Abstract

Three-dimensional digital holography with three object-illuminating beams has been successfully used for the detection of surface strain in metallic objects. The optical setup that uses illuminating beams to irradiate the object from three directions means that all three object surface displacement components, x, y, and z, can be independently calculated and used to find the strain gradients on the surface. The results show the conversion of the complete surface displacement field into a surface strain field. The method is capable of measuring microstrains for out-of-plane surface displacements of less than 10 μm.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2000 (1)

1999 (3)

J. F. Roman, J. N. Petzing, J. R. Tyrer, “Analysis of loaded mandible behavior using speckle pattern interferometry,” Strain 35, 3–6 (1999).
[CrossRef]

S. Schedin, G. Pedrini, H. J. Tiziani, F. Mendoza Santoyo, “Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography,” Appl. Opt. 38, 7056–7062 (1999).
[CrossRef]

F. Mendoza Santoyo, G. Pedrini, S. Schendin, H. J. Tiziani, “3D displacement measurements of vibrating objects with multi-pulse digital holography,” Meas. Sci. Technol. 10, 1305–1308 (1999).
[CrossRef]

1997 (1)

1991 (1)

1989 (1)

F. Mendoza Santoyo, D. Kerr, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–204 (1989).
[CrossRef]

1982 (1)

1981 (1)

1973 (1)

Blanco-García, J.

Cloud, G.

G. Cloud, Optical Methods of Engineering Analysis, 1st ed. (Cambridge U. Press, New York, 1995).
[CrossRef]

Dally, J. W.

J. W. Dally, W. F. Riley, Experimental Stress Analysis, 3rd ed. (Mc Graw-Hill, New York, 1991).

Doval, A. F.

Feiel, R.

Fernández, A.

Gilbert, J. A.

Hertzberg, R. W.

R. W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials (Wiley, New York, 1996).

Ina, H.

Kerr, D.

F. Mendoza Santoyo, D. Kerr, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–204 (1989).
[CrossRef]

Khan, A. S.

A. S. Khan, X. Wang, Strain Measurements and Stress Analysis, 1st ed. (Prentice-Hall, Upper Saddle River, N.J., 2001).

Kobayashi, S.

Mendoza Santoyo, F.

F. Mendoza Santoyo, G. Pedrini, S. Schendin, H. J. Tiziani, “3D displacement measurements of vibrating objects with multi-pulse digital holography,” Meas. Sci. Technol. 10, 1305–1308 (1999).
[CrossRef]

S. Schedin, G. Pedrini, H. J. Tiziani, F. Mendoza Santoyo, “Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography,” Appl. Opt. 38, 7056–7062 (1999).
[CrossRef]

F. Mendoza Santoyo, M. C. Shellabear, J. R. Tyrer, “Whole field in-plane vibration analysis using pulsed phase-stepped ESPI,” Appl. Opt. 30, 717–721 (1991).
[CrossRef]

F. Mendoza Santoyo, D. Kerr, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–204 (1989).
[CrossRef]

Monneret, J.

Moore, A. J.

Pedrini, G.

S. Schedin, G. Pedrini, H. J. Tiziani, F. Mendoza Santoyo, “Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography,” Appl. Opt. 38, 7056–7062 (1999).
[CrossRef]

F. Mendoza Santoyo, G. Pedrini, S. Schendin, H. J. Tiziani, “3D displacement measurements of vibrating objects with multi-pulse digital holography,” Meas. Sci. Technol. 10, 1305–1308 (1999).
[CrossRef]

Pérez-López, C.

Petzing, J. N.

J. F. Roman, J. N. Petzing, J. R. Tyrer, “Analysis of loaded mandible behavior using speckle pattern interferometry,” Strain 35, 3–6 (1999).
[CrossRef]

Rastogi, P. K.

Riley, W. F.

J. W. Dally, W. F. Riley, Experimental Stress Analysis, 3rd ed. (Mc Graw-Hill, New York, 1991).

Roman, J. F.

J. F. Roman, J. N. Petzing, J. R. Tyrer, “Analysis of loaded mandible behavior using speckle pattern interferometry,” Strain 35, 3–6 (1999).
[CrossRef]

Schedin, S.

Schendin, S.

F. Mendoza Santoyo, G. Pedrini, S. Schendin, H. J. Tiziani, “3D displacement measurements of vibrating objects with multi-pulse digital holography,” Meas. Sci. Technol. 10, 1305–1308 (1999).
[CrossRef]

Sciammarella, C. A.

Shellabear, M. C.

Spajer, M.

Takeda, M.

Tiziani, H. J.

F. Mendoza Santoyo, G. Pedrini, S. Schendin, H. J. Tiziani, “3D displacement measurements of vibrating objects with multi-pulse digital holography,” Meas. Sci. Technol. 10, 1305–1308 (1999).
[CrossRef]

S. Schedin, G. Pedrini, H. J. Tiziani, F. Mendoza Santoyo, “Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography,” Appl. Opt. 38, 7056–7062 (1999).
[CrossRef]

Tyrer, J. R.

J. F. Roman, J. N. Petzing, J. R. Tyrer, “Analysis of loaded mandible behavior using speckle pattern interferometry,” Strain 35, 3–6 (1999).
[CrossRef]

F. Mendoza Santoyo, M. C. Shellabear, J. R. Tyrer, “Whole field in-plane vibration analysis using pulsed phase-stepped ESPI,” Appl. Opt. 30, 717–721 (1991).
[CrossRef]

F. Mendoza Santoyo, D. Kerr, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–204 (1989).
[CrossRef]

Wang, X.

A. S. Khan, X. Wang, Strain Measurements and Stress Analysis, 1st ed. (Prentice-Hall, Upper Saddle River, N.J., 2001).

Wilksch, P.

Appl. Opt. (6)

J. Mod. Opt. (1)

F. Mendoza Santoyo, D. Kerr, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–204 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

F. Mendoza Santoyo, G. Pedrini, S. Schendin, H. J. Tiziani, “3D displacement measurements of vibrating objects with multi-pulse digital holography,” Meas. Sci. Technol. 10, 1305–1308 (1999).
[CrossRef]

Strain (1)

J. F. Roman, J. N. Petzing, J. R. Tyrer, “Analysis of loaded mandible behavior using speckle pattern interferometry,” Strain 35, 3–6 (1999).
[CrossRef]

Other (4)

J. W. Dally, W. F. Riley, Experimental Stress Analysis, 3rd ed. (Mc Graw-Hill, New York, 1991).

R. W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials (Wiley, New York, 1996).

A. S. Khan, X. Wang, Strain Measurements and Stress Analysis, 1st ed. (Prentice-Hall, Upper Saddle River, N.J., 2001).

G. Cloud, Optical Methods of Engineering Analysis, 1st ed. (Cambridge U. Press, New York, 1995).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Out-of-plane optical setup for either ESPI or DH: M1, M2, mirrors 1 and 2; BS1, BS2, beam splitters 1 and 2; OF1, OF2, optical fibers 1 and 2; A, aperture; L, lens; P1, P2, P3, illumination positions 1, 2, and 3. (b) Imaginary sphere with minimum optical path difference. P1, P2, P3, object illumination positions 1, 2, and 3, respectively.

Fig. 2
Fig. 2

(a) Dented surface, (b) planar surface.

Fig. 3
Fig. 3

ɛxx for the surface in Fig. 2(a).

Fig. 4
Fig. 4

ɛyy for the surface in Fig. 2(a).

Fig. 5
Fig. 5

ɛxx for the surface in Fig. 2(b).

Fig. 6
Fig. 6

Surface with abrupt relief.

Fig. 7
Fig. 7

ɛxx for the surface in Fig. 6.

Fig. 8
Fig. 8

ɛyy for the surface in Fig. 6.

Equations (10)

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σ = E ɛ ,
ɛ y y = σ y y / E ,
ɛ x x = ɛ z z = - ( ν σ y y / E ) ,
ɛ x x = [ 1 + 2 u x + ( u x ) 2 + ( v x ) 2 + ( w x ) 2 ] 1 / 2 - 1 ,
ɛ y y = [ 1 + 2 v y + ( v y ) 2 + ( w y ) 2 + ( u y ) 2 ] 1 / 2 - 1 ,
ɛ z z = [ 1 + 2 w z + ( w z ) 2 + ( u z ) 2 + ( v z ) 2 ] 1 / 2 - 1 ,
ɛ x x = u x ,
ɛ y y = v y ,
I ( x , y ) = I A + I B + 2 I A I B cos ( ϕ + ψ ) ,
λ 2 π ( Δ ψ 1 Δ ψ 2 Δ ψ 3 ) = [ k 1 x k 1 y k 1 z k 2 x k 2 y k 2 z k 3 x k 3 y k 3 z ] ( u v w ) ,

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