Abstract

In this study, a novel moiré fringe analysis technique is proposed for measuring the surface profile of an object. After applying a relative displacement between two gratings at a constant velocity, every pixel of CMOS camera can capture a heterodyne moiré signal. The precise phase distribution of the moiré fringes can be extracted using a one-dimensional fast Fourier transform (FFT) analysis on every pixel, simultaneously filtering the harmonic noise of the moiré fringes. Finally, the surface profile of the tested objected can be generated by substituting the phase distribution into the relevant equation. The findings demonstrate the feasibility of this measuring method, and the measurement error was approximately 4.3 μm. The proposed method exhibits the merits of the Talbot effect, projection moiré method, FFT analysis, and heterodyne interferometry.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. J. Y. Lee, Y. H. Wang, L. J. Lai, Y. J. Lin, Y. H. Chang, “Development of an auto-focus system based on the moiré method,” Measurement 44(10), 1793–1800 (2011).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. M. Ramulu, P. Labossiere, T. Greenwell, “Elastic–plastic stress/strain response of friction stir-welded titanium butt joints using moiré interferometry,” Opt. Lasers Eng. 48(3), 385–392 (2010).
    [CrossRef]
  9. K. S. Lee, C. J. Tang, H. C. Chen, C. C. Lee, “Measurement of stress in aluminum film coated on a flexible substrate by the shadow moiré method,” Appl. Opt. 47(13), C315–C318 (2008).
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    [CrossRef]
  11. Y. M. He, C. J. Tay, H. M. Shang, “Deformation and profile measurement using the digital projection grating method,” Opt. Lasers Eng. 30(5), 367–377 (1998).
    [CrossRef]
  12. S. Mirza, C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44(1), 013601 (2005).
    [CrossRef]
  13. C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1-3), 23–33 (2004).
    [CrossRef]
  14. Y. B. Choi, S. W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37(3), 1005–1010 (1998).
    [CrossRef]
  15. J. A. N. Buytaert, J. J. J. Dirckx, “Design considerations in projection phase-shift moiré topography based on theoretical analysis of fringe formation,” J. Opt. Soc. Am. A 24(7), 2003–2013 (2007).
    [CrossRef] [PubMed]
  16. J. A. N. Buytaert, J. J. J. Dirckx, “Moiré profilometry using liquid crystals for projection and demodulation,” Opt. Express 16(1), 179–193 (2008).
    [CrossRef] [PubMed]
  17. J. J. J. Dirckx, J. A. N. Buytaert, S. A. M. Van Der Jeught, “Implementation of phase-shifting moire profilometry on a low-cost commercial data projector,” Opt. Lasers Eng. 48(2), 244–250 (2010).
    [CrossRef]
  18. J. A. N. Buytaert, J. J. J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt. 40(3), 114–131 (2011).
    [CrossRef]
  19. M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129(3-4), 167–172 (1996).
    [CrossRef]
  20. D. C. Su, M. H. Chiu, C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacement,” J. Opt. 27(1), 19–23 (1996).
    [CrossRef]

2011

J. Dhanotia, S. Prakash, “Automated collimation testing by incorporating the Fourier transform method in Talbot interferometry,” Appl. Opt. 50(10), 1446–1452 (2011).
[CrossRef] [PubMed]

J. Y. Lee, Y. H. Wang, L. J. Lai, Y. J. Lin, Y. H. Chang, “Development of an auto-focus system based on the moiré method,” Measurement 44(10), 1793–1800 (2011).
[CrossRef]

J. A. N. Buytaert, J. J. J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt. 40(3), 114–131 (2011).
[CrossRef]

2010

J. J. J. Dirckx, J. A. N. Buytaert, S. A. M. Van Der Jeught, “Implementation of phase-shifting moire profilometry on a low-cost commercial data projector,” Opt. Lasers Eng. 48(2), 244–250 (2010).
[CrossRef]

A. A. Mudassar, S. Butt, “Self-imaging-based laser collimation testing technique,” Appl. Opt. 49(31), 6057–6062 (2010).
[CrossRef]

M. Ramulu, P. Labossiere, T. Greenwell, “Elastic–plastic stress/strain response of friction stir-welded titanium butt joints using moiré interferometry,” Opt. Lasers Eng. 48(3), 385–392 (2010).
[CrossRef]

2008

2007

2005

S. Mirza, C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44(1), 013601 (2005).
[CrossRef]

2004

C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1-3), 23–33 (2004).
[CrossRef]

1998

Y. B. Choi, S. W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37(3), 1005–1010 (1998).
[CrossRef]

Y. M. He, C. J. Tay, H. M. Shang, “Deformation and profile measurement using the digital projection grating method,” Opt. Lasers Eng. 30(5), 367–377 (1998).
[CrossRef]

1997

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136(5-6), 370–374 (1997).
[CrossRef]

1996

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129(3-4), 167–172 (1996).
[CrossRef]

D. C. Su, M. H. Chiu, C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacement,” J. Opt. 27(1), 19–23 (1996).
[CrossRef]

1988

1985

1982

Butt, S.

Buytaert, J. A. N.

J. A. N. Buytaert, J. J. J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt. 40(3), 114–131 (2011).
[CrossRef]

J. J. J. Dirckx, J. A. N. Buytaert, S. A. M. Van Der Jeught, “Implementation of phase-shifting moire profilometry on a low-cost commercial data projector,” Opt. Lasers Eng. 48(2), 244–250 (2010).
[CrossRef]

J. A. N. Buytaert, J. J. J. Dirckx, “Moiré profilometry using liquid crystals for projection and demodulation,” Opt. Express 16(1), 179–193 (2008).
[CrossRef] [PubMed]

J. A. N. Buytaert, J. J. J. Dirckx, “Design considerations in projection phase-shift moiré topography based on theoretical analysis of fringe formation,” J. Opt. Soc. Am. A 24(7), 2003–2013 (2007).
[CrossRef] [PubMed]

Chang, Y. H.

J. Y. Lee, Y. H. Wang, L. J. Lai, Y. J. Lin, Y. H. Chang, “Development of an auto-focus system based on the moiré method,” Measurement 44(10), 1793–1800 (2011).
[CrossRef]

Chen, C. D.

D. C. Su, M. H. Chiu, C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacement,” J. Opt. 27(1), 19–23 (1996).
[CrossRef]

Chen, H. C.

Chiu, M. H.

D. C. Su, M. H. Chiu, C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacement,” J. Opt. 27(1), 19–23 (1996).
[CrossRef]

Choi, Y. B.

Y. B. Choi, S. W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37(3), 1005–1010 (1998).
[CrossRef]

de Angelis, M.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136(5-6), 370–374 (1997).
[CrossRef]

De Nicola, S.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136(5-6), 370–374 (1997).
[CrossRef]

Decraemer, W. F.

Dhanotia, J.

Dielis, G.

Dirckx, J. J. J.

Ferraro, P.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136(5-6), 370–374 (1997).
[CrossRef]

Finizio, A.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136(5-6), 370–374 (1997).
[CrossRef]

Fu, Y.

C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1-3), 23–33 (2004).
[CrossRef]

Goncharenko, A. M.

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129(3-4), 167–172 (1996).
[CrossRef]

Greenwell, T.

M. Ramulu, P. Labossiere, T. Greenwell, “Elastic–plastic stress/strain response of friction stir-welded titanium butt joints using moiré interferometry,” Opt. Lasers Eng. 48(3), 385–392 (2010).
[CrossRef]

He, Y. M.

Y. M. He, C. J. Tay, H. M. Shang, “Deformation and profile measurement using the digital projection grating method,” Opt. Lasers Eng. 30(5), 367–377 (1998).
[CrossRef]

Ina, H.

Jahns, J.

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129(3-4), 167–172 (1996).
[CrossRef]

Khilo, N. A.

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129(3-4), 167–172 (1996).
[CrossRef]

Kim, S. W.

Y. B. Choi, S. W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37(3), 1005–1010 (1998).
[CrossRef]

Kobayashi, S.

Labossiere, P.

M. Ramulu, P. Labossiere, T. Greenwell, “Elastic–plastic stress/strain response of friction stir-welded titanium butt joints using moiré interferometry,” Opt. Lasers Eng. 48(3), 385–392 (2010).
[CrossRef]

Lai, L. J.

J. Y. Lee, Y. H. Wang, L. J. Lai, Y. J. Lin, Y. H. Chang, “Development of an auto-focus system based on the moiré method,” Measurement 44(10), 1793–1800 (2011).
[CrossRef]

Lee, C. C.

Lee, J. Y.

J. Y. Lee, Y. H. Wang, L. J. Lai, Y. J. Lin, Y. H. Chang, “Development of an auto-focus system based on the moiré method,” Measurement 44(10), 1793–1800 (2011).
[CrossRef]

Lee, K. S.

Lin, Y. J.

J. Y. Lee, Y. H. Wang, L. J. Lai, Y. J. Lin, Y. H. Chang, “Development of an auto-focus system based on the moiré method,” Measurement 44(10), 1793–1800 (2011).
[CrossRef]

Mirza, S.

S. Mirza, C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44(1), 013601 (2005).
[CrossRef]

Mudassar, A. A.

Murata, K.

Nakano, Y.

Pierattini, G.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136(5-6), 370–374 (1997).
[CrossRef]

Prakash, S.

Quan, C.

C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1-3), 23–33 (2004).
[CrossRef]

Ramulu, M.

M. Ramulu, P. Labossiere, T. Greenwell, “Elastic–plastic stress/strain response of friction stir-welded titanium butt joints using moiré interferometry,” Opt. Lasers Eng. 48(3), 385–392 (2010).
[CrossRef]

Shakher, C.

S. Mirza, C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44(1), 013601 (2005).
[CrossRef]

Shang, H. M.

Y. M. He, C. J. Tay, H. M. Shang, “Deformation and profile measurement using the digital projection grating method,” Opt. Lasers Eng. 30(5), 367–377 (1998).
[CrossRef]

Su, D. C.

D. C. Su, M. H. Chiu, C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacement,” J. Opt. 27(1), 19–23 (1996).
[CrossRef]

Takasaki, H.

H. Takasaki, “Moiré topography from its birth to practical application,” Opt. Lasers Eng. 3(1), 3–14 (1982).
[CrossRef]

Takeda, M.

Tang, C. J.

Tay, C. J.

C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1-3), 23–33 (2004).
[CrossRef]

Y. M. He, C. J. Tay, H. M. Shang, “Deformation and profile measurement using the digital projection grating method,” Opt. Lasers Eng. 30(5), 367–377 (1998).
[CrossRef]

Testorf, M.

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129(3-4), 167–172 (1996).
[CrossRef]

Van Der Jeught, S. A. M.

J. J. J. Dirckx, J. A. N. Buytaert, S. A. M. Van Der Jeught, “Implementation of phase-shifting moire profilometry on a low-cost commercial data projector,” Opt. Lasers Eng. 48(2), 244–250 (2010).
[CrossRef]

Wang, Y. H.

J. Y. Lee, Y. H. Wang, L. J. Lai, Y. J. Lin, Y. H. Chang, “Development of an auto-focus system based on the moiré method,” Measurement 44(10), 1793–1800 (2011).
[CrossRef]

Appl. Opt.

J. Opt.

J. A. N. Buytaert, J. J. J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt. 40(3), 114–131 (2011).
[CrossRef]

D. C. Su, M. H. Chiu, C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacement,” J. Opt. 27(1), 19–23 (1996).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Measurement

J. Y. Lee, Y. H. Wang, L. J. Lai, Y. J. Lin, Y. H. Chang, “Development of an auto-focus system based on the moiré method,” Measurement 44(10), 1793–1800 (2011).
[CrossRef]

Opt. Commun.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform,” Opt. Commun. 136(5-6), 370–374 (1997).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129(3-4), 167–172 (1996).
[CrossRef]

C. Quan, Y. Fu, C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1-3), 23–33 (2004).
[CrossRef]

Opt. Eng.

Y. B. Choi, S. W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37(3), 1005–1010 (1998).
[CrossRef]

S. Mirza, C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44(1), 013601 (2005).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

J. J. J. Dirckx, J. A. N. Buytaert, S. A. M. Van Der Jeught, “Implementation of phase-shifting moire profilometry on a low-cost commercial data projector,” Opt. Lasers Eng. 48(2), 244–250 (2010).
[CrossRef]

H. Takasaki, “Moiré topography from its birth to practical application,” Opt. Lasers Eng. 3(1), 3–14 (1982).
[CrossRef]

M. Ramulu, P. Labossiere, T. Greenwell, “Elastic–plastic stress/strain response of friction stir-welded titanium butt joints using moiré interferometry,” Opt. Lasers Eng. 48(3), 385–392 (2010).
[CrossRef]

Y. M. He, C. J. Tay, H. M. Shang, “Deformation and profile measurement using the digital projection grating method,” Opt. Lasers Eng. 30(5), 367–377 (1998).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Optical configuration. MO: microscopic objective; PH: pinhole; L1: collimating lens; L2: imaging lens; L3: camera lens; G1 and G2: linear gratings; M1 and M2: translation motorized stage; C: CMOS camera; Z1: first Talbot distance; F: focal length of imaging lens; α: projection angle; S: sample.

Fig. 2
Fig. 2

Sample image and experimental results. (a) coin image; (b) moiré fringes on coin surface; (c) phase map of moiré fringes on coin surface.; (d) reconstructed coin surface profile.

Fig. 3
Fig. 3

Contour lines depicted from experimental and reference data.

Equations (18)

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

Z 1 = p 2 λ cos 3 α,
q 1 ( x,y )= 1 2 { 1+γcos[ 2π p ( xz( x,y )tan(α) ) ϕ 1 ] },
q 2 ( x,y )= q 1 ( x,y )×W(x,y) = 1 2 { 1+γcos[ 2π p ( x+z( x,y )tanα )+ ϕ 1 ] }× 1 2 [ 1+cos( 2π p x+ ϕ 2 ) ],
q 2 ( x,y )= 1 4 { 1+γcos[ 2π p ( x+z( x,y )tanα )+ ϕ 1 ]+cos( 2π p x+ ϕ 2 ) + γ 2 cos[ 2π p ( 2x+z( x,y )tanα )+ ϕ 1 + ϕ 2 ]+ γ 2 cos[ ϕ(x,y)+ ϕ 1 ϕ 2 ] },
ϕ(x,y)= 2πtanα p z(x,y),
q 3 ( t,x,y )= q 1 ( t,x,y )×W(t,x,y) = 1 2 { 1+γcos[ 2π f 0 t+ 2πx p +ϕ+ ϕ 1 ] }× 1 2 [ 1+cos( 2π( f 0 )t+ 2πx p + ϕ 2 ) ],
q 3 ( t,x,y )= 1 4 { 1+γcos( 2π f 0 t+ 2πx p +ϕ+ ϕ 1 )+cos[ 2π( f 0 )t+ 2πx p + ϕ 2 ] + γ 2 cos( 4πx p +ϕ+ ϕ 1 + ϕ 2 )+ γ 2 cos( 2π f h t+ϕ+ ϕ 1 ϕ 2 ) },
q 3 ( t,x,y )= 1 8 { [ a(t,x,y)+ a * (t,x,y) ] +[ b(t,x,y)exp( i2π f 0 t )+ b * (t,x,y)exp( i2π f 0 t ) ] +[ c(t,x,y)exp[ i2π( f 0 )t ]+ c * (t,x,y)exp[ i2π( f 0 )t ] ] + 1 2 [ d(t,x,y)exp( i2π f h t )+ d * (t,x,y)exp( i2π f h t ) ] },
a( t,x,y )=1+ γ 2 exp[ i( 4πx p )+ϕ+ ϕ 1 + ϕ 2 ],
b( t,x,y )=γexp[ i( 2πx p +ϕ+ ϕ 1 ) ],
c( t,x,y )= γ 2 exp[ i( 2πx p + ϕ 2 ) ], and
d( t,x,y )= γ 2 exp[ i( ϕ+ ϕ 1 ϕ 2 ) ].
Q( f,x,y )= 1 8 { A( f,x,y )+ A * ( f,x,y )+B( f f 0 ,x,y )+ B * ( f+ f 0 ,x,y ) + 1 2 [ C( f+ f 0 ,x,y )+ C * ( f f 0 ,x,y ) ]+ 1 2 [ D( f f h ,x,y )+ D * ( f+ f h ,x,y ) ] },
ln[ d(x,y) ]=ln( γ 2 )+i( ϕ+ ϕ 1 ϕ 2 ).
z(x,y)= p 2πtanα ϕ(x,y).
Δz=| z p Δp |+| z α Δα |+| z ϕ Δϕ |,
q c ( k t s )= 1 t e k t s k t s + t e q 3 dt = 1 4 { 1+γsinc( f 0 t e )cos( 2π f 0 k t s + 2πx p +ϕ+ ϕ 1 +π f 0 t e ) +sinc( f 0 t e )cos[ 2π( f 0 )k t s + 2πx p + ϕ 2 +π f 0 t e ]+ γ 2 cos( 4πx p +ϕ+ ϕ 1 + ϕ 2 ) + γ 2 sinc( f h t e )cos[ 2π( f h )k t s +ϕ+ ϕ 1 ϕ 2 +π f h t e ] },
q d ( k t s )=round( q c × 2 n ),

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