Abstract

In this work, we propose a novel technique to retrieve 3D shape of dynamic objects by the simultaneous projection of a fringe pattern and a homogeneous white light pattern, both coded in an RGB image. The first one is used to retrieve the phase map by an iterative least-squares method. The second one is used to match object pixels in consecutive images, acquired at various object positions. The proposed method successfully accomplishes the requirement of projecting simultaneously two different patterns. One extracts the object's information while the other retrieves the phase map. Experimental results demonstrate the feasibility of the proposed scheme.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

K. Peng, Y. Cao, Y. Wu, C. Chen, and Y. Wan, “A dual-frequency online PMP method with phase-shifting parallel to moving direction of measured object,” Opt. Commun. 383, 491–499 (2017).
[Crossref]

2016 (3)

K. Peng, Y. Cao, Y. Wu, and M. Lu, “A new method using orthogonal two-frequency grating in online 3D measurement,” Opt. Laser Technol. 83, 81–88 (2016).
[Crossref]

X. Xu, Y. Cao, C. Chen, and Y. Wan, “On-line phase measuring profilometry based on phase matching,” Opt. Quantum Electron. 48(8), 411 (2016).
[Crossref]

B. Li, Z. Liu, and S. Zhang, “Motion-induced error reduction by combining Fourier transform profilometry with phase-shifting profilometry,” Opt. Express 24(20), 23289–23303 (2016).
[Crossref] [PubMed]

2015 (3)

Z. Chen, X. Wang, and R. Liang, “Snapshot phase shift fringe projection 3D surface measurement,” Opt. Express 23(2), 667–673 (2015).
[Crossref] [PubMed]

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2015).
[Crossref]

C. Chen, Y. P. Cao, L. J. Zhong, and K. Peng, “An on-line phase measuring profilometry for objects moving with straight-line motion,” Opt. Commun. 336, 301–305 (2015).
[Crossref]

2014 (3)

2013 (4)

2012 (1)

Y. Li, Y. P. Cao, Z. F. Huang, D. L. Chen, and S. P. Shi, “A three dimensional on-line measurement method based on five unequal steps phase shifting,” Opt. Commun. 285(21), 4285–4289 (2012).
[Crossref]

2011 (2)

T. Hoang, Z. Wang, M. Vo, J. Ma, L. Luu, and B. Pan, “Phase extraction from optical interferograms in presence of intensity nonlinearity and arbitrary phase shifts,” Appl. Phys. Lett. 99(3), 031104 (2011).
[Crossref]

J. F. Mosiño, J. C. Gutiérrez-García, T. A. Gutiérrez-García, F. Castillo, M. A. García-González, and V. A. Gutiérrez-García, “Algorithm for phase extraction from a set of interferograms with arbitrary phase shifts,” Opt. Express 19(6), 4908–4923 (2011).
[Crossref] [PubMed]

2010 (5)

2009 (1)

R. E. Guerrero-Moreno and J. Álvarez-Borrego, “Nonlinear composite filter performance,” Opt. Eng. 48(6), 067201 (2009).
[Crossref]

2004 (1)

2001 (1)

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

1994 (1)

1992 (1)

C. T. Farrell and M. A. Player, “Phase step measurement and variable step algorithms in phase-shifting interferometry,” Meas. Sci. Technol. 3(10), 953–958 (1992).
[Crossref]

Álvarez-Borrego, J.

R. E. Guerrero-Moreno and J. Álvarez-Borrego, “Nonlinear composite filter performance,” Opt. Eng. 48(6), 067201 (2009).
[Crossref]

Ayubi, G. A.

Cao, Y.

K. Peng, Y. Cao, Y. Wu, C. Chen, and Y. Wan, “A dual-frequency online PMP method with phase-shifting parallel to moving direction of measured object,” Opt. Commun. 383, 491–499 (2017).
[Crossref]

X. Xu, Y. Cao, C. Chen, and Y. Wan, “On-line phase measuring profilometry based on phase matching,” Opt. Quantum Electron. 48(8), 411 (2016).
[Crossref]

K. Peng, Y. Cao, Y. Wu, and M. Lu, “A new method using orthogonal two-frequency grating in online 3D measurement,” Opt. Laser Technol. 83, 81–88 (2016).
[Crossref]

K. Peng, Y. Cao, Y. Wu, and Y. Xiao, “A new pixel matching method using the modulation of shadow areas in online 3D measurement,” Opt. Lasers Eng. 51(9), 1078–1084 (2013).
[Crossref]

Cao, Y. P.

C. Chen, Y. P. Cao, L. J. Zhong, and K. Peng, “An on-line phase measuring profilometry for objects moving with straight-line motion,” Opt. Commun. 336, 301–305 (2015).
[Crossref]

Y. Li, Y. P. Cao, Z. F. Huang, D. L. Chen, and S. P. Shi, “A three dimensional on-line measurement method based on five unequal steps phase shifting,” Opt. Commun. 285(21), 4285–4289 (2012).
[Crossref]

Castillo, F.

Chen, C.

K. Peng, Y. Cao, Y. Wu, C. Chen, and Y. Wan, “A dual-frequency online PMP method with phase-shifting parallel to moving direction of measured object,” Opt. Commun. 383, 491–499 (2017).
[Crossref]

X. Xu, Y. Cao, C. Chen, and Y. Wan, “On-line phase measuring profilometry based on phase matching,” Opt. Quantum Electron. 48(8), 411 (2016).
[Crossref]

C. Chen, Y. P. Cao, L. J. Zhong, and K. Peng, “An on-line phase measuring profilometry for objects moving with straight-line motion,” Opt. Commun. 336, 301–305 (2015).
[Crossref]

Chen, D. L.

Y. Li, Y. P. Cao, Z. F. Huang, D. L. Chen, and S. P. Shi, “A three dimensional on-line measurement method based on five unequal steps phase shifting,” Opt. Commun. 285(21), 4285–4289 (2012).
[Crossref]

Chen, W.

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

Chen, Z.

Di Martino, J. M.

Estrada, J. C.

Farrell, C. T.

C. T. Farrell and M. A. Player, “Phase step measurement and variable step algorithms in phase-shifting interferometry,” Meas. Sci. Technol. 3(10), 953–958 (1992).
[Crossref]

Ferrari, J. A.

Flores, J. L.

García-González, M. A.

Ghiglia, D. C.

Gorthi, S. S.

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

Guerrero-Moreno, R. E.

R. E. Guerrero-Moreno and J. Álvarez-Borrego, “Nonlinear composite filter performance,” Opt. Eng. 48(6), 067201 (2009).
[Crossref]

Guerrero-Sanchez, F.

Guo, H.

Guo, Q.

Gutiérrez-García, J. C.

Gutiérrez-García, T. A.

Gutiérrez-García, V. A.

Han, B.

Harding, K.

K. Harding, “3D profilometry: next requests from the industrial viewpoint,” Proc. SPIE 7855, 785513 (2010).
[Crossref]

Hoang, T.

T. Hoang, Z. Wang, M. Vo, J. Ma, L. Luu, and B. Pan, “Phase extraction from optical interferograms in presence of intensity nonlinearity and arbitrary phase shifts,” Appl. Phys. Lett. 99(3), 031104 (2011).
[Crossref]

T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett. 35(12), 1992–1994 (2010).
[Crossref] [PubMed]

Huang, Z. F.

Y. Li, Y. P. Cao, Z. F. Huang, D. L. Chen, and S. P. Shi, “A three dimensional on-line measurement method based on five unequal steps phase shifting,” Opt. Commun. 285(21), 4285–4289 (2012).
[Crossref]

Juarez-Salazar, R.

Li, B.

Li, Y.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2015).
[Crossref]

Y. Li, Y. P. Cao, Z. F. Huang, D. L. Chen, and S. P. Shi, “A three dimensional on-line measurement method based on five unequal steps phase shifting,” Opt. Commun. 285(21), 4285–4289 (2012).
[Crossref]

Li, Z.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2015).
[Crossref]

Liang, R.

Liu, Z.

Lu, L.

Lu, M.

K. Peng, Y. Cao, Y. Wu, and M. Lu, “A new method using orthogonal two-frequency grating in online 3D measurement,” Opt. Laser Technol. 83, 81–88 (2016).
[Crossref]

Luu, L.

T. Hoang, Z. Wang, M. Vo, J. Ma, L. Luu, and B. Pan, “Phase extraction from optical interferograms in presence of intensity nonlinearity and arbitrary phase shifts,” Appl. Phys. Lett. 99(3), 031104 (2011).
[Crossref]

Ma, J.

T. Hoang, Z. Wang, M. Vo, J. Ma, L. Luu, and B. Pan, “Phase extraction from optical interferograms in presence of intensity nonlinearity and arbitrary phase shifts,” Appl. Phys. Lett. 99(3), 031104 (2011).
[Crossref]

Mosiño, J. F.

Nguyen, D.

Oliver, J.

Pan, B.

T. Hoang, Z. Wang, M. Vo, J. Ma, L. Luu, and B. Pan, “Phase extraction from optical interferograms in presence of intensity nonlinearity and arbitrary phase shifts,” Appl. Phys. Lett. 99(3), 031104 (2011).
[Crossref]

T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett. 35(12), 1992–1994 (2010).
[Crossref] [PubMed]

Peng, K.

K. Peng, Y. Cao, Y. Wu, C. Chen, and Y. Wan, “A dual-frequency online PMP method with phase-shifting parallel to moving direction of measured object,” Opt. Commun. 383, 491–499 (2017).
[Crossref]

K. Peng, Y. Cao, Y. Wu, and M. Lu, “A new method using orthogonal two-frequency grating in online 3D measurement,” Opt. Laser Technol. 83, 81–88 (2016).
[Crossref]

C. Chen, Y. P. Cao, L. J. Zhong, and K. Peng, “An on-line phase measuring profilometry for objects moving with straight-line motion,” Opt. Commun. 336, 301–305 (2015).
[Crossref]

K. Peng, Y. Cao, Y. Wu, and Y. Xiao, “A new pixel matching method using the modulation of shadow areas in online 3D measurement,” Opt. Lasers Eng. 51(9), 1078–1084 (2013).
[Crossref]

Perciante, C. D.

Player, M. A.

C. T. Farrell and M. A. Player, “Phase step measurement and variable step algorithms in phase-shifting interferometry,” Meas. Sci. Technol. 3(10), 953–958 (1992).
[Crossref]

Quiroga, J. A.

Rangel-Huerta, A.

Rastogi, P.

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

Robledo-Sanchez, C.

Romero, L. A.

Servin, M.

Shi, S. P.

Y. Li, Y. P. Cao, Z. F. Huang, D. L. Chen, and S. P. Shi, “A three dimensional on-line measurement method based on five unequal steps phase shifting,” Opt. Commun. 285(21), 4285–4289 (2012).
[Crossref]

Shi, Y.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2015).
[Crossref]

Su, X.

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

Van Der Weide, D.

Vo, M.

T. Hoang, Z. Wang, M. Vo, J. Ma, L. Luu, and B. Pan, “Phase extraction from optical interferograms in presence of intensity nonlinearity and arbitrary phase shifts,” Appl. Phys. Lett. 99(3), 031104 (2011).
[Crossref]

Wan, Y.

K. Peng, Y. Cao, Y. Wu, C. Chen, and Y. Wan, “A dual-frequency online PMP method with phase-shifting parallel to moving direction of measured object,” Opt. Commun. 383, 491–499 (2017).
[Crossref]

X. Xu, Y. Cao, C. Chen, and Y. Wan, “On-line phase measuring profilometry based on phase matching,” Opt. Quantum Electron. 48(8), 411 (2016).
[Crossref]

Wang, C.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2015).
[Crossref]

Wang, X.

Wang, Z.

Wu, Y.

K. Peng, Y. Cao, Y. Wu, C. Chen, and Y. Wan, “A dual-frequency online PMP method with phase-shifting parallel to moving direction of measured object,” Opt. Commun. 383, 491–499 (2017).
[Crossref]

K. Peng, Y. Cao, Y. Wu, and M. Lu, “A new method using orthogonal two-frequency grating in online 3D measurement,” Opt. Laser Technol. 83, 81–88 (2016).
[Crossref]

K. Peng, Y. Cao, Y. Wu, and Y. Xiao, “A new pixel matching method using the modulation of shadow areas in online 3D measurement,” Opt. Lasers Eng. 51(9), 1078–1084 (2013).
[Crossref]

Xi, J.

Xiao, Y.

K. Peng, Y. Cao, Y. Wu, and Y. Xiao, “A new pixel matching method using the modulation of shadow areas in online 3D measurement,” Opt. Lasers Eng. 51(9), 1078–1084 (2013).
[Crossref]

Xu, X.

X. Xu, Y. Cao, C. Chen, and Y. Wan, “On-line phase measuring profilometry based on phase matching,” Opt. Quantum Electron. 48(8), 411 (2016).
[Crossref]

Yu, Y.

Zhang, S.

Zhang, Z.

Zhong, K.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2015).
[Crossref]

Zhong, L. J.

C. Chen, Y. P. Cao, L. J. Zhong, and K. Peng, “An on-line phase measuring profilometry for objects moving with straight-line motion,” Opt. Commun. 336, 301–305 (2015).
[Crossref]

Zhou, X.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2015).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

T. Hoang, Z. Wang, M. Vo, J. Ma, L. Luu, and B. Pan, “Phase extraction from optical interferograms in presence of intensity nonlinearity and arbitrary phase shifts,” Appl. Phys. Lett. 99(3), 031104 (2011).
[Crossref]

Int. J. Adv. Manuf. Technol. (1)

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2015).
[Crossref]

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

Meas. Sci. Technol. (1)

C. T. Farrell and M. A. Player, “Phase step measurement and variable step algorithms in phase-shifting interferometry,” Meas. Sci. Technol. 3(10), 953–958 (1992).
[Crossref]

Opt. Commun. (3)

K. Peng, Y. Cao, Y. Wu, C. Chen, and Y. Wan, “A dual-frequency online PMP method with phase-shifting parallel to moving direction of measured object,” Opt. Commun. 383, 491–499 (2017).
[Crossref]

C. Chen, Y. P. Cao, L. J. Zhong, and K. Peng, “An on-line phase measuring profilometry for objects moving with straight-line motion,” Opt. Commun. 336, 301–305 (2015).
[Crossref]

Y. Li, Y. P. Cao, Z. F. Huang, D. L. Chen, and S. P. Shi, “A three dimensional on-line measurement method based on five unequal steps phase shifting,” Opt. Commun. 285(21), 4285–4289 (2012).
[Crossref]

Opt. Eng. (1)

R. E. Guerrero-Moreno and J. Álvarez-Borrego, “Nonlinear composite filter performance,” Opt. Eng. 48(6), 067201 (2009).
[Crossref]

Opt. Express (8)

R. Juarez-Salazar, C. Robledo-Sanchez, F. Guerrero-Sanchez, and A. Rangel-Huerta, “Generalized phase-shifting algorithm for inhomogeneous phase shift and spatio-temporal fringe visibility variation,” Opt. Express 22(4), 4738–4750 (2014).
[Crossref] [PubMed]

J. F. Mosiño, J. C. Gutiérrez-García, T. A. Gutiérrez-García, F. Castillo, M. A. García-González, and V. A. Gutiérrez-García, “Algorithm for phase extraction from a set of interferograms with arbitrary phase shifts,” Opt. Express 19(6), 4908–4923 (2011).
[Crossref] [PubMed]

J. C. Estrada, M. Servin, and J. A. Quiroga, “A self-tuning phase-shifting algorithm for interferometry,” Opt. Express 18(3), 2632–2638 (2010).
[Crossref] [PubMed]

B. Li, Z. Liu, and S. Zhang, “Motion-induced error reduction by combining Fourier transform profilometry with phase-shifting profilometry,” Opt. Express 24(20), 23289–23303 (2016).
[Crossref] [PubMed]

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the accuracy of 3-D shape measurement of moving object using phase shifting profilometry,” Opt. Express 21(25), 30610–30622 (2013).
[Crossref] [PubMed]

Z. Chen, X. Wang, and R. Liang, “Snapshot phase shift fringe projection 3D surface measurement,” Opt. Express 23(2), 667–673 (2015).
[Crossref] [PubMed]

S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18(9), 9684–9689 (2010).
[Crossref] [PubMed]

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the accuracy of 3-D shape measurement of moving object using phase shifting profilometry,” Opt. Express 21(25), 30610–30622 (2013).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

K. Peng, Y. Cao, Y. Wu, and M. Lu, “A new method using orthogonal two-frequency grating in online 3D measurement,” Opt. Laser Technol. 83, 81–88 (2016).
[Crossref]

Opt. Lasers Eng. (3)

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

K. Peng, Y. Cao, Y. Wu, and Y. Xiao, “A new pixel matching method using the modulation of shadow areas in online 3D measurement,” Opt. Lasers Eng. 51(9), 1078–1084 (2013).
[Crossref]

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

Opt. Lett. (3)

Opt. Quantum Electron. (1)

X. Xu, Y. Cao, C. Chen, and Y. Wan, “On-line phase measuring profilometry based on phase matching,” Opt. Quantum Electron. 48(8), 411 (2016).
[Crossref]

Proc. SPIE (1)

K. Harding, “3D profilometry: next requests from the industrial viewpoint,” Proc. SPIE 7855, 785513 (2010).
[Crossref]

Supplementary Material (3)

NameDescription
» Visualization 1       sinusoidal fringe pattern modulated by the object under test
» Visualization 2       the photograph of the object.
» Visualization 3       Fringe patterns segmented and extracted from the acquired video.

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Figures (8)

Fig. 1
Fig. 1 Experimental setup, which depicts the projector, the CCD camera and object under test as it moves at a given velocity.
Fig. 2
Fig. 2 Numerical simulation results for the phase recovery. (a) Test phase (peaks-function Matlab TM). (b) Synthetic fringe pattern in gray scale. (c) Phase estimation with 7 samples in [0, 2π]. (d) Phase error obtained with our proposal.
Fig. 3
Fig. 3 The Δ ϕ rms a function of number of samples or phase steps. Simulation results are given for uniformly distributed phase shifts.
Fig. 4
Fig. 4 The Δ ϕ rms from multiple-step AIA implementation in the presence of harmonics and phase-shift error.
Fig. 5
Fig. 5 (a) A frame captured from the RGB video, (b) the region circumscribed by the square in (a) corresponds to the segmented and extracted fringe pattern that has been centered; (c) the red channel contains the deformed fringe pattern; (d) blue channel contains the photograph of the object.
Fig. 6
Fig. 6 A set of segmented and extracted fringe patterns from the consecutive frames of the acquired RGB video. Using the Guo and Zhang algorithm [13], phase-step values are δ = k [0, 1.2283, 2.2822, 3.4881, 4.7125, 5.9278]; and for AIA they are δ = k [0, 1.1699, 2.1453, 3.2671, 4.4269, 5.6816].
Fig. 7
Fig. 7 Phase-map retrieved by: (a) the classical three-step algorithm; (b) 5 arbitrarily spaced phase-steps algorithm described in Eq. (18), Ref [10]; (c) and (d) 5 and 16 sample-AIA.
Fig. 8
Fig. 8 Horizontal cut of height profile: Red, blue, green and black line corresponding to 3D reconstruction shown in Fig. 7(a)–(d) respectively.

Equations (11)

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I k ( x,y )=a( x,y )+b( x,y )cos[ 2πfx+ϕ( x,y )kδ ],( k=1,2,,N ).
α( x,y )= k=1 N I k ( x,y ) cos( 2πk/N )
β( x,y )= k=1 N I k ( x,y ) sin( 2πk/N )
ϕ( x,y )=arctan[ β( x,y )/α( x,y ) ].
I k ( x,y )=a( x,y )+b( x,y )cos[ 2πfx+ϕ( xk δ x ,y ) ],( k=1,2,,N ).
I k ( x+kδ,y )=a( x+kδ,y )+b( x+kδ,y )cos[ 2πfx+2πfkδ+ϕ( x,y ) ].
I k ( x,y )=a( x,y )+b( x,y )cos[ 2πfx+ϕ( x,y )+2πfkδ ].
ε i = k=1 M ( a i + α i cos δ k + β i sin δ k I i k ) 2 .
ε k = i=1 N ( a k +α ' k cos ϕ i +β ' k sin ϕ i I i k ) 2 .
I k ( x,y )=a( x,y )+ j=1 p b j ( x,y )cos{ j[ ϕ( x,y )+2πf+δ ] } .
ϕ( x,y )= tan 1 { X 1 [ cos( δ 1 )+2cos( δ 3 )cos( δ 5 ) ] X 2 [ cos( δ 2 )+cos( δ 4 ) ] X 1 [ sin( δ 1 )+2sin( δ 3 )sin( δ 5 ) ] X 2 [ sin( δ 2 )+sin( δ 4 ) ] }

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