Abstract

We studied the use of multiwavelength diode lasers for surface profilometry through holographic recording in sillenite Bi12TiO20 crystals. When such lasers are used, the holographic image from single-exposure recordings appears covered with interference fringes providing information on the surface relief of the object. By taking advantage of the narrow interference fringes due to the multiwavelength emission of the laser, we obtained interferograms by holographic recording with two reference beams, which improves the surface analysis by visual inspection and enhances the profilometry sensitivity.

© 2005 Optical Society of America

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References

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  1. P. Hariharan, Optical Holography: Principles, Techniques and Applications (Cambridge U. Press, 1984).
  2. C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. (Bellingham) 20, 79–85 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
  5. F. M. Kuchel, H. J. Tiziani, “Real-time contour holography using BSO crystals,” Opt. Commun. 38, 17–21 (1981).
    [CrossRef]
  6. E. A. Barbosa, “Holographic imaging with multimode, large free spectral range lasers in photorefractive sillenite crystals,” Appl. Phys. B: Lasers Opt. 80, 345–350 (2005).
    [CrossRef]
  7. K. Creath, “Phase measurement techniques,” in Progress in Optics, Vol. XXVI, E. Wolf, ed. (Elsevier, 1988).
    [CrossRef]
  8. M. R. R. Gesualdi, D. Soga, M. Muramatsu, “Real-time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
    [CrossRef]
  9. D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. 4, 210–219 (1987).
    [CrossRef]
  10. A. Spik, W. Robinson, “Investigation of cellular-automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14, 25–37 (1991).
    [CrossRef]
  11. W. Koechner, Solid State Laser Engineering, (Springer-Verlag, 1998).
  12. A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
    [CrossRef]
  13. S. Mallick, D. Rouède, “Influence of the polarization direction on two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B: Photophys. Laser Chem. 43, 239–245 (1987).
    [CrossRef]
  14. S. V. Miridonov, A. A. Kamshilin, E. Barbosa, “Recyclable holographic interferometer with a photorefractive crystal: optical scheme optimization,” J. Opt. Soc. Am. A 11, 1780–1788 (1994).
    [CrossRef]

2006 (1)

M. R. R. Gesualdi, D. Soga, M. Muramatsu, “Real-time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
[CrossRef]

2005 (1)

E. A. Barbosa, “Holographic imaging with multimode, large free spectral range lasers in photorefractive sillenite crystals,” Appl. Phys. B: Lasers Opt. 80, 345–350 (2005).
[CrossRef]

2003 (1)

2000 (1)

C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. (Bellingham) 20, 79–85 (2000).
[CrossRef]

1997 (1)

1994 (1)

1991 (1)

A. Spik, W. Robinson, “Investigation of cellular-automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14, 25–37 (1991).
[CrossRef]

1987 (2)

D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. 4, 210–219 (1987).
[CrossRef]

S. Mallick, D. Rouède, “Influence of the polarization direction on two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B: Photophys. Laser Chem. 43, 239–245 (1987).
[CrossRef]

1985 (1)

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

1981 (1)

F. M. Kuchel, H. J. Tiziani, “Real-time contour holography using BSO crystals,” Opt. Commun. 38, 17–21 (1981).
[CrossRef]

Barbastathis, G.

Barbosa, E.

Barbosa, E. A.

E. A. Barbosa, “Holographic imaging with multimode, large free spectral range lasers in photorefractive sillenite crystals,” Appl. Phys. B: Lasers Opt. 80, 345–350 (2005).
[CrossRef]

Brock, N. J.

Creath, K.

K. Creath, “Phase measurement techniques,” in Progress in Optics, Vol. XXVI, E. Wolf, ed. (Elsevier, 1988).
[CrossRef]

Gesualdi, M. R. R.

M. R. R. Gesualdi, D. Soga, M. Muramatsu, “Real-time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. 4, 210–219 (1987).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical Holography: Principles, Techniques and Applications (Cambridge U. Press, 1984).

Kamshilin, A. A.

S. V. Miridonov, A. A. Kamshilin, E. Barbosa, “Recyclable holographic interferometer with a photorefractive crystal: optical scheme optimization,” J. Opt. Soc. Am. A 11, 1780–1788 (1994).
[CrossRef]

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

Koechner, W.

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

Kuchel, F. M.

F. M. Kuchel, H. J. Tiziani, “Real-time contour holography using BSO crystals,” Opt. Commun. 38, 17–21 (1981).
[CrossRef]

Mallick, S.

S. Mallick, D. Rouède, “Influence of the polarization direction on two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B: Photophys. Laser Chem. 43, 239–245 (1987).
[CrossRef]

Mastin, G. A.

D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. 4, 210–219 (1987).
[CrossRef]

Millerd, J. E.

Miridonov, S. V.

Muramatsu, M.

M. R. R. Gesualdi, D. Soga, M. Muramatsu, “Real-time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
[CrossRef]

Osten, W.

C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. (Bellingham) 20, 79–85 (2000).
[CrossRef]

Petrov, M. P.

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

Robinson, W.

A. Spik, W. Robinson, “Investigation of cellular-automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14, 25–37 (1991).
[CrossRef]

Romero, L. A.

D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. 4, 210–219 (1987).
[CrossRef]

Rouède, D.

S. Mallick, D. Rouède, “Influence of the polarization direction on two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B: Photophys. Laser Chem. 43, 239–245 (1987).
[CrossRef]

Seebacher, S.

C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. (Bellingham) 20, 79–85 (2000).
[CrossRef]

Sinha, A.

Soga, D.

M. R. R. Gesualdi, D. Soga, M. Muramatsu, “Real-time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
[CrossRef]

Spik, A.

A. Spik, W. Robinson, “Investigation of cellular-automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14, 25–37 (1991).
[CrossRef]

Tiziani, H. J.

F. M. Kuchel, H. J. Tiziani, “Real-time contour holography using BSO crystals,” Opt. Commun. 38, 17–21 (1981).
[CrossRef]

Wagner, C.

C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. (Bellingham) 20, 79–85 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B: Lasers Opt. (1)

E. A. Barbosa, “Holographic imaging with multimode, large free spectral range lasers in photorefractive sillenite crystals,” Appl. Phys. B: Lasers Opt. 80, 345–350 (2005).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem. (1)

S. Mallick, D. Rouède, “Influence of the polarization direction on two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B: Photophys. Laser Chem. 43, 239–245 (1987).
[CrossRef]

J. Opt. Soc. Am. (1)

D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. 4, 210–219 (1987).
[CrossRef]

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

Opt. Commun. (2)

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

F. M. Kuchel, H. J. Tiziani, “Real-time contour holography using BSO crystals,” Opt. Commun. 38, 17–21 (1981).
[CrossRef]

Opt. Eng. (Bellingham) (1)

C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. (Bellingham) 20, 79–85 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (2)

M. R. R. Gesualdi, D. Soga, M. Muramatsu, “Real-time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
[CrossRef]

A. Spik, W. Robinson, “Investigation of cellular-automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14, 25–37 (1991).
[CrossRef]

Other (3)

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

P. Hariharan, Optical Holography: Principles, Techniques and Applications (Cambridge U. Press, 1984).

K. Creath, “Phase measurement techniques,” in Progress in Optics, Vol. XXVI, E. Wolf, ed. (Elsevier, 1988).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Interference fringe profile as a function of Γ S for N = 2 (dotted curve), N = 5 (dashed curve), N = 8 (solid curve) oscillating modes.[6] In this case, Δ k = 1.39 rad mm and λ = 670 nm .

Fig. 2
Fig. 2

Interferogram intensity distribution as a function of surface depth z for holographic recording with (a) one reference beam, (b) two reference beams.

Fig. 3
Fig. 3

Phase distribution as a function of depth z resulting from holographic recording with (a) one reference beam, (b) two reference beams.

Fig. 4
Fig. 4

Scheme of the optical setup: M1–M5, mirrors; BS1 and BS2, beam splitters; L1–L3, lenses; P1 and P2, polarizers; PR1 and PR2, 90° prisms; CCD, camera; PC, computer.

Fig. 5
Fig. 5

Surface analysis of a 30°-tilted flat bar: (a) Interferogram, (b) phase map, (c) unwrapped phase pattern, (d) 3D plot.

Fig. 6
Fig. 6

The same analysis as depicted in Fig. 5 for a metallic cylinder: (a) Interferogram, (b) phase map, (c) unwrapped phase pattern, (d) 3D plot.

Fig. 7
Fig. 7

The same analysis as shown in Figs. 5, 6 for a loudspeaker surface: (a) Interferogram, (b) phase map, (c) unwrapped phase pattern, (d) 3D plot.

Fig. 8
Fig. 8

Contour analysis of a 22°-tilted bar through holographic recording with two reference beams: (a) Interferogram, (b) phase map, (c) unwrapped phase pattern, (d) 3D plot.

Fig. 9
Fig. 9

Interferogram of the cylinder obtained by holographic recording with two reference beams.

Fig. 10
Fig. 10

Same as Fig. 9 for the loudspeaker surface.

Equations (11)

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R N ( 0 ) = R 0 n = ( N 1 ) 2 n = ( N 1 ) 2 A n exp { i [ ( k + n Δ k ) Γ R + ϕ n ] } ,
S N ( 0 ) = S 0 n = ( N 1 ) 2 n = ( N 1 ) 2 A n exp { i [ ( k + n Δ k ) Γ S + ϕ n ] } ,
I D = η I R m 2 I R = 2 ( R N * S N R N 2 + S N 2 ) I R ,
I D 2 m 0 { sin [ N Δ k ( Γ S Γ R ) 2 ] sin [ Δ k ( Γ S Γ R ) 2 ] } 2 I R ,
Γ S , B Γ S , A = 2 π Δ k = λ 2 Δ λ λ S ,
I D , l ( x , y ) 2 m 0 { sin [ N ( Δ k Γ S ( x , y ) + l π 2 ) 2 ] sin [ ( Δ k Γ S ( x , y ) 2 + l π 2 ) 2 ] } 2 I R ,
ϕ S ( x , y ) = 1 2 arctan ( I D 1 I D 3 I D 0 I D 2 ) .
I D 2 m 0 { [ sin [ N Δ k ( Γ S Γ R 1 ) 2 ] sin [ Δ k ( Γ S Γ R 1 ) 2 ] ] 2 + [ sin [ N Δ k ( Γ S Γ R 2 ) 2 ] sin [ Δ k ( Γ S Γ R 2 ) 2 ] ] 2 } I R ,
I D 4 m 0 I R { 4 cos 2 [ Δ k eff ( Γ S Γ R 1 ) 2 ] + 1 } .
I D , l 4 m 0 I R { 4 cos 2 [ ( Δ k eff Γ S + l π 2 ) 2 ] + 1 } , l = 0 , 1 , 2 , 3 .
ϕ S ( x , y ) = 1 4 arctan ( I D 1 I D 3 I D 0 I D 2 ) .

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