Abstract

The paper introduces a method for simultaneously measuring the in-plane and out-of-plane displacement derivatives of a deformed object in digital holographic interferometry. In the proposed method, lasers of different wavelengths are used to simultaneously illuminate the object along various directions such that a unique wavelength is used for a given direction. The holograms formed by multiple reference-object beam pairs of different wavelengths are recorded by a 3-color CCD camera with red, green, and blue channels. Each channel stores the hologram related to the corresponding wavelength and hence for the specific direction. The complex reconstructed interference field is obtained for each wavelength by numerical reconstruction and digital processing of the recorded holograms before and after deformation. Subsequently, the phase derivative is estimated for a given wavelength using two-dimensional pseudo Wigner-Ville distribution and the in-plane and out-of-plane components are obtained from the estimated phase derivatives using the sensitivity vectors of the optical configuration.

© 2011 Optical Society of America

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References

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    [PubMed]
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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] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2010

2009

G. Rajshekhar, S. S. Gorthi, and P. Rastogi, “Strain, curvature, and twist measurements in digital holographic interferometry using pseudo-Wigner-Ville distribution based method,” Rev. Sci. Instrum. 80, 093107 (2009).
[CrossRef] [PubMed]

2008

Y. Morimoto, T. Matui, M. Fujigaki, and A. Matsui, “Three-dimensional displacement analysis by windowed phase-shifting digital holographic interferometry,” Strain 44, 49–56 (2008).
[CrossRef]

Y. Morimoto, T. Matui, and M. Fujigaki, “Application of three-dimensional displacement and strain distribution measurement by windowed phase-shifting digital holographic interferometry,” Adv. Mater. Res. 47–50, 1262–1265 (2008).
[CrossRef]

P. Picart, D. Mounier, and J. M. Desse, “High-resolution digital two-color holographic metrology,” Opt. Lett. 33, 276–278(2008).
[CrossRef] [PubMed]

2006

M. De la Torre-Ibarra, F. M. Santoyo, C. Perez-Lopez, T. S. Anaya, and D. D. Aguayo, “Surface strain distribution on thin metallic plates using 3-D digital holographic interferometry,” Opt. Eng. 45 (2006).
[CrossRef]

2005

2003

2002

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

1997

Aguayo, D. D.

M. De la Torre-Ibarra, F. M. Santoyo, C. Perez-Lopez, T. S. Anaya, and D. D. Aguayo, “Surface strain distribution on thin metallic plates using 3-D digital holographic interferometry,” Opt. Eng. 45 (2006).
[CrossRef]

Anaya, T. S.

M. De la Torre-Ibarra, F. M. Santoyo, C. Perez-Lopez, T. S. Anaya, and D. D. Aguayo, “Surface strain distribution on thin metallic plates using 3-D digital holographic interferometry,” Opt. Eng. 45 (2006).
[CrossRef]

De la Torre-Ibarra, M.

M. De la Torre-Ibarra, F. M. Santoyo, C. Perez-Lopez, T. S. Anaya, and D. D. Aguayo, “Surface strain distribution on thin metallic plates using 3-D digital holographic interferometry,” Opt. Eng. 45 (2006).
[CrossRef]

M. De La Torre-Ibarra, F. Mendoza-Santoyo, C. Perez-Lopez, and T. Saucedo-A, “Detection of surface strain by three-dimensional digital holography,” Appl. Opt. 44, 27–31(2005).
[PubMed]

De La Torre-Ibarra, M. H.

Desse, J. M.

Fujigaki, M.

Y. Morimoto, T. Matui, M. Fujigaki, and A. Matsui, “Three-dimensional displacement analysis by windowed phase-shifting digital holographic interferometry,” Strain 44, 49–56 (2008).
[CrossRef]

Y. Morimoto, T. Matui, and M. Fujigaki, “Application of three-dimensional displacement and strain distribution measurement by windowed phase-shifting digital holographic interferometry,” Adv. Mater. Res. 47–50, 1262–1265 (2008).
[CrossRef]

Gorthi, S. S.

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Matsui, A.

Y. Morimoto, T. Matui, M. Fujigaki, and A. Matsui, “Three-dimensional displacement analysis by windowed phase-shifting digital holographic interferometry,” Strain 44, 49–56 (2008).
[CrossRef]

Matui, T.

Y. Morimoto, T. Matui, M. Fujigaki, and A. Matsui, “Three-dimensional displacement analysis by windowed phase-shifting digital holographic interferometry,” Strain 44, 49–56 (2008).
[CrossRef]

Y. Morimoto, T. Matui, and M. Fujigaki, “Application of three-dimensional displacement and strain distribution measurement by windowed phase-shifting digital holographic interferometry,” Adv. Mater. Res. 47–50, 1262–1265 (2008).
[CrossRef]

Mendoza-Santoyo, F.

Moisson, E.

Moreno, I.

Morimoto, Y.

Y. Morimoto, T. Matui, M. Fujigaki, and A. Matsui, “Three-dimensional displacement analysis by windowed phase-shifting digital holographic interferometry,” Strain 44, 49–56 (2008).
[CrossRef]

Y. Morimoto, T. Matui, and M. Fujigaki, “Application of three-dimensional displacement and strain distribution measurement by windowed phase-shifting digital holographic interferometry,” Adv. Mater. Res. 47–50, 1262–1265 (2008).
[CrossRef]

Mounier, D.

Pedrini, G.

Perez-Lopez, C.

M. De la Torre-Ibarra, F. M. Santoyo, C. Perez-Lopez, T. S. Anaya, and D. D. Aguayo, “Surface strain distribution on thin metallic plates using 3-D digital holographic interferometry,” Opt. Eng. 45 (2006).
[CrossRef]

M. De La Torre-Ibarra, F. Mendoza-Santoyo, C. Perez-Lopez, and T. Saucedo-A, “Detection of surface strain by three-dimensional digital holography,” Appl. Opt. 44, 27–31(2005).
[PubMed]

Picart, P.

Rajshekhar, G.

Rastogi, P.

Santoyo, F. M.

T. Saucedo-A, M. H. De La Torre-Ibarra, F. M. Santoyo, and I. Moreno, “Digital holographic interferometer using simultaneously three lasers and a single monochrome sensor for 3d displacement measurements,” Opt. Express 18, 19867–19875 (2010).
[CrossRef] [PubMed]

M. De la Torre-Ibarra, F. M. Santoyo, C. Perez-Lopez, T. S. Anaya, and D. D. Aguayo, “Surface strain distribution on thin metallic plates using 3-D digital holographic interferometry,” Opt. Eng. 45 (2006).
[CrossRef]

Saucedo-A, T.

Schnars, U.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Tiziani, H. J.

Zou, Y. L.

Adv. Mater. Res.

Y. Morimoto, T. Matui, and M. Fujigaki, “Application of three-dimensional displacement and strain distribution measurement by windowed phase-shifting digital holographic interferometry,” Adv. Mater. Res. 47–50, 1262–1265 (2008).
[CrossRef]

Appl. Opt.

Meas. Sci. Technol.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Opt. Eng.

M. De la Torre-Ibarra, F. M. Santoyo, C. Perez-Lopez, T. S. Anaya, and D. D. Aguayo, “Surface strain distribution on thin metallic plates using 3-D digital holographic interferometry,” Opt. Eng. 45 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Rev. Sci. Instrum.

G. Rajshekhar, S. S. Gorthi, and P. Rastogi, “Strain, curvature, and twist measurements in digital holographic interferometry using pseudo-Wigner-Ville distribution based method,” Rev. Sci. Instrum. 80, 093107 (2009).
[CrossRef] [PubMed]

Strain

Y. Morimoto, T. Matui, M. Fujigaki, and A. Matsui, “Three-dimensional displacement analysis by windowed phase-shifting digital holographic interferometry,” Strain 44, 49–56 (2008).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Dual-beam illumination with red and green wavelengths.

Fig. 2
Fig. 2

Schematic of DHI setup with dual-color illumination. BS1-BS3: Beam splitters, BE1-BE3: Beam Expanders, M1-M3: Mirrors, OBJ: Object.

Fig. 3
Fig. 3

(a) Intensity recorded in green channel. (b) Intensity recorded in red channel. (c)  | Γ g 0 ( x g , y g ) | 2 (d)  | Γ r 0 ( x r , y r ) | 2 (e) Fringe pattern for green wavelength. (f) Fringe pattern for red wavelength.

Fig. 4
Fig. 4

Phase derivatives (a)  ω g ( x g , y g ) , (b)  ω r ( x r , y r ) , and (c)  w interp ( x g , y g ) in radians / μm . (d) The sum λ r ω interp + λ g ω g . (e) The difference λ r ω interp λ g ω g .

Equations (20)

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I r ( x , y ) = | R r ( x , y ) + O r ( x , y ) | 2 = I r 0 ( x , y ) + R r ( x , y ) O r * ( x , y ) + R r * ( x , y ) O r ( x , y )
I g ( x , y ) = | R g ( x , y ) + O g ( x , y ) | 2 = I g 0 ( x , y ) + R g ( x , y ) O g * ( x , y ) + R g * ( x , y ) O g ( x , y ) ,
Γ k 0 ( x , y ) = j λ k d exp [ j π λ k d ( x 2 + y 2 ) ] exp [ j 2 π d λ k ] R k ( x , y ) I k ( x , y ) exp [ j π λ k d ( x 2 + y 2 ) ] exp [ j 2 π λ k d ( x x + y y ) ] x y ,
Γ k 0 ( x , y ) = R k ( x , y ) I k ( x , y ) exp [ j π λ k d ( x 2 + y 2 ) ] exp [ j 2 π λ k d ( x x + y y ) ] x y .
Γ k 0 ( m Δ x k , n Δ y k ) = p = 0 N x 1 q = 0 N y 1 R k ( p Δ x , q Δ y ) I k ( p Δ x , q Δ y ) exp [ j π λ k d ( ( p Δ x ) 2 + ( q Δ y ) 2 ) ] exp [ j 2 π ( p m N x + q n N y ) ]     m [ 0 , N x 1 ] , n [ 0 , N y 1 ] ,
Δ x k = λ k d N x Δ x
Δ y k = λ k d N y Δ y .
Γ k ( x k , y k ) = Γ k 1 ( x k , y k ) Γ k 0 * ( x k , y k ) = a k ( x k , y k ) exp [ j Δ ϕ k ( x k , y k ) ] ,
Δ ϕ r = 2 π λ r d · ( u ^ e ^ r ) = 2 π λ r [ d z ( 1 + cos ( θ ) ) + d x sin ( θ ) ]
Δ ϕ g = 2 π λ g d · ( u ^ e ^ g ) = 2 π λ g [ d z ( 1 + cos ( θ ) ) d x sin ( θ ) ] .
Δ ϕ r y = 2 π λ r [ d z y ( 1 + cos ( θ ) ) + d x y sin ( θ ) ]
Δ ϕ g y = 2 π λ g [ d z y ( 1 + cos ( θ ) ) d x y sin ( θ ) ] .
λ r Δ ϕ r y + λ g Δ ϕ g y = 4 π d z y ( 1 + cos ( θ ) )
λ r Δ ϕ r y λ g Δ ϕ g y = 4 π d x y sin ( θ ) .
G k ( x k , y k , ω 1 , ω 2 ) = w ( τ 1 , τ 2 ) Γ k ( x k + τ 1 , y k + τ 2 ) Γ k * ( x k τ 1 , y k τ 2 ) exp [ 2 j ( ω 1 τ 1 + ω 2 τ 2 ) ] τ 1 τ 2 .
w ( τ 1 , τ 2 ) = 1 2 π σ x σ y exp [ ( τ 1 2 2 σ x 2 + τ 2 2 2 σ y 2 ) ]     τ 1 [ σ x 2 , σ x 2 ] , τ 2 [ σ y 2 , σ y 2 ] ,
[ Δ ϕ k ( x k , y k ) x k , Δ ϕ k ( x k , y k ) y k ] = arg max ω 1 , ω 2 G k ( x k , y k , ω 1 , ω 2 ) .
ω interp ( x g , y g ) = interp 2 ( x r , y r , ω r ( x r , y r ) , x g , y g , spline ) .
λ r ω interp + λ g ω g = 4 π d z y ( 1 + cos ( θ ) )
λ r ω interp λ g ω g = 4 π d x y sin ( θ ) .

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