Abstract

Fringe projection profilometry (FPP) is a widely used technique for real-time three-dimensional (3D) shape measurement. However, it tends to compromise when measuring objects that have a large variation range of surface reflectivity. In this paper, we present a FPP method that can increase the dynamic range for real-time 3D measurements. First, binary fringe patterns are projected to generate grayscale sinusoidal patterns with the defocusing technique. Each pattern is then captured twice with different exposure values in one projection period. With image fusion, surfaces under appropriate exposure are retained. To improve the real-time performance of high dynamic range (HDR) 3D shape measurements, we build a binocular fringe projection profilometry system that saves the number of patterns by geometry constraint. Further, to ensure the accuracy and robustness of HDR 3D measurements, we propose a mixed phase unwrapping method that can reduce phase unwrapping errors for dense fringe patterns. Experiment results show that the proposed method can realize accurate and real-time 3D measurement for HDR scenes at 28 frames per second.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
  30. T. Chen, H. P. Lensch, C. Fuchs, and H.-P. Seidel, “Polarization and phase-shifting for 3d scanning of translucent objects,” in 2007 IEEE conference on computer vision and pattern recognition (IEEE, 2007), pp. 1–8.
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2019 (2)

L. Zhang, Q. Chen, C. Zuo, T. Tao, Y. Zhang, and S. Feng, “High-dynamic-range 3d shape measurement based on time domain superposition,” Meas. Sci. Technol. 30(6), 065004 (2019).
[Crossref]

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
[Crossref]

2018 (7)

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3d shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (μftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Meas. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

L. Zhang, Q. Chen, C. Zuo, and S. Feng, “High dynamic range 3d shape measurement based on the intensity response function of a camera,” Appl. Opt. 57(6), 1378–1386 (2018).
[Crossref]

V. Suresh, Y. Wang, and B. Li, “High-dynamic-range 3d shape measurement utilizing the transitioning state of digital micromirror device,” Opt. Lasers Eng. 107, 176–181 (2018).
[Crossref]

2017 (1)

2016 (4)

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

C. Jiang, T. Bell, and S. Zhang, “High dynamic range real-time 3d shape measurement,” Opt. Express 24(7), 7337–7346 (2016).
[Crossref]

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3d shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Lasers Eng. 84, 74–81 (2016).
[Crossref]

Z. Cai, X. Liu, X. Peng, Y. Yin, A. Li, J. Wu, and B. Z. Gao, “Structured light field 3d imaging,” Opt. Express 24(18), 20324–20334 (2016).
[Crossref]

2014 (3)

B. Salahieh, Z. Chen, J. J. Rodriguez, and R. Liang, “Multi-polarization fringe projection imaging for high dynamic range objects,” Opt. Express 22(8), 10064–10071 (2014).
[Crossref]

C. Zhang, J. Xu, N. Xi, J. Zhao, and Q. Shi, “A robust surface coding method for optically challenging objects using structured light,” IEEE Trans. Automat. Sci. Eng. 11(3), 775–788 (2014).
[Crossref]

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Lasers Eng. 59, 56–71 (2014).
[Crossref]

2013 (1)

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

2012 (3)

R. R. Garcia and A. Zakhor, “Consistent stereo-assisted absolute phase unwrapping methods for structured light systems,” IEEE J. Sel. Top. Signal Process. 6(5), 411–424 (2012).
[Crossref]

H. Jiang, H. Zhao, and X. Li, “High dynamic range fringe acquisition: a novel 3-d scanning technique for high-reflective surfaces,” Opt. Lasers Eng. 50(10), 1484–1493 (2012).
[Crossref]

Z. Zhang, “Review of single-shot 3d shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
[Crossref]

2011 (1)

J. Geng, “Structured-light 3d surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

2010 (3)

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik 121(1), 23–28 (2010).
[Crossref]

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-d shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref]

2009 (2)

S. Lei and S. Zhang, “Flexible 3-d shape measurement using projector defocusing,” Opt. Lett. 34(20), 3080–3082 (2009).
[Crossref]

S. Zhang and S.-T. Yau, “High dynamic range scanning technique,” Opt. Eng. 48(3), 033604 (2009).
[Crossref]

1987 (1)

1983 (1)

Asundi, A.

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (μftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Bell, T.

Breitbarth, A.

A. Breitbarth, E. Müller, P. Kühmstedt, G. Notni, and J. Denzler, “Phase unwrapping of fringe images for dynamic 3d measurements without additional pattern projection,” in Dimensional Optical Metrology and Inspection for Practical Applications IV, vol. 9489 (International Society for Optics and Photonics, 2015), p. 948903.

Cai, Z.

Chen, Q.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
[Crossref]

L. Zhang, Q. Chen, C. Zuo, T. Tao, Y. Zhang, and S. Feng, “High-dynamic-range 3d shape measurement based on time domain superposition,” Meas. Sci. Technol. 30(6), 065004 (2019).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (μftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3d shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Meas. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

L. Zhang, Q. Chen, C. Zuo, and S. Feng, “High dynamic range 3d shape measurement based on the intensity response function of a camera,” Appl. Opt. 57(6), 1378–1386 (2018).
[Crossref]

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25(17), 20381–20400 (2017).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Lasers Eng. 59, 56–71 (2014).
[Crossref]

Chen, T.

T. Chen, H. P. Lensch, C. Fuchs, and H.-P. Seidel, “Polarization and phase-shifting for 3d scanning of translucent objects,” in 2007 IEEE conference on computer vision and pattern recognition (IEEE, 2007), pp. 1–8.

Chen, Y.

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik 121(1), 23–28 (2010).
[Crossref]

Chen, Z.

Creath, K.

Denzler, J.

A. Breitbarth, E. Müller, P. Kühmstedt, G. Notni, and J. Denzler, “Phase unwrapping of fringe images for dynamic 3d measurements without additional pattern projection,” in Dimensional Optical Metrology and Inspection for Practical Applications IV, vol. 9489 (International Society for Optics and Photonics, 2015), p. 948903.

Feng, S.

L. Zhang, Q. Chen, C. Zuo, T. Tao, Y. Zhang, and S. Feng, “High-dynamic-range 3d shape measurement based on time domain superposition,” Meas. Sci. Technol. 30(6), 065004 (2019).
[Crossref]

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (μftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3d shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Meas. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

L. Zhang, Q. Chen, C. Zuo, and S. Feng, “High dynamic range 3d shape measurement based on the intensity response function of a camera,” Appl. Opt. 57(6), 1378–1386 (2018).
[Crossref]

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25(17), 20381–20400 (2017).
[Crossref]

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Lasers Eng. 59, 56–71 (2014).
[Crossref]

Fernandez, S.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Fuchs, C.

T. Chen, H. P. Lensch, C. Fuchs, and H.-P. Seidel, “Polarization and phase-shifting for 3d scanning of translucent objects,” in 2007 IEEE conference on computer vision and pattern recognition (IEEE, 2007), pp. 1–8.

Gao, B. Z.

Garcia, R. R.

R. R. Garcia and A. Zakhor, “Consistent stereo-assisted absolute phase unwrapping methods for structured light systems,” IEEE J. Sel. Top. Signal Process. 6(5), 411–424 (2012).
[Crossref]

Geng, J.

J. Geng, “Structured-light 3d surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

Gu, G.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Meas. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

Guo, H.

H. Guo and P. S. Huang, “3-d shape measurement by use of a modified fourier transform method,” in Two-and Three-Dimensional Methods for Inspection and Metrology VI, vol. 7066 (International Society for Optics and Photonics, 2008), p. 70660E.

Hao, Q.

Hassebrook, L. G.

He, Y.

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik 121(1), 23–28 (2010).
[Crossref]

Hu, E.

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik 121(1), 23–28 (2010).
[Crossref]

Hu, S.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3d shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Lasers Eng. 84, 74–81 (2016).
[Crossref]

Hu, Y.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
[Crossref]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3d shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25(17), 20381–20400 (2017).
[Crossref]

Huang, L.

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3d shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (μftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Huang, P. S.

H. Guo and P. S. Huang, “3-d shape measurement by use of a modified fourier transform method,” in Two-and Three-Dimensional Methods for Inspection and Metrology VI, vol. 7066 (International Society for Optics and Photonics, 2008), p. 70660E.

Jiang, C.

Jiang, H.

H. Jiang, H. Zhao, and X. Li, “High dynamic range fringe acquisition: a novel 3-d scanning technique for high-reflective surfaces,” Opt. Lasers Eng. 50(10), 1484–1493 (2012).
[Crossref]

Kofman, J.

C. Waddington and J. Kofman, “Saturation avoidance by adaptive fringe projection in phase-shifting 3d surface-shape measurement,” in Optomechatronic Technologies (ISOT), 2010 International Symposium on, (IEEE, 2010), pp. 1–4.

Kühmstedt, P.

A. Breitbarth, E. Müller, P. Kühmstedt, G. Notni, and J. Denzler, “Phase unwrapping of fringe images for dynamic 3d measurements without additional pattern projection,” in Dimensional Optical Metrology and Inspection for Practical Applications IV, vol. 9489 (International Society for Optics and Photonics, 2015), p. 948903.

Lau, D. L.

Lei, S.

Lei, Y.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Leibe, B.

T. Weise, B. Leibe, and L. Van Gool, “Fast 3d scanning with automatic motion compensation,” in 2007 IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2007), pp. 1–8.

Lensch, H. P.

T. Chen, H. P. Lensch, C. Fuchs, and H.-P. Seidel, “Polarization and phase-shifting for 3d scanning of translucent objects,” in 2007 IEEE conference on computer vision and pattern recognition (IEEE, 2007), pp. 1–8.

Li, A.

Li, B.

V. Suresh, Y. Wang, and B. Li, “High-dynamic-range 3d shape measurement utilizing the transitioning state of digital micromirror device,” Opt. Lasers Eng. 107, 176–181 (2018).
[Crossref]

Li, H.

Li, R.

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Lasers Eng. 59, 56–71 (2014).
[Crossref]

Li, X.

H. Jiang, H. Zhao, and X. Li, “High dynamic range fringe acquisition: a novel 3-d scanning technique for high-reflective surfaces,” Opt. Lasers Eng. 50(10), 1484–1493 (2012).
[Crossref]

Li, Z.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Liang, R.

Liu, K.

Liu, X.

Llado, X.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Müller, E.

A. Breitbarth, E. Müller, P. Kühmstedt, G. Notni, and J. Denzler, “Phase unwrapping of fringe images for dynamic 3d measurements without additional pattern projection,” in Dimensional Optical Metrology and Inspection for Practical Applications IV, vol. 9489 (International Society for Optics and Photonics, 2015), p. 948903.

Mutoh, K.

Notni, G.

A. Breitbarth, E. Müller, P. Kühmstedt, G. Notni, and J. Denzler, “Phase unwrapping of fringe images for dynamic 3d measurements without additional pattern projection,” in Dimensional Optical Metrology and Inspection for Practical Applications IV, vol. 9489 (International Society for Optics and Photonics, 2015), p. 948903.

Peng, X.

Pribanic, T.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Qian, J.

Rodriguez, J. J.

Salahieh, B.

Salvi, J.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Seidel, H.-P.

T. Chen, H. P. Lensch, C. Fuchs, and H.-P. Seidel, “Polarization and phase-shifting for 3d scanning of translucent objects,” in 2007 IEEE conference on computer vision and pattern recognition (IEEE, 2007), pp. 1–8.

Shen, G.

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Lasers Eng. 59, 56–71 (2014).
[Crossref]

Shi, Q.

C. Zhang, J. Xu, N. Xi, J. Zhao, and Q. Shi, “A robust surface coding method for optically challenging objects using structured light,” IEEE Trans. Automat. Sci. Eng. 11(3), 775–788 (2014).
[Crossref]

Shi, Y.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Song, K.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3d shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Lasers Eng. 84, 74–81 (2016).
[Crossref]

Suresh, V.

V. Suresh, Y. Wang, and B. Li, “High-dynamic-range 3d shape measurement utilizing the transitioning state of digital micromirror device,” Opt. Lasers Eng. 107, 176–181 (2018).
[Crossref]

Takeda, M.

Tao, T.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
[Crossref]

L. Zhang, Q. Chen, C. Zuo, T. Tao, Y. Zhang, and S. Feng, “High-dynamic-range 3d shape measurement based on time domain superposition,” Meas. Sci. Technol. 30(6), 065004 (2019).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (μftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3d shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Meas. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25(17), 20381–20400 (2017).
[Crossref]

Van Gool, L.

T. Weise, B. Leibe, and L. Van Gool, “Fast 3d scanning with automatic motion compensation,” in 2007 IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2007), pp. 1–8.

Waddington, C.

C. Waddington and J. Kofman, “Saturation avoidance by adaptive fringe projection in phase-shifting 3d surface-shape measurement,” in Optomechatronic Technologies (ISOT), 2010 International Symposium on, (IEEE, 2010), pp. 1–4.

Wang, C.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Wang, Y.

V. Suresh, Y. Wang, and B. Li, “High-dynamic-range 3d shape measurement utilizing the transitioning state of digital micromirror device,” Opt. Lasers Eng. 107, 176–181 (2018).
[Crossref]

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-d shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref]

Weise, T.

T. Weise, B. Leibe, and L. Van Gool, “Fast 3d scanning with automatic motion compensation,” in 2007 IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2007), pp. 1–8.

Wen, X.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3d shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Lasers Eng. 84, 74–81 (2016).
[Crossref]

Wu, J.

Xi, N.

C. Zhang, J. Xu, N. Xi, J. Zhao, and Q. Shi, “A robust surface coding method for optically challenging objects using structured light,” IEEE Trans. Automat. Sci. Eng. 11(3), 775–788 (2014).
[Crossref]

Xu, J.

C. Zhang, J. Xu, N. Xi, J. Zhao, and Q. Shi, “A robust surface coding method for optically challenging objects using structured light,” IEEE Trans. Automat. Sci. Eng. 11(3), 775–788 (2014).
[Crossref]

Yan, Y.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3d shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Lasers Eng. 84, 74–81 (2016).
[Crossref]

Yau, S.-T.

S. Zhang and S.-T. Yau, “High dynamic range scanning technique,” Opt. Eng. 48(3), 033604 (2009).
[Crossref]

Yin, W.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

Yin, Y.

Zakhor, A.

R. R. Garcia and A. Zakhor, “Consistent stereo-assisted absolute phase unwrapping methods for structured light systems,” IEEE J. Sel. Top. Signal Process. 6(5), 411–424 (2012).
[Crossref]

Zhang, C.

C. Zhang, J. Xu, N. Xi, J. Zhao, and Q. Shi, “A robust surface coding method for optically challenging objects using structured light,” IEEE Trans. Automat. Sci. Eng. 11(3), 775–788 (2014).
[Crossref]

Zhang, L.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
[Crossref]

L. Zhang, Q. Chen, C. Zuo, T. Tao, Y. Zhang, and S. Feng, “High-dynamic-range 3d shape measurement based on time domain superposition,” Meas. Sci. Technol. 30(6), 065004 (2019).
[Crossref]

L. Zhang, Q. Chen, C. Zuo, and S. Feng, “High dynamic range 3d shape measurement based on the intensity response function of a camera,” Appl. Opt. 57(6), 1378–1386 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Meas. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

Zhang, M.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25(17), 20381–20400 (2017).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Zhang, S.

Zhang, Y.

L. Zhang, Q. Chen, C. Zuo, T. Tao, Y. Zhang, and S. Feng, “High-dynamic-range 3d shape measurement based on time domain superposition,” Meas. Sci. Technol. 30(6), 065004 (2019).
[Crossref]

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Lasers Eng. 59, 56–71 (2014).
[Crossref]

Zhang, Z.

Z. Zhang, “Review of single-shot 3d shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
[Crossref]

Zhao, H.

H. Jiang, H. Zhao, and X. Li, “High dynamic range fringe acquisition: a novel 3-d scanning technique for high-reflective surfaces,” Opt. Lasers Eng. 50(10), 1484–1493 (2012).
[Crossref]

Zhao, J.

C. Zhang, J. Xu, N. Xi, J. Zhao, and Q. Shi, “A robust surface coding method for optically challenging objects using structured light,” IEEE Trans. Automat. Sci. Eng. 11(3), 775–788 (2014).
[Crossref]

Zhong, K.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Zuo, C.

L. Zhang, Q. Chen, C. Zuo, T. Tao, Y. Zhang, and S. Feng, “High-dynamic-range 3d shape measurement based on time domain superposition,” Meas. Sci. Technol. 30(6), 065004 (2019).
[Crossref]

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
[Crossref]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3d shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (μftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

L. Zhang, Q. Chen, C. Zuo, and S. Feng, “High dynamic range 3d shape measurement based on the intensity response function of a camera,” Appl. Opt. 57(6), 1378–1386 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Meas. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25(17), 20381–20400 (2017).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Lasers Eng. 59, 56–71 (2014).
[Crossref]

Adv. Opt. Photonics (1)

J. Geng, “Structured-light 3d surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

Adv. Photonics (1)

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
[Crossref]

Appl. Opt. (3)

IEEE J. Sel. Top. Signal Process. (1)

R. R. Garcia and A. Zakhor, “Consistent stereo-assisted absolute phase unwrapping methods for structured light systems,” IEEE J. Sel. Top. Signal Process. 6(5), 411–424 (2012).
[Crossref]

IEEE Trans. Automat. Sci. Eng. (1)

C. Zhang, J. Xu, N. Xi, J. Zhao, and Q. Shi, “A robust surface coding method for optically challenging objects using structured light,” IEEE Trans. Automat. Sci. Eng. 11(3), 775–788 (2014).
[Crossref]

Meas. Sci. Technol. (2)

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Meas. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

L. Zhang, Q. Chen, C. Zuo, T. Tao, Y. Zhang, and S. Feng, “High-dynamic-range 3d shape measurement based on time domain superposition,” Meas. Sci. Technol. 30(6), 065004 (2019).
[Crossref]

Opt. Eng. (1)

S. Zhang and S.-T. Yau, “High dynamic range scanning technique,” Opt. Eng. 48(3), 033604 (2009).
[Crossref]

Opt. Express (6)

Opt. Lasers Eng. (10)

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (μftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3d shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Lasers Eng. 84, 74–81 (2016).
[Crossref]

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

H. Jiang, H. Zhao, and X. Li, “High dynamic range fringe acquisition: a novel 3-d scanning technique for high-reflective surfaces,” Opt. Lasers Eng. 50(10), 1484–1493 (2012).
[Crossref]

Z. Zhang, “Review of single-shot 3d shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

V. Suresh, Y. Wang, and B. Li, “High-dynamic-range 3d shape measurement utilizing the transitioning state of digital micromirror device,” Opt. Lasers Eng. 107, 176–181 (2018).
[Crossref]

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Lasers Eng. 59, 56–71 (2014).
[Crossref]

Opt. Lett. (1)

Optik (1)

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik 121(1), 23–28 (2010).
[Crossref]

Pattern Recognit. (1)

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Other (5)

H. Guo and P. S. Huang, “3-d shape measurement by use of a modified fourier transform method,” in Two-and Three-Dimensional Methods for Inspection and Metrology VI, vol. 7066 (International Society for Optics and Photonics, 2008), p. 70660E.

T. Weise, B. Leibe, and L. Van Gool, “Fast 3d scanning with automatic motion compensation,” in 2007 IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2007), pp. 1–8.

T. Chen, H. P. Lensch, C. Fuchs, and H.-P. Seidel, “Polarization and phase-shifting for 3d scanning of translucent objects,” in 2007 IEEE conference on computer vision and pattern recognition (IEEE, 2007), pp. 1–8.

A. Breitbarth, E. Müller, P. Kühmstedt, G. Notni, and J. Denzler, “Phase unwrapping of fringe images for dynamic 3d measurements without additional pattern projection,” in Dimensional Optical Metrology and Inspection for Practical Applications IV, vol. 9489 (International Society for Optics and Photonics, 2015), p. 948903.

C. Waddington and J. Kofman, “Saturation avoidance by adaptive fringe projection in phase-shifting 3d surface-shape measurement,” in Optomechatronic Technologies (ISOT), 2010 International Symposium on, (IEEE, 2010), pp. 1–4.

Supplementary Material (4)

NameDescription
» Visualization 1       The visual interface our program.
» Visualization 2       Real-time measurement process and result of the statue of a captain.
» Visualization 3       Real-time measurement process and result of the HDR scene.
» Visualization 4       Real-time measurement process and result of the HDR scene with specular reflection.

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Figures (17)

Fig. 1.
Fig. 1. Timing Diagram of the DLP technology.
Fig. 2.
Fig. 2. (a) Photograph of the HDR scene; (b) Image in the first capture; (c) Image in the second capture; (d) Fusion image; (e) Cross-section plot of the 250th column of (b); (f) Cross-section plot of the 250th column of (c).
Fig. 3.
Fig. 3. (a) Low-frequency binary pattern; (b) (a) after Gaussian filtering; (c) High-frequency binary pattern; (d) (c) after Gaussian filtering.
Fig. 4.
Fig. 4. Diagram of the binocular system.
Fig. 5.
Fig. 5. Diagram of SPU. (a) Low-frequency fringe patterns in SPU; (b) High-frequency fringe patterns in SPU.
Fig. 6.
Fig. 6. Overview of the mixed phase unwrapping method. (a)-(c) Fusion images $I^{f}_{1}\sim I^{f}_{3}$; (d) Wrapped phase of $I^{f}_{1}$; (e) Wrapped phase of $I^{f}_{3}$; (f) Synthetic wrapped phase $\phi _{syn}$; (g) Refined wrapped phase $\phi ^{c1}_{ref}$ of Camera1; (h) Refined wrapped phase $\phi ^{c2}_{ref}$ of Camera2; (i) Final unwrapped phase $\Phi ^{c1}$ of Camera1.
Fig. 7.
Fig. 7. (a) Defocusing binary pattern with $f_{1}$ of Camera1; (b) Pattern with uniform intensity of Camera1; (c) Defocusing binary pattern with $f_{2}$ of Camera1; (d) Synthetic wrapped phase $\phi ^{c1}_{syn}$ of the red dotted line; (e) Refined wrapped phase $\phi ^{c1}_{ref}$ of the red dotted line.
Fig. 8.
Fig. 8. Our binocular FPP system.
Fig. 9.
Fig. 9. (a) Photograph of the standard ceramic spheres; (b) Photograph of the HDR scene.
Fig. 10.
Fig. 10. (a) 3D reconstruction result of Sphere A; (b) Measurement error of Sphere A; (c) Error distribution of Sphere A; (d) 3D reconstruction result of Sphere B; (e) Measurement error of Sphere B; (f) Error distribution of Sphere B.
Fig. 11.
Fig. 11. (a) $I^{c}_{1}$ of Camera1 and the corresponding cross section; (b) $I^{c}_{4}$ of Camera1 and the corresponding cross section; (c) $I^{f}_{1}$ of Camera1 and the corresponding cross section; (d) $I^{c}_{1}$ of Camera2 and the corresponding cross section; (e) $I^{c}_{4}$ of Camera2 and the corresponding cross section; (f) $I^{f}_{1}$ of Camera2 and the corresponding cross section.
Fig. 12.
Fig. 12. (a) Fitting result of the dotted line in (b); (b) 3D reconstruction result of the HDR scene with the exposure of $T5$; (c) Enlarged detail of the plastic toy in (b); (d) Fitting result of the dotted line in (e); (e) 3D reconstruction result of the HDR scene with the exposures of $T6$ and $T7$; (f) Enlarged detail of the plastic toy in (e); (g) Fitting result of the dotted line in (h); (h) 3D reconstruction result of the HDR scene with our method; (i) Enlarged detail of the plastic toy in (h).
Fig. 13.
Fig. 13. (a) Photograph of the statue of a captain; (b) Photograph of the HDR scene; (c) Photograph of the HDR scene with specular reflection.
Fig. 14.
Fig. 14. The measurement result of the statue of a captain. (a) Normal display mode; (b) Depth display mode; (c) Zoom in on the statue; (d) Zoom out on the statue.
Fig. 15.
Fig. 15. (a) Real-time measurement process and result of the statue of a captain; (b) Real-time measurement process and result of the HDR scene.
Fig. 16.
Fig. 16. (a) Captured image of Camera1 without polarizer; (b) Captured image of Camera1 with polarizer; (c) Captured image of Camera2 without polarizer; (d) Captured image of Camera2 with polarizer.
Fig. 17.
Fig. 17. (a)-(f) $I^{c}_{1}\sim I^{c}_{6}$ of Camera1; (g)-(i) $I^{f}_{1}\sim I^{f}_{3}$ of Camera1; (j)-(o) $I^{c}_{1}\sim I^{c}_{6}$ of Camera2; (p)-(r) $I^{f}_{1}\sim I^{f}_{3}$ of Camera2; (s) 3D measurement result.

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

I c = α r t I p .
I f ( x c , y c ) = { I 1 ( x c , y c ) ,       I 1 ( x c , y c ) L t h I 2 ( x c , y c ) ,       I 1 ( x c , y c ) > L t h   ,
I c 1 ( x c , y c ) = α r t { A + B c o s [ ϕ ( x p , y p ) ] } .
z w ( x c 1 , y c 1 ) = M 1 ( x c 1 , y c 1 ) M 2 ( x c 1 , y c 1 ) x c 2 ( x c 1 , y c 1 ) + 1 + M 3 ( x c 1 , y c 1 ) ,
x w ( x c 1 , y c 1 ) = M 4 ( x c 1 , y c 1 ) z w ( x c 1 , y c 1 ) + M 5 ( x c 1 , y c 1 ) ,
y w ( x c 1 , y c 1 ) = M 6 ( x c 1 , y c 1 ) z w ( x c 1 , y c 1 ) + M 7 ( x c 1 , y c 1 ) ,
Φ c 1 ( x c 1 , y c 1 ) = ϕ c 1 ( x c 1 , y c 1 ) + k ( x c 1 , y c 1 ) 2 π ,     k ( x c 1 , y c 1 ) [ 0 , N 1 ] ,
I c ^ ( f x , f y ) = A ^ ( f x , f y ) + C ^ ( f x f 0 , f y ) + C ^ ( f x + f 0 , f y ) ,
I 1 c ( x c , y c ) = α r T 5 { A + B c o s [ ϕ 1 ( x p , y p ) ] } , I 2 c ( x c , y c ) = α r T 5 ( A + B ) , I 3 c ( x c , y c ) = α r T 5 { A + B c o s [ ϕ 2 ( x p , y p ) ] } , I 4 c ( x c , y c ) = α r T 6 { A + B c o s [ ϕ 1 ( x p , y p ) ] } , I 5 c ( x c , y c ) = α r T 6 ( A + B ) , I 6 c ( x c , y c ) = α r T 6 { A + B c o s [ ϕ 2 ( x p , y p ) ] } ,
I 1 f ( x c , y c ) = { I 1 c ( x c , y c ) , f u n c t i o n L t h I 4 c ( x c , y c ) , f u n c t i o n > L t h ,
I 2 f ( x c , y c ) = { I 2 c ( x c , y c ) , f u n c t i o n L t h I 5 c ( x c , y c ) , f u n c t i o n > L t h ,
I 3 f ( x c , y c ) = { I 3 c ( x c , y c ) , f u n c t i o n L t h I 6 c ( x c , y c ) , f u n c t i o n > L t h ,
f u n c t i o n = m a x [ I 1 c ( x c , y c ) , I 2 c ( x c , y c ) , I 3 c ( x c , y c ) ] ,
I 1 d ( x c , y c ) = 2 I 1 f ( x c , y c ) I 2 f ( x c , y c ) I 2 f ( x c , y c ) + γ ,
I 2 d ( x c , y c ) = 2 I 3 f ( x c , y c ) I 2 f ( x c , y c ) I 2 f ( x c , y c ) + γ ,
ϕ s y n = ( ϕ 1 ϕ 2 ) m o d ( 2 π ) ,
f s y n = | f 1 f 2 | .
λ s y n = λ 1 λ 2 λ 1 λ 2 ,
k s y n ( x c , y c ) = R o u n d [ λ s y n / λ 1 ϕ s y n ( x c , y c ) ϕ 1 ( x c , y c ) 2 π ] ,
ϕ r e f ( x c , y c ) = ϕ 1 ( x c , y c ) + k s y n ( x c , y c ) 2 π ,
f 1 = 912 16 = 57 ,       f 2 = 912 12 = 76 , f r e f = f s y n = | 57 76 | = 19 .
Φ n c 1 ( x c 1 , y c 1 ) = ϕ r e f c 1 ( x c 1 , y c 1 ) + k n 2 π ,     k n [ 0 , N 1 ] .
Z m i n < z n w ( x c 1 , y c 1 ) < Z m a x ,
P n w ( x n w , y n w , z n w ) P n c 2 ( x c 2 , y c 2 ) .
Δ ϕ = | ϕ r e f c 1 ( x c 1 , y c 1 ) ϕ r e f c 2 ( x c 2 , y c 2 ) | ,
T 2 + T 3 = 9000   μ s + 3000   μ s = 12000   μ s .
1   s 3 × 12000   μ s = 1 × 10 6   μ s 3 × 12000   μ s 28   H z .

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