Abstract

Profilometry by electronic speckle pattern interferometry with multimode diode lasers is both theoretically and experimentally studied. The multiwavelength character of the laser emission provides speckled images covered with interference fringes corresponding to the surface relief in single-exposure processes. For fringe pattern evaluation, variations of the phase-stepping technique are investigated for phase mapping as a function of the number of laser modes. Expressions for two, three, and four modes in four and eight stepping are presented, and the performances of those techniques are compared in the experiments through the surface shaping of a flat bar. The surface analysis of a peach points out the possibility of applying the technique in the quality control of food production and agricultural research.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
  4. G. Pedrini, P. Fröning, H. J. Tiziani, and F. M. Santoyo, "Shape measurement of microscopic structures using digital holograms," Opt. Commun. 164, 257-268 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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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] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. Q. Yu, S. Fu, X. Yang, X. Sun, and X. Liu, "Extraction of phase field from a single contoured fringe pattern of ESPI," Opt. Express 12, 75-83 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  22. R. A. Braga, Jr., I. M. dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. J. Rabal, and M. R. Trivi, "Assessment of seed viability by laser speckle techniques," J. Agric. Eng. Res. 86, 287-294 (2003).

2006

E. A. Barbosa, R. Verzini, and J. F. Carvalho, "Multiwavelength holography in Bi12TiO20 crystals: applications in refractometry," Opt. Commun. 263, 189-196 (2006).
[CrossRef]

2005

2004

2003

T. Harimoto, "Phase calculation based on curve fitting with a two-wavelength interferometer," Opt. Express 11, 895-898 (2003).
[CrossRef] [PubMed]

R. A. Braga, Jr., I. M. dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. J. Rabal, and M. R. Trivi, "Assessment of seed viability by laser speckle techniques," J. Agric. Eng. Res. 86, 287-294 (2003).

1999

G. Pedrini, P. Fröning, H. J. Tiziani, and F. M. Santoyo, "Shape measurement of microscopic structures using digital holograms," Opt. Commun. 164, 257-268 (1999).
[CrossRef]

B. Gutmann and H. Weber, "Phase unwrapping with the branch-cut method: clustering of discontinuity sources and reverse simulated annealing," Appl. Opt. 38, 5577-5593 (1999).
[CrossRef]

1998

1997

J. E. Millerd and N. J. Brock, "Holographic profilometry with a rhodium-doped barium titanate crystal and a diode laser," Appl. Opt. 36, 2427-2431 (1997).
[CrossRef] [PubMed]

D. R. Schmitt and R. W. Hunt, "Optimization of fringe pattern calculation with direct correlations in speckle interferometry," Appl. Opt. 36, 8848-8857 (1997).
[CrossRef]

M. R. R. Gesualdi, E. Gonçalves, R. de Souza, F. F. Palácios, M. Muramatsu, and J. Valin, "Two-source method in digital holographic contouring," in Fifth Iberoamerican Meeting on Optics and Eighth Latin American Meeting on Optics, Lasers and their Applications, Proc. SPIE 5622, 1422-1427 (1997).

1993

Y. Zou, X. Peng, and H. Tiziani, "Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode," Optik (Stuttgart) 94, 155-158 (1993).

1992

1990

R. P. Tatam, J. C. Davies, C. H. Buckberry, and J. D. C. Jones, "Electronic speckle pattern surface contouring using optical fibers and wavelength modulation of laser diodes," in Fiber Optics '90, Proc. SPIE 1314, 278-283 (1990).

1989

1987

1981

F. M. Kuchel and J. H. Tiziani, "Real-time contour holography using BSO crystals," Opt. Commun. 38, 249-254 (1981).
[CrossRef]

Arizaga, R.

R. A. Braga, Jr., I. M. dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. J. Rabal, and M. R. Trivi, "Assessment of seed viability by laser speckle techniques," J. Agric. Eng. Res. 86, 287-294 (2003).

Barbosa, E. A.

E. A. Barbosa, R. Verzini, and J. F. Carvalho, "Multiwavelength holography in Bi12TiO20 crystals: applications in refractometry," Opt. Commun. 263, 189-196 (2006).
[CrossRef]

E. A. Barbosa, "Holographic imaging with multimode, large free spectral range lasers in photorefractive sillenite crystals," Appl. Phys. B 80, 345-350 (2005).
[CrossRef]

E. A. Barbosa, A. A. V. Filho, M. R. R. Gesualdi, D. Curcio, M. Muramatsu, and D. Soga, "Single-exposure, photorefractive holographic surface contouring with multiwavelength diode lasers," J. Opt. Soc. Am. A 22, 2872-2879 (2005).
[CrossRef]

Borém, F. M.

R. A. Braga, Jr., I. M. dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. J. Rabal, and M. R. Trivi, "Assessment of seed viability by laser speckle techniques," J. Agric. Eng. Res. 86, 287-294 (2003).

Braga, R. A.

R. A. Braga, Jr., I. M. dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. J. Rabal, and M. R. Trivi, "Assessment of seed viability by laser speckle techniques," J. Agric. Eng. Res. 86, 287-294 (2003).

Brock, N. J.

Buckberry, C. H.

R. P. Tatam, J. C. Davies, C. H. Buckberry, and J. D. C. Jones, "Electronic speckle pattern surface contouring using optical fibers and wavelength modulation of laser diodes," in Fiber Optics '90, Proc. SPIE 1314, 278-283 (1990).

Carvalho, J. F.

E. A. Barbosa, R. Verzini, and J. F. Carvalho, "Multiwavelength holography in Bi12TiO20 crystals: applications in refractometry," Opt. Commun. 263, 189-196 (2006).
[CrossRef]

Curcio, D.

dal Fabbro, I. M.

R. A. Braga, Jr., I. M. dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. J. Rabal, and M. R. Trivi, "Assessment of seed viability by laser speckle techniques," J. Agric. Eng. Res. 86, 287-294 (2003).

Davies, J. C.

R. P. Tatam, J. C. Davies, C. H. Buckberry, and J. D. C. Jones, "Electronic speckle pattern surface contouring using optical fibers and wavelength modulation of laser diodes," in Fiber Optics '90, Proc. SPIE 1314, 278-283 (1990).

de Souza, R.

M. R. R. Gesualdi, E. Gonçalves, R. de Souza, F. F. Palácios, M. Muramatsu, and J. Valin, "Two-source method in digital holographic contouring," in Fifth Iberoamerican Meeting on Optics and Eighth Latin American Meeting on Optics, Lasers and their Applications, Proc. SPIE 5622, 1422-1427 (1997).

Eiju, T.

Endo, T.

Erf, R. K.

R. K. Erf, Speckle Metrology(Academic, 1984).

Filho, A. A. V.

Frei, B.

Fröning, P.

G. Pedrini, P. Fröning, H. J. Tiziani, and F. M. Santoyo, "Shape measurement of microscopic structures using digital holograms," Opt. Commun. 164, 257-268 (1999).
[CrossRef]

Fu, S.

Gesualdi, M. R. R.

E. A. Barbosa, A. A. V. Filho, M. R. R. Gesualdi, D. Curcio, M. Muramatsu, and D. Soga, "Single-exposure, photorefractive holographic surface contouring with multiwavelength diode lasers," J. Opt. Soc. Am. A 22, 2872-2879 (2005).
[CrossRef]

M. R. R. Gesualdi, E. Gonçalves, R. de Souza, F. F. Palácios, M. Muramatsu, and J. Valin, "Two-source method in digital holographic contouring," in Fifth Iberoamerican Meeting on Optics and Eighth Latin American Meeting on Optics, Lasers and their Applications, Proc. SPIE 5622, 1422-1427 (1997).

Gonçalves, E.

M. R. R. Gesualdi, E. Gonçalves, R. de Souza, F. F. Palácios, M. Muramatsu, and J. Valin, "Two-source method in digital holographic contouring," in Fifth Iberoamerican Meeting on Optics and Eighth Latin American Meeting on Optics, Lasers and their Applications, Proc. SPIE 5622, 1422-1427 (1997).

Gülker, G.

Gutmann, B.

Haack, O.

Hack, E.

Hariharan, P.

Harimoto, T.

Hinsch, K. D.

Hölscher, C.

Hunt, R. W.

Huntley, J. M.

Itoh, M.

Jones, J. D. C.

R. P. Tatam, J. C. Davies, C. H. Buckberry, and J. D. C. Jones, "Electronic speckle pattern surface contouring using optical fibers and wavelength modulation of laser diodes," in Fiber Optics '90, Proc. SPIE 1314, 278-283 (1990).

Kästle, R.

Koechner, W.

W. Koechner, Solid State Lasers Engineering (Springer-Verlag, 1998).

Kuchel, F. M.

F. M. Kuchel and J. H. Tiziani, "Real-time contour holography using BSO crystals," Opt. Commun. 38, 249-254 (1981).
[CrossRef]

Kuls, J.

Liu, X.

Makita, S.

Millerd, J. E.

Muramatsu, M.

E. A. Barbosa, A. A. V. Filho, M. R. R. Gesualdi, D. Curcio, M. Muramatsu, and D. Soga, "Single-exposure, photorefractive holographic surface contouring with multiwavelength diode lasers," J. Opt. Soc. Am. A 22, 2872-2879 (2005).
[CrossRef]

M. R. R. Gesualdi, E. Gonçalves, R. de Souza, F. F. Palácios, M. Muramatsu, and J. Valin, "Two-source method in digital holographic contouring," in Fifth Iberoamerican Meeting on Optics and Eighth Latin American Meeting on Optics, Lasers and their Applications, Proc. SPIE 5622, 1422-1427 (1997).

Oreb, B. F.

Palácios, F. F.

M. R. R. Gesualdi, E. Gonçalves, R. de Souza, F. F. Palácios, M. Muramatsu, and J. Valin, "Two-source method in digital holographic contouring," in Fifth Iberoamerican Meeting on Optics and Eighth Latin American Meeting on Optics, Lasers and their Applications, Proc. SPIE 5622, 1422-1427 (1997).

Pedrini, G.

G. Pedrini, P. Fröning, H. J. Tiziani, and F. M. Santoyo, "Shape measurement of microscopic structures using digital holograms," Opt. Commun. 164, 257-268 (1999).
[CrossRef]

Peng, X.

Y. Zou, X. Peng, and H. Tiziani, "Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode," Optik (Stuttgart) 94, 155-158 (1993).

Platen, W.

Rabal, H. J.

R. A. Braga, Jr., I. M. dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. J. Rabal, and M. R. Trivi, "Assessment of seed viability by laser speckle techniques," J. Agric. Eng. Res. 86, 287-294 (2003).

Rabelo, G. F.

R. A. Braga, Jr., I. M. dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. J. Rabal, and M. R. Trivi, "Assessment of seed viability by laser speckle techniques," J. Agric. Eng. Res. 86, 287-294 (2003).

Santoyo, F. M.

G. Pedrini, P. Fröning, H. J. Tiziani, and F. M. Santoyo, "Shape measurement of microscopic structures using digital holograms," Opt. Commun. 164, 257-268 (1999).
[CrossRef]

Schmitt, D. R.

Sennhauser, U.

Soga, D.

Sun, X.

Tatam, R. P.

R. P. Tatam, J. C. Davies, C. H. Buckberry, and J. D. C. Jones, "Electronic speckle pattern surface contouring using optical fibers and wavelength modulation of laser diodes," in Fiber Optics '90, Proc. SPIE 1314, 278-283 (1990).

Tiziani, H.

Y. Zou, X. Peng, and H. Tiziani, "Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode," Optik (Stuttgart) 94, 155-158 (1993).

Tiziani, H. J.

G. Pedrini, P. Fröning, H. J. Tiziani, and F. M. Santoyo, "Shape measurement of microscopic structures using digital holograms," Opt. Commun. 164, 257-268 (1999).
[CrossRef]

Tiziani, J. H.

F. M. Kuchel and J. H. Tiziani, "Real-time contour holography using BSO crystals," Opt. Commun. 38, 249-254 (1981).
[CrossRef]

Trivi, M. R.

R. A. Braga, Jr., I. M. dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. J. Rabal, and M. R. Trivi, "Assessment of seed viability by laser speckle techniques," J. Agric. Eng. Res. 86, 287-294 (2003).

Valin, J.

M. R. R. Gesualdi, E. Gonçalves, R. de Souza, F. F. Palácios, M. Muramatsu, and J. Valin, "Two-source method in digital holographic contouring," in Fifth Iberoamerican Meeting on Optics and Eighth Latin American Meeting on Optics, Lasers and their Applications, Proc. SPIE 5622, 1422-1427 (1997).

Verzini, R.

E. A. Barbosa, R. Verzini, and J. F. Carvalho, "Multiwavelength holography in Bi12TiO20 crystals: applications in refractometry," Opt. Commun. 263, 189-196 (2006).
[CrossRef]

Weber, H.

Yang, X.

Yasuno, Y.

Yatagai, T.

Yu, Q.

Zou, Y.

Y. Zou, X. Peng, and H. Tiziani, "Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode," Optik (Stuttgart) 94, 155-158 (1993).

Appl. Opt.

Appl. Phys. B

E. A. Barbosa, "Holographic imaging with multimode, large free spectral range lasers in photorefractive sillenite crystals," Appl. Phys. B 80, 345-350 (2005).
[CrossRef]

J. Agric. Eng. Res.

R. A. Braga, Jr., I. M. dal Fabbro, F. M. Borém, G. F. Rabelo, R. Arizaga, H. J. Rabal, and M. R. Trivi, "Assessment of seed viability by laser speckle techniques," J. Agric. Eng. Res. 86, 287-294 (2003).

J. Opt. Soc. Am. A

Opt. Commun.

E. A. Barbosa, R. Verzini, and J. F. Carvalho, "Multiwavelength holography in Bi12TiO20 crystals: applications in refractometry," Opt. Commun. 263, 189-196 (2006).
[CrossRef]

F. M. Kuchel and J. H. Tiziani, "Real-time contour holography using BSO crystals," Opt. Commun. 38, 249-254 (1981).
[CrossRef]

G. Pedrini, P. Fröning, H. J. Tiziani, and F. M. Santoyo, "Shape measurement of microscopic structures using digital holograms," Opt. Commun. 164, 257-268 (1999).
[CrossRef]

Opt. Express

Optik

Y. Zou, X. Peng, and H. Tiziani, "Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode," Optik (Stuttgart) 94, 155-158 (1993).

Other

W. Koechner, Solid State Lasers Engineering (Springer-Verlag, 1998).

M. R. R. Gesualdi, E. Gonçalves, R. de Souza, F. F. Palácios, M. Muramatsu, and J. Valin, "Two-source method in digital holographic contouring," in Fifth Iberoamerican Meeting on Optics and Eighth Latin American Meeting on Optics, Lasers and their Applications, Proc. SPIE 5622, 1422-1427 (1997).

R. K. Erf, Speckle Metrology(Academic, 1984).

R. P. Tatam, J. C. Davies, C. H. Buckberry, and J. D. C. Jones, "Electronic speckle pattern surface contouring using optical fibers and wavelength modulation of laser diodes," in Fiber Optics '90, Proc. SPIE 1314, 278-283 (1990).

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Figures (7)

Fig. 1
Fig. 1

Signal V as a function of Γ S . The solid curve was obtained through Eq. (7), while the dashed curve was calculated by Eq. (8) for N e f f = 4 modes.

Fig. 2
Fig. 2

Optical setup: BS1–BS3, beam splitters; L1–L3, lenses; M1–M3, mirrors; SF, spatial filter; CCD, camera.

Fig. 3
Fig. 3

Multiwavelength speckle profilometry of a glass bar through the four-stepping technique. (a) Speckle pattern, (b) low-pass-filtered intensity distribution of the interference pattern (dotted curve) and fitting curve for V after Eq. (8) for N e f f 2 (solid curve), (c) 3D plot.

Fig. 4
Fig. 4

Profilometry of the glass bar through the four-stepping technique. (a) Speckle pattern, (b) intensity distribution of the interference pattern (dotted curve) and fitting curve for V after Eq. (8) for N e f f 3 (solid curve), (c) resulting 3D plot.

Fig. 5
Fig. 5

Profilometry of the glass bar through the eight-stepping technique. (a) Measured intensity of the fringe pattern (dotted curve) and fitting curve for N e f f 4 (solid curve), (b) resulting 3D plot.

Fig. 6
Fig. 6

Reconstructed z coordinate of the bar cross section. (a) Four-frame technique for N e f f = 2 , (b) four-frame technique for N e f f = 3 , (c) eight-frame technique for N e f f = 3 , and (d) eight-frame technique for N e f f = 4 . The solid curve is the expected z value.

Fig. 7
Fig. 7

Multiwavelength speckle profilometry of a peach for N e f f = 2 . (a) Speckle pattern, (b) phase map, and (c) 3D reconstruction.

Equations (101)

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

λ 1
λ 2
λ S = λ 1 λ 2 / | λ 1 λ 2 |
B i 12 T i O 20
150   μm
( S N )
( R N )
λ ¯
Δ λ
S N
R N
R N = R 0 n = ( N 1 ) / 2 n = ( N 1 ) / 2 A n exp { i [ ( k ¯ + n Δ k ) Γ R + ϕ n ] } ,
S N = S 0 n = ( N 1 ) / 2 n = ( N 1 ) / 2 A n exp { i [ ( k ¯ + n Δ k ) Γ S + ϕ n ] } ,
ϕ n
k ¯ 2 π / λ ¯
Δ k 2 π Δ λ / λ ¯
A n
Γ S
Γ R
I 1 = | S N | 2 + | R N | 2 + S N * R N + R N * S N .
S n * R m = δ n , m S 0 R 0 A n A m exp { i [ ( k ¯ + n Δ k ) Γ S + ϕ n ] } × exp { i [ ( k ¯ + m Δ k ) Γ R + ϕ m ] } .
I 1 = S 0 2 + R 0 2 + S 0 R 0 exp [ i k ¯ ( Γ S Γ R ) ] n = ( N 1 ) / 2 n = ( N 1 ) / 2 A n 2    × exp [ i n Δ k ( Γ S Γ R ) ] + R 0 S 0 exp [ i k ¯ ( Γ S Γ R ) ] × n = ( N 1 ) / 2 n = ( N 1 ) / 2 A n 2 exp [ i n Δ k ( Γ S Γ R ) ] .
   I 1 = S 0 2 + R 0 2 + 2 R 0 S 0 cos [ k ¯ ( Γ S Γ R ) ] n = ( N 1 ) / 2 n = ( N 1 ) / 2 A n 2    × exp [ i n Δ k ( Γ S Γ R ) ] .
I 2 = S 0 2 + R 0 2
I = I 2 I 1 = 2 R 0 S 0 | cos [ k ¯ ( Γ S Γ R ) ] n = ( N 1 ) / 2 n = ( N 1 ) / 2 A n 2 × exp [ i n Δ k ( Γ S Γ R ) ] | .
λ ¯
k ¯ Δ k
V I 2 = 2 R 0 S 0 ( n = ( N 1 ) / 2 n = ( N 1 ) / 2 A n 2 exp [ i n Δ k ( Γ S Γ R ) ] ) 2 .
A n = 1
V = 2 R 0 S 0 sin 2 [ N Δ k ( Γ S Γ R ) / 2 ] sin 2 [ Δ k ( Γ S Γ R ) / 2 ] .
Δ z
Δ z = λ 2 2 Δ λ λ S 2 ,
λ S
Δ v = c / 2 L
Δ λ
Δ v = c Δ λ / λ 2
Δ z = L
λ ¯
N e f f
A i 2
A 0 2 = 1
A 1 2 = A 1 2 = 0.43
A 2 2 = A 2 2 = 0.16
Γ S
Γ R = 0
N e f f = 4
Δ k = 1.18 rad / mm
λ ¯ = 670   nm
  V l = { 2 R 0 S 0 sin [ N e f f ( Δ k Γ S ( x , y ) + l ϕ ) / 2 ] sin [ ( Δ k Γ S ( x , y ) / 2 + l ϕ ) / 2 ] } 2 ,
ϕ = π / 2   rad
N e f f = 2
ϕ 4 s t e p ( N e f f = 2 ) = arctan ( V 3 V 1 V 0 V 2 ) .
N e f f = 3
ϕ 4 s t e p ( N e f f = 3 ) = 1 2 arctan ( V 1 V 3 V 0 V 2 ) .
N e f f = 4
ϕ 4 s t e p ( N e f f = 4 ) = arctan [ V 0 V 2 V 1 V 3 ( V 1 V 3 V 0 V 2 ) ] .
π / 4
ϕ = π / 4   rad
ϕ 8 s t e p = arctan ( V 7 + V 3 V 5 V 1 V 4 + V 0 V 6 V 2 ) .
N e f f = 3
N e f f = 4
V l + V l + 4
cos 2
cos 2
λ S / 2
30 m W
670   nm
53 G H z
Δ λ = 0.082   nm
λ ¯ = 670   nm
2 λ ¯
Γ S
N e f f = 2.001 ± 0.008
λ ¯ = 671   nm
N e f f = 3.00 ± 0.01
λ ¯ = 671.5   nm
N e f f = 3.99 ± 0.01
N e f f = 3
N e f f = 2
N e f f = 3
N e f f = 3
N e f f = 4
1.5   mm
N e f f = 3
0.3   mm
N e f f = 4
N e f f = 4
λ ¯ = 670   nm
N e f f = 2
Δ z
N e f f
Γ S
N e f f = 4
N e f f 2
N e f f 3
N e f f 4
N e f f = 2
N e f f = 3
N e f f = 3
N e f f = 4
N e f f = 2

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