–20 (2000).
[Crossref]

Teixeira, D. B.

C. D. Ferreira, G. P. Ripper, R. S. Dias, and D. B. Teixeira, “Primary calibration system for vibration transducers from 0.4 Hz to 160 Hz,” J. Phys. Conf. Ser. 575, 012003 (2015).
[Crossref]

Tian, J.

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51(5), 538–541 (2013).
[Crossref]

Usuda, T.

M. Dobosz, T. Usuda, and T. Kurosawa, “Methods for the calibration of vibration pick-ups by laser interferometry: 1. Theoretical analysis,” Meas. Sci. Technol. 9(2), 232–239 (1998).
[Crossref]

Veldman, C. S.

C. S. Veldman, “A novel implementation of an ISO standard method for primary vibration calibration by laser interferometry,” Metrologia 40(2), 1–8 (2003).
[Crossref]

von Martens, H. J.

H. J. von Martens, A. Täubner, W. Wabinski, A. Link, and H. J. Schlaak, “Traceability of vibration and shock measurements by laser interferometry,” Measurement 28(1), 3–20 (2000).
[Crossref]

Wabinski, W.

H. J. von Martens, A. Täubner, W. Wabinski, A. Link, and H. J. Schlaak, “Traceability of vibration and shock measurements by laser interferometry,” Measurement 28(1), 3–20 (2000).
[Crossref]

Walia, E.

C. Singh and E. Walia, “Fast and numerically stable methods for the computation of Zernike moments,” Pattern Recognit. 43(7), 2497–2506 (2010).
[Crossref]

Wang, C.

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

Wang, K.

K. Wang, L. Xiao, and Z. Wei, “Motion blur kernel estimation in steerable gradient domain of decomposed image,” Multidimens. Syst. Signal Proc. 27(2), 577–596 (2016).
[Crossref]

Wang, Y.

Y. Cui, F. Zhou, Y. Wang, L. Liu, and H. Gao, “Precise calibration of binocular vision system used for vision measurement,” Opt. Express 22(8), 9134–9149 (2014).
[Crossref] [PubMed]

F. Zhou, Y. Cui, B. Peng, and Y. Wang, “A novel optimization method of camera parameters used for vision measurement,” Opt. Laser Technol. 44(6), 1840–1849 (2012).
[Crossref]

Wang, Z.

Y. Liu, S. Liu, Y. Cao, and Z. Wang, “Automatic chessboard corner detection method,” IET Image Process. 10(1), 16–23 (2016).
[Crossref]

Z. Wang, “Removal of noise and radial lens distortion during calibration of computer vision systems,” Opt. Express 23(9), 11341–11356 (2015).
[Crossref] [PubMed]

W. He, Z. Wang, Y. Mei, and R. Shen, “A novel vibration-level-adjustment strategy for ultralow-frequency vibration calibration based on frequency-shifted method,” Meas. Sci. Technol. 24(2), 025007 (2013).
[Crossref]

Wei, Z.

K. Wang, L. Xiao, and Z. Wei, “Motion blur kernel estimation in steerable gradient domain of decomposed image,” Multidimens. Syst. Signal Proc. 27(2), 577–596 (2016).
[Crossref]

Xiao, L.

K. Wang, L. Xiao, and Z. Wei, “Motion blur kernel estimation in steerable gradient domain of decomposed image,” Multidimens. Syst. Signal Proc. 27(2), 577–596 (2016).
[Crossref]

Xin, Y.

Y. Xin, S. Liao, and M. Pawlak, “Circularly orthogonal moments for geometrically robust image watermarking,” Pattern Recognit. 40(12), 3740–3752 (2007).
[Crossref]

Xu, S.

Xue, Z.

Yang, L.

Q. Sun, T. Bruns, A. Täubner, L. Yang, A. Liu, and A. Zuo, “Modifications of the sine-approximation method for primary vibration calibration by heterodyne interferometry,” Metrologia 46(6), 646–654 (2009).
[Crossref]

Yu, M.

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

Zhang, L. S.

R. J. Li, Y. J. Lei, L. S. Zhang, Z. X. Chang, K. C. Fan, Z. Y. Cheng, and P. H. Hu, “High-precision and low-cost vibration generator for low-frequency calibration system,” Meas. Sci. Technol. 29(3), 034008 (2018).
[Crossref]

Zhang, X.

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

Zhang, Z. Y.

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

Zhao, L.

Zhou, F.

Y. Cui, F. Zhou, Y. Wang, L. Liu, and H. Gao, “Precise calibration of binocular vision system used for vision measurement,” Opt. Express 22(8), 9134–9149 (2014).
[Crossref] [PubMed]

F. Zhou, Y. Cui, B. Peng, and Y. Wang, “A novel optimization method of camera parameters used for vision measurement,” Opt. Laser Technol. 44(6), 1840–1849 (2012).
[Crossref]

Zuo, A.

Q. Sun, T. Bruns, A. Täubner, L. Yang, A. Liu, and A. Zuo, “Modifications of the sine-approximation method for primary vibration calibration by heterodyne interferometry,” Metrologia 46(6), 646–654 (2009).
[Crossref]

Appl. Opt. (2)

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

T. Brox and J. Malik, “Large displacement optical flow: descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 33(3), 500–513 (2011).
[Crossref] [PubMed]

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

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

IET Image Process. (1)

Y. Liu, S. Liu, Y. Cao, and Z. Wang, “Automatic chessboard corner detection method,” IET Image Process. 10(1), 16–23 (2016).
[Crossref]

Inf. Sci. (1)

G. A. Papakostas, Y. S. Boutalis, D. A. Karras, and B. G. Mertzios, “A new class of Zernike moments for computer vision applications,” Inf. Sci. 177(13), 2802–2819 (2007).
[Crossref]

Int. J. Comput. Vis. (1)

S. Baker, D. Scharstein, J. P. Lewis, S. Roth, M. J. Black, and R. Szeliski, “A database and evaluation methodology for optical flow,” Int. J. Comput. Vis. 92(1), 1–31 (2011).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. Conf. Ser. (1)

C. D. Ferreira, G. P. Ripper, R. S. Dias, and D. B. Teixeira, “Primary calibration system for vibration transducers from 0.4 Hz to 160 Hz,” J. Phys. Conf. Ser. 575, 012003 (2015).
[Crossref]

Meas. Sci. Technol. (4)

W. He, Z. Wang, Y. Mei, and R. Shen, “A novel vibration-level-adjustment strategy for ultralow-frequency vibration calibration based on frequency-shifted method,” Meas. Sci. Technol. 24(2), 025007 (2013).
[Crossref]

R. J. Li, Y. J. Lei, L. S. Zhang, Z. X. Chang, K. C. Fan, Z. Y. Cheng, and P. H. Hu, “High-precision and low-cost vibration generator for low-frequency calibration system,” Meas. Sci. Technol. 29(3), 034008 (2018).
[Crossref]

M. Dobosz, T. Usuda, and T. Kurosawa, “Methods for the calibration of vibration pick-ups by laser interferometry: 1. Theoretical analysis,” Meas. Sci. Technol. 9(2), 232–239 (1998).
[Crossref]

W. He, X. Zhang, C. Wang, R. Shen, and M. Yu, “A long-stroke horizontal electromagnetic vibrator for ultralow-frequency vibration calibration,” Meas. Sci. Technol. 25(8), 085901 (2014).
[Crossref]

Measurement (2)

H. J. von Martens, A. Täubner, W. Wabinski, A. Link, and H. J. Schlaak, “Traceability of vibration and shock measurements by laser interferometry,” Measurement 28(1), 3–20 (2000).
[Crossref]

N. Garg and M. I. Schiefer, “Low frequency accelerometer calibration using an optical encoder sensor,” Measurement 111, 226–233 (2017).
[Crossref]

Metrologia (3)

T. Bruns and S. Gazioch, “Correction of shaker flatness deviations in very low frequency primary accelerometer calibration,” Metrologia 53(3), 986–990 (2016).
[Crossref]

Q. Sun, T. Bruns, A. Täubner, L. Yang, A. Liu, and A. Zuo, “Modifications of the sine-approximation method for primary vibration calibration by heterodyne interferometry,” Metrologia 46(6), 646–654 (2009).
[Crossref]

C. S. Veldman, “A novel implementation of an ISO standard method for primary vibration calibration by laser interferometry,” Metrologia 40(2), 1–8 (2003).
[Crossref]

Multidimens. Syst. Signal Proc. (1)

K. Wang, L. Xiao, and Z. Wei, “Motion blur kernel estimation in steerable gradient domain of decomposed image,” Multidimens. Syst. Signal Proc. 27(2), 577–596 (2016).
[Crossref]

Neurocomputing (1)

L. Deng, G. Lu, Y. Shao, M. Fei, and H. Hu, “A novel camera calibration technique based on differential evolution particle swarm optimization algorithm,” Neurocomputing 174, 456–465 (2016).
[Crossref]

Opt. Express (5)

Opt. Laser Technol. (1)

F. Zhou, Y. Cui, B. Peng, and Y. Wang, “A novel optimization method of camera parameters used for vision measurement,” Opt. Laser Technol. 44(6), 1840–1849 (2012).
[Crossref]

Opt. Lasers Eng. (1)

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51(5), 538–541 (2013).
[Crossref]

Pattern Recognit. (2)

Y. Xin, S. Liao, and M. Pawlak, “Circularly orthogonal moments for geometrically robust image watermarking,” Pattern Recognit. 40(12), 3740–3752 (2007).
[Crossref]

C. Singh and E. Walia, “Fast and numerically stable methods for the computation of Zernike moments,” Pattern Recognit. 43(7), 2497–2506 (2010).
[Crossref]

Pattern Recognit. Lett. (1)

Y. Bok, H. Ha, and I. S. Kweon, “Automated checkerboard detection and indexing using circular boundaries,” Pattern Recognit. Lett. 71, 66–72 (2016).
[Crossref]

Sound Vibrat. (1)

H. Nicklich and M. Mende, “Calibration of very-low-frequency accelerometers a challenging task,” Sound Vibrat. 45(5), 1521–1527 (2011).
[Crossref]

Other (2)

ISO 16063–11, “Methods for the calibration of vibration and shock sensors-part 11: primary vibration calibration by laser interferometry,” Geneva, (1999).

J. Dosch, “Low frequency accelerometer calibration using Earth’s gravity,” In: IMAC XXV: Conference & Exposition on Structural Dynamics 2007.

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Figures (13)

Fig. 1
Fig. 1 Sketch of the MV-based low-frequency vibration calibration system.
Fig. 2
Fig. 2 Sketch of the collected sequential images and the feature edges.
Fig. 3
Fig. 3 Projection geometry of the camera.
Fig. 4
Fig. 4 (a) Image with no blurred edge, (b) grayscale distribution in the neighborhood of the non-blurred edge, (c) grayscale gradient of this edge, (d) image with a blurred edge, (e) grayscale distribution in the neighborhood of the blurred edge, and (f) grayscale gradient of this edge.
Fig. 5
Fig. 5 Three-grayscale distribution edge model.
Fig. 6
Fig. 6 (a) Bend in the guideway of the long-stroke shaker, (b) additional excitation acceleration delivered to the sensor due to this bend.
Fig. 7
Fig. 7 Schematic showing the method of measuring the bending in the guideway.
Fig. 8
Fig. 8 World vertical coordinates of the positions of the circular mark at different displacements along the guideway.
Fig. 9
Fig. 9 Low-frequency vibration sensor calibration system: (I) horizontal long-stroke shaker, (II) working surface, (III) vibration sensor, (IV) high-contrast mark, (V) CCD camera, (VI) acquisition device, and (VII) heterodyne interferometer.
Fig. 10
Fig. 10 Edges of the extracted mark in the sequential images at a frequency of 1 Hz.
Fig. 11
Fig. 11 Results of vibration calibration using the LI, MV method, and EG method at frequencies between 0.04 and 2 Hz: (a) X-axial sensitivity; (b) Y-axial sensitivity; (c) and Z-axial sensitivity.
Fig. 12
Fig. 12 Calibration results for the MVC method: (a) X-axial sensitivity; (b) Y-axial sensitivity; and (c) Z-axial sensitivity.
Fig. 13
Fig. 13 The calibration results of MV method, LI, and MVC method at a frequency range of 2-8 Hz. (a) X-axial sensitivity; (b) Y-axial sensitivity; (c) Z-axial sensitivity.

Equations (21)

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S V = V p , V / a p , V .
[ x u y u 1 ] = H [ x w y w 1 ] = [ h 11 h 12 h 13 h 21 h 22 h 23 h 31 h 32 h 33 ] [ x w y w 1 ] ,
{ x u = x d [ 1 + k 1 ( x d 2 + y d 2 ) + k 2 ( x d 2 + y d 2 ) 2 ] y u = y d [ 1 + k 1 ( x d 2 + y d 2 ) + k 2 ( x d 2 + y d 2 ) 2 ] ,
J = min r , c [ ( x w ' x w ) 2 + ( y w ' y w ) 2 ] ,
g j ( p ) = a j e [ x j ( p ) μ j ] 2 2 σ j 2 ,
f E ( x , y ) = { f j ( x , y ) / ( 2 f ˜ j ( x , y ) f ˜ j 2 ( x , y ) ) , f ˜ j ( x , y ) < T 1 f j , max ( x , y ) , f ˜ j ( x , y ) T 1 ,
f E ( x , y ) = { f j , min ( x , y ) , f ˜ j ( x , y ) T 2 f j ( x , y ) ( 1 f ˜ j 2 ( x , y ) ) , f ˜ j ( x , y ) > T 2 ,
Z n m = x y f j ( x , y ) V n m * ( ρ , θ ) x 2 + y 2 1 ,
V n m ( ρ , θ ) = s = 0 ( n | m | ) / 2 ( 1 ) s ( n s ) ! ρ n 2 s s ! ( n + | m | 2 s ) ! ( n | m | 2 s ) ! e i m θ ,
Z n m ' = Z n m e i m ϕ .
d 1 = 5 Z 40 ' + 3 Z 20 ' 8 Z 20 ' , d 2 = 5 Z 31 ' + Z 11 ' 6 Z 11 ,
ϕ = t a n 1 ( Im [ Z 31 ] Re [ Z 31 ] ) ,
[ x s u b y s u b ] = [ x 0 y 0 ] + K ( d 1 + d 2 ) 4 [ cos ϕ sin ϕ ] .
d j ( t i ) = A cos ( ω v t i ) B sin ( ω v t i ) + C ,
d p , V = A 2 + B 2 .
a p , G = g l o c sin ( α ) g l o c α ,
a ^ p , E = a p , V cos ( α ) + a p , G a p , V + a p , G .
S 0 = V p , V a ^ p , E = V p , V a p , V + a p , G .
S 0 = S V a p , V a p , V + a p , G .
S 0 = S V ω v 2 ω v 2 + ω α 2 ,
α h = arc tan ( y ¯ h , c y ¯ 13 , c d h d 13 ) , h 13.

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