Abstract

Circular fringe projection profilometry (CFPP) is a recently proposed optical three-dimensional (3D) measurement technique. Theoretically, its optimal measurement accuracy should precede that of the conventional fringe projection profilometry. In practice, the measurement accuracy is impacted by many factors, and much research remains to be done in order to make CFPP reach its optimal precision. One of the dominant factors is the zero-phase point. For the usage of the cotangent function, error near the zero-phase point will be significantly amplified. This makes the overall measurement accuracy very low for CFPP with coaxial layout. To address this critical issue, CFPP with off-axis layout (called OCFPP for simplicity) is presented in this paper. The core theory of OCFPP is briefly introduced. The zero-phase point detection problem coming with OCFPP is explained. Then, two methods, one based on a two-dimensional ruler and the other based on plane constraint, are proposed to solve this additional problem. Simulation and experiments validate the effectiveness of the proposed zero-phase point detection methods, and convince the advantage of OCFPP. This paper contributes to distinctly improving the 3D measurement capability of CFPP, and lays an indispensible foundation for its practical application.

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

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References

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2017 (5)

J. Pösch, J. Schlobohm, S. Matthias, and E. Reithmeier, “Rigid and flexible endoscopes for three dimensional measurement of inside machine parts using fringe projection,” Opt. Lasers Eng. 89, 178–183 (2017).
[Crossref]

B. Li and S. Zhang, “Superfast high-resolution absolute 3D recovery of a stabilized flapping flight process,” Opt. Express 25(22), 27270–27282 (2017).
[Crossref] [PubMed]

A. Chatterjee, V. Bhatia, and S. Prakash, “Anti-spoof touchless 3D fingerprint recognition system using single shot fringe projection and biospeckle analysis,” Opt. Lasers Eng. 95, 1–7 (2017).
[Crossref]

Y. Yolanda, D. López, Martínez García, Amalia, and J. Gómez, “Apple quality study using fringe projection and colorimetry techniques,” Optik (Stuttg.) 147, 401–413 (2017).
[Crossref]

M. Wang, Y. Yin, D. Deng, X. Meng, X. Liu, and X. Peng, “Improved performance of multi-view fringe projection 3D microscopy,” Opt. Express 25(16), 19408–19421 (2017).
[Crossref] [PubMed]

2016 (3)

2015 (2)

C. Zhang, H. Zhao, F. Gu, and Y. Ma, “Phase unwrapping algorithm based on multi-frequency fringe projection and fringe background for fringe projection profilometry,” Meas. Sci. Technol. 26(4), 045203 (2015).
[Crossref]

C. Zhang, H. Zhao, and L. Zhang, “Fringe order error in multifrequency fringe projection phase unwrapping: reason and correction,” Appl. Opt. 54(32), 9390–9399 (2015).
[Crossref] [PubMed]

2014 (2)

K. Falaggis, D. P. Towers, and C. E. Towers, “Algebraic solution for phase unwrapping problems in multiwavelength interferometry,” Appl. Opt. 53(17), 3737–3747 (2014).
[Crossref] [PubMed]

H. Zhao, X. Liang, X. Diao, and H. Jiang, “Rapid in-situ 3D measurement of shiny object based on fast and high dynamic range digital fringe projector,” Opt. Lasers Eng. 54, 170–174 (2014).
[Crossref]

2013 (3)

2012 (2)

Y. Wang and S. Zhang, “Novel phase-coding method for absolute phase retrieval,” Opt. Lett. 37(11), 2067–2069 (2012).
[Crossref] [PubMed]

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

2011 (3)

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref] [PubMed]

K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
[Crossref]

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

2010 (1)

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

2008 (1)

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32(3), 215–221 (2008).
[Crossref]

2007 (1)

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
[Crossref]

2006 (1)

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

2005 (1)

1999 (1)

1984 (1)

1983 (1)

Amalia,

Y. Yolanda, D. López, Martínez García, Amalia, and J. Gómez, “Apple quality study using fringe projection and colorimetry techniques,” Optik (Stuttg.) 147, 401–413 (2017).
[Crossref]

An, Y.

Asundi, A.

Bhatia, V.

A. Chatterjee, V. Bhatia, and S. Prakash, “Anti-spoof touchless 3D fingerprint recognition system using single shot fringe projection and biospeckle analysis,” Opt. Lasers Eng. 95, 1–7 (2017).
[Crossref]

Carocci, M.

Chatterjee, A.

A. Chatterjee, V. Bhatia, and S. Prakash, “Anti-spoof touchless 3D fingerprint recognition system using single shot fringe projection and biospeckle analysis,” Opt. Lasers Eng. 95, 1–7 (2017).
[Crossref]

Chen, F.

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

Chen, X.

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32(3), 215–221 (2008).
[Crossref]

Da, F.

Deng, D.

Diao, X.

H. Zhao, X. Liang, X. Diao, and H. Jiang, “Rapid in-situ 3D measurement of shiny object based on fast and high dynamic range digital fringe projector,” Opt. Lasers Eng. 54, 170–174 (2014).
[Crossref]

Falaggis, K.

Fang, M.

García, Martínez

Y. Yolanda, D. López, Martínez García, Amalia, and J. Gómez, “Apple quality study using fringe projection and colorimetry techniques,” Optik (Stuttg.) 147, 401–413 (2017).
[Crossref]

Geng, J.

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

Gómez, J.

Y. Yolanda, D. López, Martínez García, Amalia, and J. Gómez, “Apple quality study using fringe projection and colorimetry techniques,” Optik (Stuttg.) 147, 401–413 (2017).
[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]

Gu, F.

C. Zhang, H. Zhao, F. Gu, and Y. Ma, “Phase unwrapping algorithm based on multi-frequency fringe projection and fringe background for fringe projection profilometry,” Meas. Sci. Technol. 26(4), 045203 (2015).
[Crossref]

Halioua, M.

Haskamp, K.

K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
[Crossref]

Huang, H.

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]

Hyun, J. S.

Jiang, H.

H. Zhao, X. Liang, X. Diao, and H. Jiang, “Rapid in-situ 3D measurement of shiny object based on fast and high dynamic range digital fringe projector,” Opt. Lasers Eng. 54, 170–174 (2014).
[Crossref]

Jiang, K.

Jiang, T.

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32(3), 215–221 (2008).
[Crossref]

Jin, Y.

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32(3), 215–221 (2008).
[Crossref]

Kästner, M.

K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
[Crossref]

Kemao, Q.

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref] [PubMed]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
[Crossref]

Kong, W.

Li, B.

Li, Y. F.

Li, Z.

Liang, X.

H. Zhao, X. Liang, X. Diao, and H. Jiang, “Rapid in-situ 3D measurement of shiny object based on fast and high dynamic range digital fringe projector,” Opt. Lasers Eng. 54, 170–174 (2014).
[Crossref]

Liu, H. C.

Liu, X.

López, D.

Y. Yolanda, D. López, Martínez García, Amalia, and J. Gómez, “Apple quality study using fringe projection and colorimetry techniques,” Optik (Stuttg.) 147, 401–413 (2017).
[Crossref]

Ma, Y.

C. Zhang, H. Zhao, F. Gu, and Y. Ma, “Phase unwrapping algorithm based on multi-frequency fringe projection and fringe background for fringe projection profilometry,” Meas. Sci. Technol. 26(4), 045203 (2015).
[Crossref]

Matthias, S.

J. Pösch, J. Schlobohm, S. Matthias, and E. Reithmeier, “Rigid and flexible endoscopes for three dimensional measurement of inside machine parts using fringe projection,” Opt. Lasers Eng. 89, 178–183 (2017).
[Crossref]

Meng, X.

Mutoh, K.

Patorski, K.

Peng, X.

Pokorski, K.

Pösch, J.

J. Pösch, J. Schlobohm, S. Matthias, and E. Reithmeier, “Rigid and flexible endoscopes for three dimensional measurement of inside machine parts using fringe projection,” Opt. Lasers Eng. 89, 178–183 (2017).
[Crossref]

Prakash, S.

A. Chatterjee, V. Bhatia, and S. Prakash, “Anti-spoof touchless 3D fingerprint recognition system using single shot fringe projection and biospeckle analysis,” Opt. Lasers Eng. 95, 1–7 (2017).
[Crossref]

Rao, L.

Rastogi, P.

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

Reithmeier, E.

J. Pösch, J. Schlobohm, S. Matthias, and E. Reithmeier, “Rigid and flexible endoscopes for three dimensional measurement of inside machine parts using fringe projection,” Opt. Lasers Eng. 89, 178–183 (2017).
[Crossref]

K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
[Crossref]

Rodella, R.

Sansoni, G.

Schlobohm, J.

J. Pösch, J. Schlobohm, S. Matthias, and E. Reithmeier, “Rigid and flexible endoscopes for three dimensional measurement of inside machine parts using fringe projection,” Opt. Lasers Eng. 89, 178–183 (2017).
[Crossref]

Shi, Y.

Srinivasan, V.

Su, X.

Takeda, M.

Towers, C. E.

Towers, D. P.

Trusiak, M.

Wang, M.

Wang, Y.

Weng, J.

Xi, J.

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32(3), 215–221 (2008).
[Crossref]

Yin, Y.

Yolanda, Y.

Y. Yolanda, D. López, Martínez García, Amalia, and J. Gómez, “Apple quality study using fringe projection and colorimetry techniques,” Optik (Stuttg.) 147, 401–413 (2017).
[Crossref]

Zhang, C.

Zhang, L.

Zhang, Q.

Zhang, S.

Zhao, H.

H. Zhao, C. Zhang, C. Zhou, K. Jiang, and M. Fang, “Circular fringe projection profilometry,” Opt. Lett. 41(21), 4951–4954 (2016).
[Crossref] [PubMed]

C. Zhang, H. Zhao, F. Gu, and Y. Ma, “Phase unwrapping algorithm based on multi-frequency fringe projection and fringe background for fringe projection profilometry,” Meas. Sci. Technol. 26(4), 045203 (2015).
[Crossref]

C. Zhang, H. Zhao, and L. Zhang, “Fringe order error in multifrequency fringe projection phase unwrapping: reason and correction,” Appl. Opt. 54(32), 9390–9399 (2015).
[Crossref] [PubMed]

H. Zhao, X. Liang, X. Diao, and H. Jiang, “Rapid in-situ 3D measurement of shiny object based on fast and high dynamic range digital fringe projector,” Opt. Lasers Eng. 54, 170–174 (2014).
[Crossref]

Zhao, M.

Zhong, J.

Zhong, K.

Zhou, C.

Zhou, X.

Adv. Opt. Photonics (1)

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

Appl. Opt. (7)

Meas. Sci. Technol. (1)

C. Zhang, H. Zhao, F. Gu, and Y. Ma, “Phase unwrapping algorithm based on multi-frequency fringe projection and fringe background for fringe projection profilometry,” Meas. Sci. Technol. 26(4), 045203 (2015).
[Crossref]

Opt. Eng. (1)

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

Opt. Express (5)

Opt. Lasers Eng. (5)

A. Chatterjee, V. Bhatia, and S. Prakash, “Anti-spoof touchless 3D fingerprint recognition system using single shot fringe projection and biospeckle analysis,” Opt. Lasers Eng. 95, 1–7 (2017).
[Crossref]

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

H. Zhao, X. Liang, X. Diao, and H. Jiang, “Rapid in-situ 3D measurement of shiny object based on fast and high dynamic range digital fringe projector,” Opt. Lasers Eng. 54, 170–174 (2014).
[Crossref]

J. Pösch, J. Schlobohm, S. Matthias, and E. Reithmeier, “Rigid and flexible endoscopes for three dimensional measurement of inside machine parts using fringe projection,” Opt. Lasers Eng. 89, 178–183 (2017).
[Crossref]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
[Crossref]

Opt. Lett. (4)

Optik (Stuttg.) (2)

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

Y. Yolanda, D. López, Martínez García, Amalia, and J. Gómez, “Apple quality study using fringe projection and colorimetry techniques,” Optik (Stuttg.) 147, 401–413 (2017).
[Crossref]

Precis. Eng. (1)

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32(3), 215–221 (2008).
[Crossref]

Proc. SPIE (1)

K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 Geometric model of OCFPP.
Fig. 2
Fig. 2 Hardware layout of OCFPP.
Fig. 3
Fig. 3 Error rate of the calculated z corresponding to variant values of θ: (a) the simulated error in MN is 0.02 mm, and in θ is 0 radian; (b) the simulated error in MN is 0 mm, and in θ is 0.01 radians.
Fig. 4
Fig. 4 3D model of the hardware system of OCFPP.
Fig. 5
Fig. 5 Image of a 2D ruler with a reticle projected onto it. The interval between two adjacent lines is 5 mm; the white reticle is projected by a projector, and its center C 0 is projected from the principal point of a projector (i.e., the zero-phase point of the projected circular fringe pattern); the red rectangle marks the field of view of a camera; C can be any point within the red rectangle.
Fig. 6
Fig. 6 3D measurement results of a plane in a simulation when (a) the value of k = 0.001731, ( x c0 , y c0 )=(4960,11), and (b) the value of k = 1, ( x c0 , y c0 )=(4960,1), and values of all the other parameters are ideal. During the simulation, the profile of the measured plane is z=600 mm, the true value of k is 0.001731, and the true value of ( x c0 , y c0 ) is (4960,1).
Fig. 7
Fig. 7 Illustration to the search process of PCM. The rectangle signifies the region to be searched for ( x c0 , y c0 ), the red dots denote the points to be searched, and the blue reticle represents the actual location of ( x c0 , y c0 ).
Fig. 8
Fig. 8 3D profiles of a plane with z = 600 mm recovered with (a) CFPP and (b) OCFPP respectively when Gaussian noise with mean of 0 and variance of 0.003 radians are added to the simulated phase.
Fig. 9
Fig. 9 Images of a ball (left) and a fringe pattern captured from it (right).
Fig. 10
Fig. 10 3D profiles of the measured ball reconstructed with (a) 2DRM and (b) PCM respectively.
Fig. 11
Fig. 11 Images of a medal (left) and a chinar leaf (right) to be measured.
Fig. 12
Fig. 12 3D measurement results of (a) the medal and (b) the chinar leaf.

Tables (2)

Tables Icon

Table 1 Pixel coordinates of the zero-phase point calculated with 2DRM and PCM respectively

Tables Icon

Table 2 Results of sphere fitting applied to 3D data obtained with 2DRM and PCM respectively

Equations (9)

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

z=MNcotθ.
z= μ c ( x c x c0 ) 2 + ( y c y c0 ) 2 kβΦ( x c , y c ) ,
k= μ c ( x c x c0 ) 2 + ( y c y c0 ) 2 βΔz [ 1 Φ Δz ( x c , y c ) 1 Φ 0 ( x c , y c ) ],
{ x= μ c x c / β+ ξ x y= μ c y c / β+ ξ y .
{ x c0 = x c +β( X c0 X c )/ μ c y c0 = y c +β( Y c0 Y c )/ μ c .
z virtual q ( x c , y c )= μ c ( x c x c0 q ) 2 + ( y c y c0 q ) 2 βΦ( x c , y c ) .
z fit q ( x c , y c )= a q x c + b q y c + c q .
RMSE(q)= x c =1 column y c =1 row ( z virtual q ( x c , y c ) z fit q ( x c , y c )) 2 rowcolumn ,
( x c0 , y c0 )=( x c0 q ¯ , y c0 q ¯ ),

Metrics