Abstract

We present a fast phase-shifting shadow moiré device for surface topography measurement. In our setup, multiple light sources located at different positions are controlled to illuminate the grating sequentially. Therefore, the phase shift across the field of view shadow moiré is introduced by changing the distance between the light source and the camera. Thanks to the necessity for mechanical movement being omitted here, the proposed setup can capture the phase-shifting fringe patterns at a high speed. However, affected by the bias modulation and amplitude modulation of the captured fringe patterns, the phase of interest cannot be demodulated by the standard phase-shifting algorithm directly. Thus the principal component analysis (PCA) demodulation approach is used to extract the wrapped phase map. In addition, we develop an iterative procedure to reduce the detuning error introduced by the PCA algorithm. The proposed method implements a fast way to determine the topography of a surface through a simple experimental setup. It is applied to obtain an external surface of a specimen. Both the simulation results and the experimental results show the validity of the proposed technique.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012 (2)

H. Du, H. Zhao, B. Li, and S. Cao, “Three frames phase-shifting shadow moiré using arbitrary unknown phase steps,” Meas. Sci. Technol. 23, 105201 (2012).
[CrossRef]

J. Vargas, J. A. Quiroga, C. O. S. Sorzano, J. C. Estrada, and J. M. Carazo, “Two-step demodulation based on Gram-Schmidt orthonormalization method,” Opt. Lett. 37, 443–445 (2012).
[CrossRef]

2011 (4)

2009 (1)

2007 (1)

2006 (2)

J. A. Gómez-Pedrero and J. A. Quiroga, “Measurement of surface topography by RGB shadow-moiré with direct phase demodulation,” Opt. Lasers Eng. 44, 1297–1310 (2006).
[CrossRef]

C. Han and B. Han, “Error analysis of the phase-shifting technique when applied to shadow moiré,” Appl. Opt. 45, 1124–1133 (2006).
[CrossRef]

2005 (1)

2004 (1)

2002 (1)

L. DAcquisto, L. Fratini, and A. M. Siddiolo, “A modified moiré technique for three-dimensional surface topography,” Meas. Sci. Technol. 13, 613–622 (2002).
[CrossRef]

2001 (1)

J. Degrieck, W. Van Paepegem, and P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surfaces,” Opt. Lasers Eng. 36, 29–40 (2001).
[CrossRef]

2000 (2)

H. M. Ladak, W. F. Decraemer, J. J. J. Dirckx, and W. R. J. Funnell, “Systematic errors in small deformations measured by use of shadow-moiré topography,” Appl. Opt. 39, 3266–3275 (2000).
[CrossRef]

L. Jin, Y. Kodera, T. Yoshizawa, and Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

1996 (1)

1994 (1)

1993 (1)

T. Yoshizawa and T. Tomisawa, “Shadow moiré topography by means of the phase-shift method,” Opt. Eng. 32, 1668–1674 (1993).
[CrossRef]

1988 (1)

1970 (1)

Allen, J. B.

Antonio Quiroga, J.

Atkinson, J. T.

Belenguer, T.

Boone, P.

J. Degrieck, W. Van Paepegem, and P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surfaces,” Opt. Lasers Eng. 36, 29–40 (2001).
[CrossRef]

Bremand, F.

Burton, D. R.

Cai, L. Z.

Cao, S.

H. Du, H. Zhao, B. Li, and S. Cao, “Three frames phase-shifting shadow moiré using arbitrary unknown phase steps,” Meas. Sci. Technol. 23, 105201 (2012).
[CrossRef]

H. Du, H. Zhao, B. Li, J. Zhao, and S. Cao, “Phase-shifting shadow moiré based on iterative self-tuning algorithm,” Appl. Opt. 50, 6708–6712 (2011).
[CrossRef]

Carazo, J. M.

Chen, M.

DAcquisto, L.

L. DAcquisto, L. Fratini, and A. M. Siddiolo, “A modified moiré technique for three-dimensional surface topography,” Meas. Sci. Technol. 13, 613–622 (2002).
[CrossRef]

Decraemer, W. F.

Degrieck, J.

J. Degrieck, W. Van Paepegem, and P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surfaces,” Opt. Lasers Eng. 36, 29–40 (2001).
[CrossRef]

Dielis, G.

Dirckx, J. J. J.

Du, H.

H. Du, H. Zhao, B. Li, and S. Cao, “Three frames phase-shifting shadow moiré using arbitrary unknown phase steps,” Meas. Sci. Technol. 23, 105201 (2012).
[CrossRef]

H. Du, H. Zhao, B. Li, J. Zhao, and S. Cao, “Phase-shifting shadow moiré based on iterative self-tuning algorithm,” Appl. Opt. 50, 6708–6712 (2011).
[CrossRef]

Du, H. B.

H. B. Du, H. Zhao, B. Li, Z. W. Li, L. Zheng, and L. Feng, “Algorithm for phase shifting shadow moiré with an unknown relative step,” J. Opt. 13, 1–5 (2011).

Estrada, J. C.

Feng, L.

H. B. Du, H. Zhao, B. Li, Z. W. Li, L. Zheng, and L. Feng, “Algorithm for phase shifting shadow moiré with an unknown relative step,” J. Opt. 13, 1–5 (2011).

Fratini, L.

L. DAcquisto, L. Fratini, and A. M. Siddiolo, “A modified moiré technique for three-dimensional surface topography,” Meas. Sci. Technol. 13, 613–622 (2002).
[CrossRef]

Funnell, W. R. J.

Gómez-Pedrero, J. A.

J. A. Gómez-Pedrero and J. A. Quiroga, “Measurement of surface topography by RGB shadow-moiré with direct phase demodulation,” Opt. Lasers Eng. 44, 1297–1310 (2006).
[CrossRef]

Guo, H.

Guo, J. P.

Han, B.

Han, B. T.

Han, C.

Jin, L.

L. Jin, Y. Kodera, T. Yoshizawa, and Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

Johnson, W. O.

Kodera, Y.

L. Jin, Y. Kodera, T. Yoshizawa, and Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

Ladak, H. M.

Lagarde, A.

Lalor, M. J.

Li, A. M.

Li, B.

H. Du, H. Zhao, B. Li, and S. Cao, “Three frames phase-shifting shadow moiré using arbitrary unknown phase steps,” Meas. Sci. Technol. 23, 105201 (2012).
[CrossRef]

H. Du, H. Zhao, B. Li, J. Zhao, and S. Cao, “Phase-shifting shadow moiré based on iterative self-tuning algorithm,” Appl. Opt. 50, 6708–6712 (2011).
[CrossRef]

H. B. Du, H. Zhao, B. Li, Z. W. Li, L. Zheng, and L. Feng, “Algorithm for phase shifting shadow moiré with an unknown relative step,” J. Opt. 13, 1–5 (2011).

Li, Z. W.

H. B. Du, H. Zhao, B. Li, Z. W. Li, L. Zheng, and L. Feng, “Algorithm for phase shifting shadow moiré with an unknown relative step,” J. Opt. 13, 1–5 (2011).

Marroquín, J. L.

Mauvoisin, G.

Meadows, D. M.

Meng, X. F.

Otani, Y.

L. Jin, Y. Kodera, T. Yoshizawa, and Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

Peng, X.

Quiroga, J. A.

Servin, M.

Siddiolo, A. M.

L. DAcquisto, L. Fratini, and A. M. Siddiolo, “A modified moiré technique for three-dimensional surface topography,” Meas. Sci. Technol. 13, 613–622 (2002).
[CrossRef]

Sorzano, C. O. S.

Tomisawa, T.

T. Yoshizawa and T. Tomisawa, “Shadow moiré topography by means of the phase-shift method,” Opt. Eng. 32, 1668–1674 (1993).
[CrossRef]

Van Paepegem, W.

J. Degrieck, W. Van Paepegem, and P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surfaces,” Opt. Lasers Eng. 36, 29–40 (2001).
[CrossRef]

Vargas, J.

Wang, Y. R.

Wang, Z. Y.

Xie, X.

Yoshizawa, T.

L. Jin, Y. Kodera, T. Yoshizawa, and Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

T. Yoshizawa and T. Tomisawa, “Shadow moiré topography by means of the phase-shift method,” Opt. Eng. 32, 1668–1674 (1993).
[CrossRef]

Zhao, H.

H. Du, H. Zhao, B. Li, and S. Cao, “Three frames phase-shifting shadow moiré using arbitrary unknown phase steps,” Meas. Sci. Technol. 23, 105201 (2012).
[CrossRef]

H. Du, H. Zhao, B. Li, J. Zhao, and S. Cao, “Phase-shifting shadow moiré based on iterative self-tuning algorithm,” Appl. Opt. 50, 6708–6712 (2011).
[CrossRef]

H. B. Du, H. Zhao, B. Li, Z. W. Li, L. Zheng, and L. Feng, “Algorithm for phase shifting shadow moiré with an unknown relative step,” J. Opt. 13, 1–5 (2011).

Zhao, J.

Zheng, L.

H. B. Du, H. Zhao, B. Li, Z. W. Li, L. Zheng, and L. Feng, “Algorithm for phase shifting shadow moiré with an unknown relative step,” J. Opt. 13, 1–5 (2011).

Appl. Opt. (8)

J. Opt. (1)

H. B. Du, H. Zhao, B. Li, Z. W. Li, L. Zheng, and L. Feng, “Algorithm for phase shifting shadow moiré with an unknown relative step,” J. Opt. 13, 1–5 (2011).

Meas. Sci. Technol. (2)

H. Du, H. Zhao, B. Li, and S. Cao, “Three frames phase-shifting shadow moiré using arbitrary unknown phase steps,” Meas. Sci. Technol. 23, 105201 (2012).
[CrossRef]

L. DAcquisto, L. Fratini, and A. M. Siddiolo, “A modified moiré technique for three-dimensional surface topography,” Meas. Sci. Technol. 13, 613–622 (2002).
[CrossRef]

Opt. Eng. (2)

T. Yoshizawa and T. Tomisawa, “Shadow moiré topography by means of the phase-shift method,” Opt. Eng. 32, 1668–1674 (1993).
[CrossRef]

L. Jin, Y. Kodera, T. Yoshizawa, and Y. Otani, “Shadow moiré profilometry using the phase-shifting method,” Opt. Eng. 39, 2119–2123 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (2)

J. Degrieck, W. Van Paepegem, and P. Boone, “Application of digital phase-shift shadow moiré to micro deformation measurements of curved surfaces,” Opt. Lasers Eng. 36, 29–40 (2001).
[CrossRef]

J. A. Gómez-Pedrero and J. A. Quiroga, “Measurement of surface topography by RGB shadow-moiré with direct phase demodulation,” Opt. Lasers Eng. 44, 1297–1310 (2006).
[CrossRef]

Opt. Lett. (5)

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Figures (10)

Fig. 1.
Fig. 1.

Optical arrangement of shadow moiré.

Fig. 2.
Fig. 2.

Simulation results: (a) the simulated surface, (b) the reconstructed surface by PCA, (c) the residual error by PCA, (d) the reconstructed surface by the proposed method, and (e) the residual error by the proposed method.

Fig. 3.
Fig. 3.

STD errors of the proposed method versus the number iteration.

Fig. 4.
Fig. 4.

Computation time of the proposed method versus the number frame.

Fig. 5.
Fig. 5.

STD errors of the proposed method versus the number frame.

Fig. 6.
Fig. 6.

Shadow moiré fringe pattern of the spherical surface.

Fig. 7.
Fig. 7.

Reconstructed surface: (a) the proposed method and (b) [9]’s method.

Fig. 8.
Fig. 8.

Shadow moiré fringe pattern of a piece of wafer.

Fig. 9.
Fig. 9.

Residual errors of the proposed method.

Fig. 10.
Fig. 10.

Reconstructed surface: (a) the proposed method, (b) Vargas’s method, and (c) Guo’s method.

Equations (15)

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I(x,y)=A(x,y)+B(x,y)cos[ϕ(x,y)],
ϕ(x,y)=2π·d·z(x,y)p·(h+z),
Ik(x,y)=Ak(x,y)+Bk(x,y)cos[ϕk(x,y)],k=1,2n.
δ(x,y)=2π·(d+Δd)·z(x,y)p(h+z)2π·d·z(x,y)p(h+z),=2π·Δd·z(x,y)p·(h+z(x,y)).
gσ(x,y)=e[(x2+y2)σ].
I¯k=bcos(ϕ+kδ)=[IkIk*gσh]*gσl,k=1,2n.
I¯=[B1cos(ϕ1+δ1)Bmcos(ϕm+δ1)Bncos(ϕn+δ1)B1cos(ϕ1+δ2)Bmcos(ϕm+δ2)Bncos(ϕn+δ2)B1cos(ϕ1+δn)Bmcos(ϕm+δn)Bncos(ϕn+δn)].
z˜=p·h·ϕ2·π·dp·ϕ.
δ(x,y)=2π·Δd·z˜(x,y)p·(h+z˜(x,y)).
ϕ=tan1[cot(δ)I¯2sin(δ)·I¯1].
max(|zqzq1|)<ε,
(d+n·Δd)/d=r1/r2.
n=d·(r1r2)/Δd·r2.
p=0.05mm,d=100mm,h=160mm,Δd=1mm.
h1h2=0,

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