Abstract

Three-dimensional (3D) imaging and metrology of microstructures is a critical task for the design, fabrication, and inspection of microelements. Newly developed fringe projection 3D microscopy is presented in this paper. The system is configured according to camera-projector layout and long working distance lenses. The Scheimpflug principle is employed to make full use of the limited depth of field. For such a specific system, the general imaging model is introduced to reach a full 3D reconstruction. A dedicated calibration procedure is developed to realize quantitative 3D imaging. Experiments with a prototype demonstrate the accessibility of the proposed configuration, model, and calibration approach.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]

2014 (4)

Y. Yin, D. He, Z. Liu, X. Liu, and X. Peng, “Phase aided 3D imaging and modeling: dedicated systems and case studies,” Proc. SPIE 9132, 91320Q (2014).

D. Wu, H. Xie, C. Li, and R. Wang, “Application of the digital phase-shifting method in 3D deformation measurement at micro-scale by SEM,” Meas. Sci. Technol. 25(12), 125002 (2014).
[Crossref]

D. Li, C. Liu, and J. Tian, “Telecentric 3D profilometry based on phase-shifting fringe projection,” Opt. Express 22(26), 31826–31835 (2014).
[Crossref] [PubMed]

Y. Yin, M. Wang, A. Li, X. Liu, and X. Peng, “Ray-based calibration for the micro optical metrology system,” Proc. SPIE 9132, 91320K (2014).

2013 (6)

C. Li, Z. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol. 24(4), 045401 (2013).
[Crossref]

J. Notbohm, A. Rosakis, S. Kumagai, S. Xia, and G. Ravichandran, “Three-dimensional displacement and shape measurement with a diffraction-assisted grid method,” Strain 49(5), 399–408 (2013).

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “Noninterferometric single-shot quantitative phase microscopy,” Opt. Lett. 38(18), 3538–3541 (2013).
[Crossref] [PubMed]

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik 124(21), 5052–5056 (2013).
[Crossref]

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” Proc. SPIE 8759, 87594U (2013).
[Crossref]

D. S. Mehta, M. Inam, J. Prakash, and A. M. Biradar, “Liquid-crystal phase-shifting lateral shearing interferometer with improved fringe contrast for 3D surface profilometry,” Appl. Opt. 52(25), 6119–6125 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (2)

2010 (3)

2009 (3)

G. Frankowski and R. Hainich, “DLP-based 3D metrology by structured light or projected fringe technology for life sciences and industrial metrology,” Proc. SPIE 7210, 72100C (2009).
[Crossref]

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors (Basel) 9(1), 568–601 (2009).
[Crossref] [PubMed]

R. Rodriguez-Vera, K. Genovese, J. A. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by Talbot fringe projection method,” Strain 45(3), 249–258 (2009).
[Crossref]

2008 (2)

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” Proc. SPIE 7066, 706606 (2008).
[Crossref]

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

2007 (1)

2006 (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

2005 (1)

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

2004 (2)

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

G. Notni, S. Riehemann, P. Kuehmstedt, L. Heidler, and N. Wolf, “OLED microdisplays: a new key element for fringe projection setups,” Proc. SPIE 5532, 170–177 (2004).
[Crossref]

2003 (3)

K.-P. Proll, J.-M. Nivet, K. Körner, and H. J. Tiziani, “Microscopic three-dimensional topometry with ferroelectric liquid-crystal-on-silicon displays,” Appl. Opt. 42(10), 1773–1778 (2003).
[Crossref] [PubMed]

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Error compensation for a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

2002 (2)

C. Zhang, P. S. Huang, and F.-P. Chiang, “Microscopic phase-shifting profilometry based on digital micromirror device technology,” Appl. Opt. 41(28), 5896–5904 (2002).
[Crossref] [PubMed]

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34(7), 547–552 (2002).
[Crossref]

2001 (2)

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1–3), 21–29 (2001).
[Crossref]

X. Su and W. Chen, “Fourier transform profilometry,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

1997 (1)

R. Windecker, M. Fleischer, and H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36(12), 3372–3377 (1997).
[Crossref]

Anand, A.

Asundi, A.

Bergmann, R. B.

Biradar, A. M.

Bothe, T.

Chen, J.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” Proc. SPIE 8759, 87594U (2013).
[Crossref]

Z. Zhang, H. Ma, T. Guo, S. Zhang, and J. Chen, “Simple, flexible calibration of phase calculation-based three-dimensional imaging system,” Opt. Lett. 36(7), 1257–1259 (2011).
[PubMed]

Chen, L.

Chen, M.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

Chen, Q.

Chen, W.

X. Su and W. Chen, “Fourier transform profilometry,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

Chhaniwal, V.

Chiang, F.-P.

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Error compensation for a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

C. Zhang, P. S. Huang, and F.-P. Chiang, “Microscopic phase-shifting profilometry based on digital micromirror device technology,” Appl. Opt. 41(28), 5896–5904 (2002).
[Crossref] [PubMed]

Chua, P. S. K.

Docchio, F.

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors (Basel) 9(1), 568–601 (2009).
[Crossref] [PubMed]

Du, H.

Faridian, A.

Fleischer, M.

R. Windecker, M. Fleischer, and H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36(12), 3372–3377 (1997).
[Crossref]

Frankowski, G.

G. Frankowski and R. Hainich, “DLP-based 3D metrology by structured light or projected fringe technology for life sciences and industrial metrology,” Proc. SPIE 7210, 72100C (2009).
[Crossref]

Fu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Error compensation for a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

Fu, X.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” Proc. SPIE 8759, 87594U (2013).
[Crossref]

Fujigaki, M.

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” Proc. SPIE 7066, 706606 (2008).
[Crossref]

Gao, B. Z.

Genovese, K.

R. Rodriguez-Vera, K. Genovese, J. A. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by Talbot fringe projection method,” Strain 45(3), 249–258 (2009).
[Crossref]

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Grossberg, M. D.

M. D. Grossberg and S. K. Nayar, “A general imaging model and a method for finding its parameters,” in Proceedings of Eighth IEEE International Conference on Computer Vision (ICCV 2001), (2001), 108–115.
[Crossref]

Guo, H.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

Guo, T.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” Proc. SPIE 8759, 87594U (2013).
[Crossref]

Z. Zhang, H. Ma, T. Guo, S. Zhang, and J. Chen, “Simple, flexible calibration of phase calculation-based three-dimensional imaging system,” Opt. Lett. 36(7), 1257–1259 (2011).
[PubMed]

Hainich, R.

G. Frankowski and R. Hainich, “DLP-based 3D metrology by structured light or projected fringe technology for life sciences and industrial metrology,” Proc. SPIE 7210, 72100C (2009).
[Crossref]

He, D.

Y. Yin, D. He, Z. Liu, X. Liu, and X. Peng, “Phase aided 3D imaging and modeling: dedicated systems and case studies,” Proc. SPIE 9132, 91320Q (2014).

He, H.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

He, X. Y.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34(7), 547–552 (2002).
[Crossref]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1–3), 21–29 (2001).
[Crossref]

Heidler, L.

G. Notni, S. Riehemann, P. Kuehmstedt, L. Heidler, and N. Wolf, “OLED microdisplays: a new key element for fringe projection setups,” Proc. SPIE 5532, 170–177 (2004).
[Crossref]

Hu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Error compensation for a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

Hu, X.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” Proc. SPIE 8759, 87594U (2013).
[Crossref]

Huang, L.

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Error compensation for a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

C. Zhang, P. S. Huang, and F.-P. Chiang, “Microscopic phase-shifting profilometry based on digital micromirror device technology,” Appl. Opt. 41(28), 5896–5904 (2002).
[Crossref] [PubMed]

Inam, M.

Javidi, B.

Jüptner, W. P.

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

Jüptner, W. P. O.

Kang, X.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34(7), 547–552 (2002).
[Crossref]

Körner, K.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik 124(21), 5052–5056 (2013).
[Crossref]

K.-P. Proll, J.-M. Nivet, K. Körner, and H. J. Tiziani, “Microscopic three-dimensional topometry with ferroelectric liquid-crystal-on-silicon displays,” Appl. Opt. 42(10), 1773–1778 (2003).
[Crossref] [PubMed]

Kuehmstedt, P.

G. Notni, S. Riehemann, P. Kuehmstedt, L. Heidler, and N. Wolf, “OLED microdisplays: a new key element for fringe projection setups,” Proc. SPIE 5532, 170–177 (2004).
[Crossref]

Kumagai, S.

J. Notbohm, A. Rosakis, S. Kumagai, S. Xia, and G. Ravichandran, “Three-dimensional displacement and shape measurement with a diffraction-assisted grid method,” Strain 49(5), 399–408 (2013).

Legarda-Sáenz, R.

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

Li, A.

Y. Yin, M. Wang, A. Li, X. Liu, and X. Peng, “Ray-based calibration for the micro optical metrology system,” Proc. SPIE 9132, 91320K (2014).

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik 124(21), 5052–5056 (2013).
[Crossref]

Y. Yin, X. Peng, A. Li, X. Liu, and B. Z. Gao, “Calibration of fringe projection profilometry with bundle adjustment strategy,” Opt. Lett. 37(4), 542–544 (2012).
[Crossref] [PubMed]

Li, B.

Li, C.

D. Wu, H. Xie, C. Li, and R. Wang, “Application of the digital phase-shifting method in 3D deformation measurement at micro-scale by SEM,” Meas. Sci. Technol. 25(12), 125002 (2014).
[Crossref]

C. Li, Z. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol. 24(4), 045401 (2013).
[Crossref]

Li, D.

Li, W.

Li, Z.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Liu, C.

Liu, H.

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

Liu, X.

Y. Yin, D. He, Z. Liu, X. Liu, and X. Peng, “Phase aided 3D imaging and modeling: dedicated systems and case studies,” Proc. SPIE 9132, 91320Q (2014).

Y. Yin, M. Wang, A. Li, X. Liu, and X. Peng, “Ray-based calibration for the micro optical metrology system,” Proc. SPIE 9132, 91320K (2014).

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik 124(21), 5052–5056 (2013).
[Crossref]

Y. Yin, X. Peng, A. Li, X. Liu, and B. Z. Gao, “Calibration of fringe projection profilometry with bundle adjustment strategy,” Opt. Lett. 37(4), 542–544 (2012).
[Crossref] [PubMed]

Liu, Z.

Y. Yin, D. He, Z. Liu, X. Liu, and X. Peng, “Phase aided 3D imaging and modeling: dedicated systems and case studies,” Proc. SPIE 9132, 91320Q (2014).

C. Li, Z. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol. 24(4), 045401 (2013).
[Crossref]

Lodha, S. K.

S. Ramalingam, P. Sturm, and S. K. Lodha, “Towards complete generic camera calibration,” in Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2005), (2005), 1093–1098.
[Crossref]

Ma, H.

Ma, S.

Matui, T.

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” Proc. SPIE 7066, 706606 (2008).
[Crossref]

Mehta, D. S.

Mendoza-Santoyo, F.

R. Rodriguez-Vera, K. Genovese, J. A. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by Talbot fringe projection method,” Strain 45(3), 249–258 (2009).
[Crossref]

Morimoto, Y.

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” Proc. SPIE 7066, 706606 (2008).
[Crossref]

Nayar, S. K.

M. D. Grossberg and S. K. Nayar, “A general imaging model and a method for finding its parameters,” in Proceedings of Eighth IEEE International Conference on Computer Vision (ICCV 2001), (2001), 108–115.
[Crossref]

Nivet, J.-M.

Notbohm, J.

J. Notbohm, A. Rosakis, S. Kumagai, S. Xia, and G. Ravichandran, “Three-dimensional displacement and shape measurement with a diffraction-assisted grid method,” Strain 49(5), 399–408 (2013).

Notni, G.

G. Notni, S. Riehemann, P. Kuehmstedt, L. Heidler, and N. Wolf, “OLED microdisplays: a new key element for fringe projection setups,” Proc. SPIE 5532, 170–177 (2004).
[Crossref]

Osten, W.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik 124(21), 5052–5056 (2013).
[Crossref]

A. Anand, A. Faridian, V. Chhaniwal, G. Pedrini, W. Osten, and B. Javidi, “High-resolution quantitative phase microscopic imaging in deep UV with phase retrieval,” Opt. Lett. 36(22), 4362–4364 (2011).
[Crossref] [PubMed]

Pedrini, G.

Peng, X.

Y. Yin, M. Wang, A. Li, X. Liu, and X. Peng, “Ray-based calibration for the micro optical metrology system,” Proc. SPIE 9132, 91320K (2014).

Y. Yin, D. He, Z. Liu, X. Liu, and X. Peng, “Phase aided 3D imaging and modeling: dedicated systems and case studies,” Proc. SPIE 9132, 91320Q (2014).

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik 124(21), 5052–5056 (2013).
[Crossref]

Y. Yin, X. Peng, A. Li, X. Liu, and B. Z. Gao, “Calibration of fringe projection profilometry with bundle adjustment strategy,” Opt. Lett. 37(4), 542–544 (2012).
[Crossref] [PubMed]

Prakash, J.

Proll, K.-P.

Qu, W.

Quan, C.

S. Ma, R. Zhu, C. Quan, L. Chen, C. J. Tay, and B. Li, “Flexible structured-light-based three-dimensional profile reconstruction method considering lens projection-imaging distortion,” Appl. Opt. 51(13), 2419–2428 (2012).
[Crossref] [PubMed]

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34(7), 547–552 (2002).
[Crossref]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1–3), 21–29 (2001).
[Crossref]

Ramalingam, S.

S. Ramalingam, P. Sturm, and S. K. Lodha, “Towards complete generic camera calibration,” in Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2005), (2005), 1093–1098.
[Crossref]

Rastogi, P.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Ravichandran, G.

J. Notbohm, A. Rosakis, S. Kumagai, S. Xia, and G. Ravichandran, “Three-dimensional displacement and shape measurement with a diffraction-assisted grid method,” Strain 49(5), 399–408 (2013).

Rayas, J. A.

R. Rodriguez-Vera, K. Genovese, J. A. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by Talbot fringe projection method,” Strain 45(3), 249–258 (2009).
[Crossref]

Reichard, K.

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

Riehemann, S.

G. Notni, S. Riehemann, P. Kuehmstedt, L. Heidler, and N. Wolf, “OLED microdisplays: a new key element for fringe projection setups,” Proc. SPIE 5532, 170–177 (2004).
[Crossref]

Rodriguez-Vera, R.

R. Rodriguez-Vera, K. Genovese, J. A. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by Talbot fringe projection method,” Strain 45(3), 249–258 (2009).
[Crossref]

Rosakis, A.

J. Notbohm, A. Rosakis, S. Kumagai, S. Xia, and G. Ravichandran, “Three-dimensional displacement and shape measurement with a diffraction-assisted grid method,” Strain 49(5), 399–408 (2013).

Sansoni, G.

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors (Basel) 9(1), 568–601 (2009).
[Crossref] [PubMed]

Schulte, M.

Shang, H. M.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34(7), 547–552 (2002).
[Crossref]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1–3), 21–29 (2001).
[Crossref]

Shi, Y.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Sturm, P.

S. Ramalingam, P. Sturm, and S. K. Lodha, “Towards complete generic camera calibration,” in Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2005), (2005), 1093–1098.
[Crossref]

Su, W.-H.

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

Su, X.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

X. Su and W. Chen, “Fourier transform profilometry,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

Sun, X.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

Takagishi, A.

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” Proc. SPIE 7066, 706606 (2008).
[Crossref]

Tay, C. J.

S. Ma, R. Zhu, C. Quan, L. Chen, C. J. Tay, and B. Li, “Flexible structured-light-based three-dimensional profile reconstruction method considering lens projection-imaging distortion,” Appl. Opt. 51(13), 2419–2428 (2012).
[Crossref] [PubMed]

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34(7), 547–552 (2002).
[Crossref]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1–3), 21–29 (2001).
[Crossref]

Tian, J.

Tiziani, H. J.

Trebeschi, M.

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors (Basel) 9(1), 568–601 (2009).
[Crossref] [PubMed]

von Kopylow, C.

Wang, C.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Wang, C. F.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1–3), 21–29 (2001).
[Crossref]

Wang, L.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” Proc. SPIE 8759, 87594U (2013).
[Crossref]

Wang, M.

Y. Yin, M. Wang, A. Li, X. Liu, and X. Peng, “Ray-based calibration for the micro optical metrology system,” Proc. SPIE 9132, 91320K (2014).

Wang, R.

D. Wu, H. Xie, C. Li, and R. Wang, “Application of the digital phase-shifting method in 3D deformation measurement at micro-scale by SEM,” Meas. Sci. Technol. 25(12), 125002 (2014).
[Crossref]

Wang, Y.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Wang, Z.

Windecker, R.

R. Windecker, M. Fleischer, and H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36(12), 3372–3377 (1997).
[Crossref]

Wolf, N.

G. Notni, S. Riehemann, P. Kuehmstedt, L. Heidler, and N. Wolf, “OLED microdisplays: a new key element for fringe projection setups,” Proc. SPIE 5532, 170–177 (2004).
[Crossref]

Wu, D.

D. Wu, H. Xie, C. Li, and R. Wang, “Application of the digital phase-shifting method in 3D deformation measurement at micro-scale by SEM,” Meas. Sci. Technol. 25(12), 125002 (2014).
[Crossref]

Wu, Z.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” Proc. SPIE 8759, 87594U (2013).
[Crossref]

Xia, S.

J. Notbohm, A. Rosakis, S. Kumagai, S. Xia, and G. Ravichandran, “Three-dimensional displacement and shape measurement with a diffraction-assisted grid method,” Strain 49(5), 399–408 (2013).

Xiang, L.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

Xie, H.

D. Wu, H. Xie, C. Li, and R. Wang, “Application of the digital phase-shifting method in 3D deformation measurement at micro-scale by SEM,” Meas. Sci. Technol. 25(12), 125002 (2014).
[Crossref]

C. Li, Z. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol. 24(4), 045401 (2013).
[Crossref]

Yin, S.

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

Yin, Y.

Y. Yin, D. He, Z. Liu, X. Liu, and X. Peng, “Phase aided 3D imaging and modeling: dedicated systems and case studies,” Proc. SPIE 9132, 91320Q (2014).

Y. Yin, M. Wang, A. Li, X. Liu, and X. Peng, “Ray-based calibration for the micro optical metrology system,” Proc. SPIE 9132, 91320K (2014).

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik 124(21), 5052–5056 (2013).
[Crossref]

Y. Yin, X. Peng, A. Li, X. Liu, and B. Z. Gao, “Calibration of fringe projection profilometry with bundle adjustment strategy,” Opt. Lett. 37(4), 542–544 (2012).
[Crossref] [PubMed]

Yu, Y.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

Zhang, C.

Zhang, Q.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

Zhang, S.

Zhang, Z.

Zhao, Q.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik 124(21), 5052–5056 (2013).
[Crossref]

Zhu, R.

Zuo, C.

Appl. Opt. (6)

Meas. Sci. Technol. (2)

C. Li, Z. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol. 24(4), 045401 (2013).
[Crossref]

D. Wu, H. Xie, C. Li, and R. Wang, “Application of the digital phase-shifting method in 3D deformation measurement at micro-scale by SEM,” Meas. Sci. Technol. 25(12), 125002 (2014).
[Crossref]

Opt. Commun. (2)

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1–3), 21–29 (2001).
[Crossref]

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

Opt. Eng. (6)

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Error compensation for a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

R. Windecker, M. Fleischer, and H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36(12), 3372–3377 (1997).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34(7), 547–552 (2002).
[Crossref]

Opt. Lasers Eng. (3)

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

X. Su and W. Chen, “Fourier transform profilometry,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

Opt. Lett. (5)

Optik (1)

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik 124(21), 5052–5056 (2013).
[Crossref]

Proc. SPIE (6)

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” Proc. SPIE 8759, 87594U (2013).
[Crossref]

G. Notni, S. Riehemann, P. Kuehmstedt, L. Heidler, and N. Wolf, “OLED microdisplays: a new key element for fringe projection setups,” Proc. SPIE 5532, 170–177 (2004).
[Crossref]

G. Frankowski and R. Hainich, “DLP-based 3D metrology by structured light or projected fringe technology for life sciences and industrial metrology,” Proc. SPIE 7210, 72100C (2009).
[Crossref]

Y. Yin, D. He, Z. Liu, X. Liu, and X. Peng, “Phase aided 3D imaging and modeling: dedicated systems and case studies,” Proc. SPIE 9132, 91320Q (2014).

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” Proc. SPIE 7066, 706606 (2008).
[Crossref]

Y. Yin, M. Wang, A. Li, X. Liu, and X. Peng, “Ray-based calibration for the micro optical metrology system,” Proc. SPIE 9132, 91320K (2014).

Sensors (Basel) (1)

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors (Basel) 9(1), 568–601 (2009).
[Crossref] [PubMed]

Strain (2)

J. Notbohm, A. Rosakis, S. Kumagai, S. Xia, and G. Ravichandran, “Three-dimensional displacement and shape measurement with a diffraction-assisted grid method,” Strain 49(5), 399–408 (2013).

R. Rodriguez-Vera, K. Genovese, J. A. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by Talbot fringe projection method,” Strain 45(3), 249–258 (2009).
[Crossref]

Other (2)

S. Ramalingam, P. Sturm, and S. K. Lodha, “Towards complete generic camera calibration,” in Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2005), (2005), 1093–1098.
[Crossref]

M. D. Grossberg and S. K. Nayar, “A general imaging model and a method for finding its parameters,” in Proceedings of Eighth IEEE International Conference on Computer Vision (ICCV 2001), (2001), 108–115.
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 Traditional FP-3DM. (a) Schematic of setup. (b) Common focus area (marked with a red ellipse in (a)).
Fig. 2
Fig. 2 System configuration.
Fig. 3
Fig. 3 The general imaging model.
Fig. 4
Fig. 4 3D schematic of the system with general imaging model.
Fig. 5
Fig. 5 System calibration. (a) Planar target. (b) Elements of system calibration. (c) Target coordinate system.
Fig. 6
Fig. 6 The proposed calibration approach.
Fig. 7
Fig. 7 Coordinate evaluation from PCS to TCS.
Fig. 8
Fig. 8 Photograph of some experimental components. (a) The calibration target. (b) The fifty-cent coin. (c) The ceramic flat.
Fig. 9
Fig. 9 Experiment to demonstrate the common focus area. (a) Translating the flat 20 times along the z-axis. (b) Projected binary fringe and capture fringe image. (c) 5 selected areas within the FOV. (d) Contrast curves.
Fig. 10
Fig. 10 Standard fringe patterns. (a), (c) Phase-shifting patterns in orthogonal directions. (b), (d) Gray-code patterns in orthogonal directions.
Fig. 11
Fig. 11 Target data for calibration.
Fig. 12
Fig. 12 The 3D-range images acquired with the calibrated prototype.

Tables (2)

Tables Icon

Table 1 Details of the coupled pose parameters and corresponding coefficients

Tables Icon

Table 2 Measured translation distance on selected points

Equations (8)

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

ml(X=A-sD)
{ m i l i (X= A i - s i D i ) m p l p (X= A p - s p D p ) X=( l i l p ), φ i ( m i )= φ p ( m p )
Q i = ( Q 1 i , Q 2 i ,0,1 ) T , i=null,,
Q ˜ , ( R 0 T t 1 ) Q ˜ , ( I 0 T t 1 ) Q ˜
M=( Q 1 R 11 Q 1 + R 12 Q 2 + t 1 Q 1 + t 1 Q 2 0 R 21 Q 1 + R 22 Q 2 + t 2 R 31 Q 1 + R 32 Q 2 + t 3 Q 2 + t 2 t 3 1 1 1 )
i=1 10 C i T i k =0, k=1,2,4
( Q 1 , Q 2 ,1) T =Η ( m u , m v ,1) T
R =[ 0.9875 0.0008 0.1574 0.0020 0.9998 0.0178 0.1574 0.0179 0.9874 ], t =[ 0.095 0.005 0.266 ], t =[ 0.019 0.039 0.498 ]

Metrics