Abstract

An acoustic-optics heterodyne fringe interferometry coupled with a three-camera system is developed for dynamic 3D imaging. In this system, first-order beams with a slight frequency difference diffracted from two acousto-optic deflectors (AODs) form a beat intensity fringe pattern. Setting the frequency of the trigger signal for the CCD cameras into four times the beat frequency, four-step phase-shifting fringe patterns can be obtained, and the wrapped phase map (WPM) can be calculated. Under the epipolar constraint among three cameras, the homologous points can be determined unambiguously with the assistant of a WPM; thus the 3D shape can be reconstructed while skipping the phase unwrapping step. Experimental results are presented to validate this approach.

© 2014 Optical Society of America

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References

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  1. X. Su and Q. Zhang, Opt. Lasers Eng. 48, 191 (2010).
    [CrossRef]
  2. S. Zhang, Opt. Lasers Eng. 48, 149 (2010).
    [CrossRef]
  3. Z. Zhang, Opt. Lasers Eng. 50, 1097 (2012).
    [CrossRef]
  4. M. Mermelstein, D. Feldkhun, and L. Shirley, Opt. Eng. 39, 106 (2000).
    [CrossRef]
  5. X. Yin, H. Zhao, J. Zeng, and Y. Qu, Appl. Opt. 46, 3046 (2007).
    [CrossRef]
  6. X. Peng, J. Tian, P. Zhang, L. Wei, W. Qiu, E. Li, and D. Zhang, Opt. Lett. 30, 1965 (2005).
    [CrossRef]
  7. S. Dupont, J. C. Kastelik, and F. Causa, Rev. Sci. Instrum. 78, 105102 (2007).
    [CrossRef]
  8. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).
  9. V. Srinivasan, H. Liu, and M. Halioua, Appl. Opt. 23, 3105 (1984).
    [CrossRef]
  10. C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422–432.
  11. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

2012 (1)

Z. Zhang, Opt. Lasers Eng. 50, 1097 (2012).
[CrossRef]

2010 (2)

X. Su and Q. Zhang, Opt. Lasers Eng. 48, 191 (2010).
[CrossRef]

S. Zhang, Opt. Lasers Eng. 48, 149 (2010).
[CrossRef]

2007 (2)

X. Yin, H. Zhao, J. Zeng, and Y. Qu, Appl. Opt. 46, 3046 (2007).
[CrossRef]

S. Dupont, J. C. Kastelik, and F. Causa, Rev. Sci. Instrum. 78, 105102 (2007).
[CrossRef]

2005 (1)

2000 (1)

M. Mermelstein, D. Feldkhun, and L. Shirley, Opt. Eng. 39, 106 (2000).
[CrossRef]

1984 (1)

Bräuer-Burchardt, C.

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422–432.

Causa, F.

S. Dupont, J. C. Kastelik, and F. Causa, Rev. Sci. Instrum. 78, 105102 (2007).
[CrossRef]

Dupont, S.

S. Dupont, J. C. Kastelik, and F. Causa, Rev. Sci. Instrum. 78, 105102 (2007).
[CrossRef]

Feldkhun, D.

M. Mermelstein, D. Feldkhun, and L. Shirley, Opt. Eng. 39, 106 (2000).
[CrossRef]

Halioua, M.

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

Heinze, M.

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422–432.

Kastelik, J. C.

S. Dupont, J. C. Kastelik, and F. Causa, Rev. Sci. Instrum. 78, 105102 (2007).
[CrossRef]

Kühmstedt, P.

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422–432.

Li, E.

Liu, H.

Mermelstein, M.

M. Mermelstein, D. Feldkhun, and L. Shirley, Opt. Eng. 39, 106 (2000).
[CrossRef]

Munkelt, C.

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422–432.

Notni, G.

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422–432.

Peng, X.

Qiu, W.

Qu, Y.

Shirley, L.

M. Mermelstein, D. Feldkhun, and L. Shirley, Opt. Eng. 39, 106 (2000).
[CrossRef]

Srinivasan, V.

Su, X.

X. Su and Q. Zhang, Opt. Lasers Eng. 48, 191 (2010).
[CrossRef]

Tian, J.

Wei, L.

Yin, X.

Zeng, J.

Zhang, D.

Zhang, P.

Zhang, Q.

X. Su and Q. Zhang, Opt. Lasers Eng. 48, 191 (2010).
[CrossRef]

Zhang, S.

S. Zhang, Opt. Lasers Eng. 48, 149 (2010).
[CrossRef]

Zhang, Z.

Z. Zhang, Opt. Lasers Eng. 50, 1097 (2012).
[CrossRef]

Zhao, H.

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

Appl. Opt. (2)

Opt. Eng. (1)

M. Mermelstein, D. Feldkhun, and L. Shirley, Opt. Eng. 39, 106 (2000).
[CrossRef]

Opt. Lasers Eng. (3)

X. Su and Q. Zhang, Opt. Lasers Eng. 48, 191 (2010).
[CrossRef]

S. Zhang, Opt. Lasers Eng. 48, 149 (2010).
[CrossRef]

Z. Zhang, Opt. Lasers Eng. 50, 1097 (2012).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

S. Dupont, J. C. Kastelik, and F. Causa, Rev. Sci. Instrum. 78, 105102 (2007).
[CrossRef]

Other (3)

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422–432.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

Supplementary Material (1)

» Media 1: MOV (3113 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Configuration of 3D imaging system.

Fig. 2.
Fig. 2.

Time variation of signals for a certain point. (a) Two optical waves (E1 and E2) with slight different frequencies. (b) Beat signal (E1+E2) derived from coherent superposition. (c) Intensity (I) variation. (d) Sequence of exposure times.

Fig. 3.
Fig. 3.

Illustration of homologous searching by using WPM in conjunction with geometric constraints of three cameras. (a) WPM of camera 1 with selected point p. (b) WPM of camera 3 with three corresponding point candidates (m1, m2, m3), epipolar line L31 and epipolar lines resulting from five corresponding point candidates (n1, n2, n3, n4, n5). (c) WPM of camera 2 with epipolar line L21 and five corresponding point candidates (n1, n2, n3, n4, n5).

Fig. 4.
Fig. 4.

Experiment setup.

Fig. 5.
Fig. 5.

Experiment result (see Media 1). (a) Images of four-step phase shifting captured by three cameras. (b) WPM of three cameras derived from (a). (c) Range image reconstructed by using (b).

Equations (11)

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

E1=E0r1cos(k1r12πf1t),E2=E0r2cos(k2r22πf2t+δ0).
E1=Ercos(k1r12πf1t)E2=Ercos(k1r22π(f1+Δf)t+δ0).
I=2Er2(1+cos(k1(r2r1)2πΔft+δ0)).
r1,2=(xd)2+y2+z2z(1+12(xdz)2+12(yz)2)r2r1=12z((x+d)2(xd)2)=2dzx.
I=2Er2(1+cos(kzx2πΔft+δ0)),
I=A+Bcos(ϕ2πΔft).
Ii=A+Bcos(ϕiπ2)i=1,2,3,4.
ϕ=tan1I1I3I4I2.
fi(t)={1i4Δfti4Δf+Δt0elsei=1,2,3,4.
Ii=i4Δfi4Δf+ΔtIdt=AΔt+B(sin(ϕΔϕiπ2)sin(ϕiπ2)),
ϕ=tan1I1I3I4I2=tan1cos(ϕ+Δϕ)+cosϕsin(ϕ+Δϕ)sinϕ=ϕ+Δϕ2.

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