Abstract

Projection moiré is a high resolution, non-contact, full field method for measuring out-of-plane displacements. Here, we develop a novel model for projection moiré system and derive a universal formula expressing the relation between phase variation and out-of-plane displacement. In order to eliminate the error caused by mismatching of pixels and changing of sensitivity coefficient, an iterative algorithm is presented which expands measurements to the magnitude of depth of field. Computer simulations and actual experiments prove the validity of the proposed method.

© 2016 Optical Society of America

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References

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  1. D. M. Meadows, W. O. Johnson, and J. B. Allen, “Generation of surface contours by moiré patterns,” Appl. Opt. 9(4), 942–947 (1970).
    [Crossref] [PubMed]
  2. H. Takasaki, “Moiré topography,” Appl. Opt. 9(6), 1467–1472 (1970).
    [Crossref] [PubMed]
  3. G. A. Fleming, S. M. Bartram, M. R. Waszak, and L. N. Jenkins, “Projection moiré interferometry measurements of micro air vehicle wings,” Proc. SPIE 4448, 90–101 (2001).
    [Crossref]
  4. J. J. J. Dirckx and W. F. Decraemer, “Optoelectronic moire projector for real-time shape and deformation studies of the tympanic membrane,” J. Biomed. Opt. 2(2), 176–185 (1997).
    [Crossref] [PubMed]
  5. T. Laulund, J. O. Søjbjerg, and E. Hørlyck, “Moiré topography in school screening for structural scoliosis,” Acta Orthop. Scand. 53(5), 765–768 (1982).
    [Crossref] [PubMed]
  6. M. Ramulu, P. Labossiere, and 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]
  7. K. S. Lee, C. J. Tang, H. C. Chen, and 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).
    [Crossref] [PubMed]
  8. J. A. N. Buytaert and 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]
  9. J. A. N. Buytaert and J. J. J. Dirckx, “Moiré profilometry using liquid crystals for projection and demodulation,” Opt. Express 16(1), 179–193 (2008).
    [Crossref] [PubMed]
  10. Y.-B. Choi and S.-W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37(3), 1005–1010 (1998).
    [Crossref]
  11. M.-S. Jeong and S.-W. Kim, “Phase-shifting projection moiré for out-of-plane displacement measurement,” Proc. SPIE 4317, 170–179 (2001).
    [Crossref]
  12. A. Boccaccio, F. Martino, and C. Pappalettere, “A novel moiré-based optical scanning head for high-precision contouring,” Int. J. Adv. Manuf. Technol. 80(1-4), 47–63 (2015).
    [Crossref]
  13. E. Cosola, K. Genovese, L. Lamberti, and C. Pappalettere, “A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing,” Int. J. Solids Struct. 45(24), 6074–6099 (2008).
    [Crossref]
  14. C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring using projection moiré,” Opt. Eng. 44(9), 093605 (2005).
    [Crossref]
  15. C. A. Sciammarella, L. Lamberti, and A. Boccaccio, “A general model for moiré contouring. Part I: Theory,” Opt. Eng. 47(3), 033605 (2008).
    [Crossref]
  16. C. A. Sciammarella, L. Lamberti, A. Boccaccio, E. Cosola, and D. Posa, “A general model for moiré contouring. Part II: Applications,” Opt. Eng. 47(3), 033606 (2008).
    [Crossref]
  17. J. Yao, Y. Tang, and J. Chen, “Three-dimensional shape measurement with an arbitrarily arranged projection moiré system,” Opt. Lett. 41(4), 717–720 (2016).
    [Crossref] [PubMed]

2016 (1)

2015 (1)

A. Boccaccio, F. Martino, and C. Pappalettere, “A novel moiré-based optical scanning head for high-precision contouring,” Int. J. Adv. Manuf. Technol. 80(1-4), 47–63 (2015).
[Crossref]

2010 (1)

M. Ramulu, P. Labossiere, and 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 (5)

C. A. Sciammarella, L. Lamberti, and A. Boccaccio, “A general model for moiré contouring. Part I: Theory,” Opt. Eng. 47(3), 033605 (2008).
[Crossref]

C. A. Sciammarella, L. Lamberti, A. Boccaccio, E. Cosola, and D. Posa, “A general model for moiré contouring. Part II: Applications,” Opt. Eng. 47(3), 033606 (2008).
[Crossref]

E. Cosola, K. Genovese, L. Lamberti, and C. Pappalettere, “A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing,” Int. J. Solids Struct. 45(24), 6074–6099 (2008).
[Crossref]

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

K. S. Lee, C. J. Tang, H. C. Chen, and 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).
[Crossref] [PubMed]

2007 (1)

2005 (1)

C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring using projection moiré,” Opt. Eng. 44(9), 093605 (2005).
[Crossref]

2001 (2)

M.-S. Jeong and S.-W. Kim, “Phase-shifting projection moiré for out-of-plane displacement measurement,” Proc. SPIE 4317, 170–179 (2001).
[Crossref]

G. A. Fleming, S. M. Bartram, M. R. Waszak, and L. N. Jenkins, “Projection moiré interferometry measurements of micro air vehicle wings,” Proc. SPIE 4448, 90–101 (2001).
[Crossref]

1998 (1)

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

1997 (1)

J. J. J. Dirckx and W. F. Decraemer, “Optoelectronic moire projector for real-time shape and deformation studies of the tympanic membrane,” J. Biomed. Opt. 2(2), 176–185 (1997).
[Crossref] [PubMed]

1982 (1)

T. Laulund, J. O. Søjbjerg, and E. Hørlyck, “Moiré topography in school screening for structural scoliosis,” Acta Orthop. Scand. 53(5), 765–768 (1982).
[Crossref] [PubMed]

1970 (2)

Allen, J. B.

Bartram, S. M.

G. A. Fleming, S. M. Bartram, M. R. Waszak, and L. N. Jenkins, “Projection moiré interferometry measurements of micro air vehicle wings,” Proc. SPIE 4448, 90–101 (2001).
[Crossref]

Boccaccio, A.

A. Boccaccio, F. Martino, and C. Pappalettere, “A novel moiré-based optical scanning head for high-precision contouring,” Int. J. Adv. Manuf. Technol. 80(1-4), 47–63 (2015).
[Crossref]

C. A. Sciammarella, L. Lamberti, and A. Boccaccio, “A general model for moiré contouring. Part I: Theory,” Opt. Eng. 47(3), 033605 (2008).
[Crossref]

C. A. Sciammarella, L. Lamberti, A. Boccaccio, E. Cosola, and D. Posa, “A general model for moiré contouring. Part II: Applications,” Opt. Eng. 47(3), 033606 (2008).
[Crossref]

Buytaert, J. A. N.

Chen, H. C.

Chen, J.

Choi, Y.-B.

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

Cosola, E.

C. A. Sciammarella, L. Lamberti, A. Boccaccio, E. Cosola, and D. Posa, “A general model for moiré contouring. Part II: Applications,” Opt. Eng. 47(3), 033606 (2008).
[Crossref]

E. Cosola, K. Genovese, L. Lamberti, and C. Pappalettere, “A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing,” Int. J. Solids Struct. 45(24), 6074–6099 (2008).
[Crossref]

Decraemer, W. F.

J. J. J. Dirckx and W. F. Decraemer, “Optoelectronic moire projector for real-time shape and deformation studies of the tympanic membrane,” J. Biomed. Opt. 2(2), 176–185 (1997).
[Crossref] [PubMed]

Dirckx, J. J. J.

Fleming, G. A.

G. A. Fleming, S. M. Bartram, M. R. Waszak, and L. N. Jenkins, “Projection moiré interferometry measurements of micro air vehicle wings,” Proc. SPIE 4448, 90–101 (2001).
[Crossref]

Genovese, K.

E. Cosola, K. Genovese, L. Lamberti, and C. Pappalettere, “A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing,” Int. J. Solids Struct. 45(24), 6074–6099 (2008).
[Crossref]

Greenwell, T.

M. Ramulu, P. Labossiere, and 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]

Hørlyck, E.

T. Laulund, J. O. Søjbjerg, and E. Hørlyck, “Moiré topography in school screening for structural scoliosis,” Acta Orthop. Scand. 53(5), 765–768 (1982).
[Crossref] [PubMed]

Jenkins, L. N.

G. A. Fleming, S. M. Bartram, M. R. Waszak, and L. N. Jenkins, “Projection moiré interferometry measurements of micro air vehicle wings,” Proc. SPIE 4448, 90–101 (2001).
[Crossref]

Jeong, M.-S.

M.-S. Jeong and S.-W. Kim, “Phase-shifting projection moiré for out-of-plane displacement measurement,” Proc. SPIE 4317, 170–179 (2001).
[Crossref]

Johnson, W. O.

Kim, S.-W.

M.-S. Jeong and S.-W. Kim, “Phase-shifting projection moiré for out-of-plane displacement measurement,” Proc. SPIE 4317, 170–179 (2001).
[Crossref]

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

Labossiere, P.

M. Ramulu, P. Labossiere, and 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]

Lamberti, L.

C. A. Sciammarella, L. Lamberti, and A. Boccaccio, “A general model for moiré contouring. Part I: Theory,” Opt. Eng. 47(3), 033605 (2008).
[Crossref]

C. A. Sciammarella, L. Lamberti, A. Boccaccio, E. Cosola, and D. Posa, “A general model for moiré contouring. Part II: Applications,” Opt. Eng. 47(3), 033606 (2008).
[Crossref]

E. Cosola, K. Genovese, L. Lamberti, and C. Pappalettere, “A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing,” Int. J. Solids Struct. 45(24), 6074–6099 (2008).
[Crossref]

C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring using projection moiré,” Opt. Eng. 44(9), 093605 (2005).
[Crossref]

Laulund, T.

T. Laulund, J. O. Søjbjerg, and E. Hørlyck, “Moiré topography in school screening for structural scoliosis,” Acta Orthop. Scand. 53(5), 765–768 (1982).
[Crossref] [PubMed]

Lee, C. C.

Lee, K. S.

Martino, F.

A. Boccaccio, F. Martino, and C. Pappalettere, “A novel moiré-based optical scanning head for high-precision contouring,” Int. J. Adv. Manuf. Technol. 80(1-4), 47–63 (2015).
[Crossref]

Meadows, D. M.

Pappalettere, C.

A. Boccaccio, F. Martino, and C. Pappalettere, “A novel moiré-based optical scanning head for high-precision contouring,” Int. J. Adv. Manuf. Technol. 80(1-4), 47–63 (2015).
[Crossref]

E. Cosola, K. Genovese, L. Lamberti, and C. Pappalettere, “A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing,” Int. J. Solids Struct. 45(24), 6074–6099 (2008).
[Crossref]

Posa, D.

C. A. Sciammarella, L. Lamberti, A. Boccaccio, E. Cosola, and D. Posa, “A general model for moiré contouring. Part II: Applications,” Opt. Eng. 47(3), 033606 (2008).
[Crossref]

Ramulu, M.

M. Ramulu, P. Labossiere, and 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]

Sciammarella, C. A.

C. A. Sciammarella, L. Lamberti, A. Boccaccio, E. Cosola, and D. Posa, “A general model for moiré contouring. Part II: Applications,” Opt. Eng. 47(3), 033606 (2008).
[Crossref]

C. A. Sciammarella, L. Lamberti, and A. Boccaccio, “A general model for moiré contouring. Part I: Theory,” Opt. Eng. 47(3), 033605 (2008).
[Crossref]

C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring using projection moiré,” Opt. Eng. 44(9), 093605 (2005).
[Crossref]

Sciammarella, F. M.

C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring using projection moiré,” Opt. Eng. 44(9), 093605 (2005).
[Crossref]

Søjbjerg, J. O.

T. Laulund, J. O. Søjbjerg, and E. Hørlyck, “Moiré topography in school screening for structural scoliosis,” Acta Orthop. Scand. 53(5), 765–768 (1982).
[Crossref] [PubMed]

Takasaki, H.

Tang, C. J.

Tang, Y.

Waszak, M. R.

G. A. Fleming, S. M. Bartram, M. R. Waszak, and L. N. Jenkins, “Projection moiré interferometry measurements of micro air vehicle wings,” Proc. SPIE 4448, 90–101 (2001).
[Crossref]

Yao, J.

Acta Orthop. Scand. (1)

T. Laulund, J. O. Søjbjerg, and E. Hørlyck, “Moiré topography in school screening for structural scoliosis,” Acta Orthop. Scand. 53(5), 765–768 (1982).
[Crossref] [PubMed]

Appl. Opt. (3)

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

A. Boccaccio, F. Martino, and C. Pappalettere, “A novel moiré-based optical scanning head for high-precision contouring,” Int. J. Adv. Manuf. Technol. 80(1-4), 47–63 (2015).
[Crossref]

Int. J. Solids Struct. (1)

E. Cosola, K. Genovese, L. Lamberti, and C. Pappalettere, “A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing,” Int. J. Solids Struct. 45(24), 6074–6099 (2008).
[Crossref]

J. Biomed. Opt. (1)

J. J. J. Dirckx and W. F. Decraemer, “Optoelectronic moire projector for real-time shape and deformation studies of the tympanic membrane,” J. Biomed. Opt. 2(2), 176–185 (1997).
[Crossref] [PubMed]

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

Opt. Eng. (4)

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

C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring using projection moiré,” Opt. Eng. 44(9), 093605 (2005).
[Crossref]

C. A. Sciammarella, L. Lamberti, and A. Boccaccio, “A general model for moiré contouring. Part I: Theory,” Opt. Eng. 47(3), 033605 (2008).
[Crossref]

C. A. Sciammarella, L. Lamberti, A. Boccaccio, E. Cosola, and D. Posa, “A general model for moiré contouring. Part II: Applications,” Opt. Eng. 47(3), 033606 (2008).
[Crossref]

Opt. Express (1)

Opt. Lasers Eng. (1)

M. Ramulu, P. Labossiere, and 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]

Opt. Lett. (1)

Proc. SPIE (2)

G. A. Fleming, S. M. Bartram, M. R. Waszak, and L. N. Jenkins, “Projection moiré interferometry measurements of micro air vehicle wings,” Proc. SPIE 4448, 90–101 (2001).
[Crossref]

M.-S. Jeong and S.-W. Kim, “Phase-shifting projection moiré for out-of-plane displacement measurement,” Proc. SPIE 4317, 170–179 (2001).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Schematic illustration of a generalized projection moiré system.
Fig. 2
Fig. 2 Contour shapes utilized for simulating PM measurements.
Fig. 3
Fig. 3 Simulation results for the displacement field of Fig. 2(a): (a) Wrapped phase of reference plane; (b) Wrapped phase of shifted plane; (c) Comparison of displacement maps determined with conventional method and iterative algorithm; (d) Comparison of profiles extracted from the 612nd row of the image.
Fig. 4
Fig. 4 Simulation results for the displacement field of Fig. 2(b): (a) Displacement map determined with conventional approach; (b) Displacement map determined with iterative algorithm; (c) Comparison of profiles extracted from the 200th row of the image.
Fig. 5
Fig. 5 Optical set up used in the experimental tests.
Fig. 6
Fig. 6 Schematic plot of two involved angles (α = ∠MO1N,β = ∠O3O1N) to determine R1.
Fig. 7
Fig. 7 Out-of-plane displacement of a pyramid placed near the edge of field of view: (a) Projection moiré pattern recorded by CCD for a pyramid located near the edge of the field of view; (b) 3D shape reconstructed with the new algorithm; (c) Profile comparison for a control path located on the 186th row of the image.
Fig. 8
Fig. 8 Out-of-plane displacement of the pyramid: (a) Projection moiré recorded by CCD for a pyramid located closer to O4; (b) 3D shape reconstructed with the new algorithm; (c) Profile comparison for a control path located on the 651st row of the image.
Fig. 9
Fig. 9 Out-of-plane displacement of a circular cone: (a) Projection moiré recorded by CCD for a cone with projected tip very close to O4; (b) 3D shape reconstructed with the new algorithm; (c) Profile comparison for a control path located on the 421st row of the image.
Fig. 10
Fig. 10 Out-of-plane displacement of an unknown surface: (a) The paper-made platform with an embossed paper sticked on the upper suface of the platform; (b) Moiré pattern recorded by the CCD for the unkown surface; (c) close-up shot of the embossed paper; (d) Displacement map of the embossed paper reconstructed with the new algorithm; (e) The reconstructed surface with the new algorithm of a small region limited by a square in (c) and (d)

Tables (3)

Tables Icon

Table 1 System parameters selected for simulating projection moiré measurements

Tables Icon

Table 2 System parameters selected for a projection moiré experiment

Tables Icon

Table 3 Results of real projection moiré measurements

Equations (27)

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

O O 1 = T 1 =( e 1 , e 2 , e 3 ) ( T 11 , T 12 , T 13 ) T
O O 2 = T 2 =( e 1 , e 2 , e 3 ) ( T 21 , T 22 , T 23 ) T
( e 1 1 , e 2 1 , e 3 1 )=( e 1 , e 2 , e 3 ) R 1
( e 1 2 , e 2 2 , e 3 2 )=( e 1 , e 2 , e 3 ) R 2
( X 1 , Y 1 , Z 1 ) T = R 1 T [ ( X,Y,Z ) T T 1 ]
( X 2 , Y 2 , Z 2 ) T = R 2 T [ ( X,Y,Z ) T T 2 ]
φ 1( X,Y,Z ) = 2π f 1 p 1 × X 1 Z 1 2π f 2 p 2 × X 2 Z 2
( X 1 , Y 1 , Z 1 ) T = R 1 T (X T 11 ,Y T 12 ,Z+ h (X,Y) T 13 ) T
( X 2 , Y 2 , Z 2 ) T = R 2 T (X T 21 ,Y T 22 ,Z+ h (X,Y) T 23 ) T
φ 2( X,Y,Z, h ( X,Y ) ) = 2π f 1 p 1 × X 1 ' Z 1 ' 2π f 2 p 2 × X 2 ' Z 2 '
Δφ= φ 2( X,Y,Z, h ( X,Y ) ) φ 1( X,Y,Z ) = 2π f 2 p 2 ×( X 2 ' Z 2 ' X 2 Z 2 ) 2π f 1 p 1 ×( X 1 ' Z 1 ' X 1 Z 1 )
R 1 = ( R 11 , R 12 , R 13 )
R 2 = ( R 21 , R 22 , R 23 )
Δ φ ( X,Y,Z, h ( X,Y ) ) = 2π f 2 p 2 ×[ ( X T 21 Y T 22 Z+ h ( X,Y ) T 23 ) R 21 ( X T 21 Y T 22 Z+ h ( X,Y ) T 23 ) R 23 ( X T 21 Y T 22 Z T 23 ) R 21 ( X T 21 Y T 22 Z T 23 ) R 23 ] 2π f 1 p 1 ×[ ( X T 11 Y T 12 Z+ h ( X,Y ) T 13 ) R 11 ( X T 11 Y T 12 Z+ h ( X,Y ) T 13 ) R 13 ( X T 11 Y T 12 Z T 13 ) R 11 ( X T 11 Y T 12 Z T 13 ) R 13 ]
X=cu
Y=cv
k 0 = 1 φ 2( X,Y,Z, h ( X,Y ) ) | Z=0, h ( X,Y ) =1 φ 1( X,Y,Z ) | Z=0
h 0 = k 0 ×( φ 2 - φ 1 )
X n+1 =Xc×( X c u C )× h n T 23
Y n+1 =Yc×( Y c v C )× h n T 23
φ 1 n+1 = φ 1( X n+1 , Y n+1 )
k n+1 = h n φ 2( X n+1 , Y n+1 ,Z, h n ) | Z=0 φ 1( X,Y,Z ) | Z=0
h n+1 = k n+1 ×( φ 2 φ 1 n+1 )
R 1 = Q 1 Q 2 =[ cosα 0 sinα 0 1 0 sinα 0 cosα ][ 1 0 0 0 cosβ sinβ 0 sinβ cosβ ]
R 2 =[ 1 0 0 0 1 0 0 0 1 ]
f 1 = p 1 × O 1 O 3 p O 3 ×cosα
f 2 = L CD × O 2 O 4 L AB

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