Abstract

This paper presents a method to measure nanometric displacement fields using digital speckle pattern interferometry, which can be applied when the generated correlation fringes show less than one complete fringe. The method is based on the evaluation of the correlation between the two speckle interferograms generated by both deformation states of the object. The performance of the proposed method is analyzed using computer-simulated speckle interferograms. A comparison with the performance given by a phase-shifting technique is also presented, and the advantages and limitations of the proposed method are discussed. Finally, the performance of the proposed method to process real data is illustrated.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Optical Inspection of Microsystems, W.Osten, ed. (Taylor & Francis, 2007).
  2. Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001).
  3. R. Höfling and P. Aswendt, “Speckle metrology for microsystem inspection,” in Optical Inspection of Microsystems, W.Osten, ed. (Taylor & Francis, 2007), pp. 427–458.
  4. J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 59–139.
  5. J. M. Huntley, “Automated analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105–125 (1998).
    [CrossRef]
  6. B. V. Dorrío and J. L. Fernández, “Phase-evaluation methods in whole-field optical measurement techniques,” Meas. Sci. Technol. 10, R33–R55 (1999).
    [CrossRef]
  7. Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1989).
  8. R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge Univ. Press, 1983).
  9. 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]
  10. J. D. Dobson, Applied Multivariate Data Analysis Volume I: Regression and Experimental Design (Springer-Verlag, 1991).
  11. G. H. Kaufmann, A. Dávila, and D. Kerr, “Digital processing of ESPI addition fringes,” Appl. Opt. 33, 5964–5969 (1994).
    [CrossRef] [PubMed]
  12. L. P. Tendela, A. Federico, and G. H. Kaufmann, “Evaluation of the piezoelectric behavior produced by a thick-film transducer using digital speckle pattern interferometry,” Opt. Lasers Eng. 49, 281–284 (2011).
    [CrossRef]
  13. P. K. Rastogi, “Measurement of static surface displacements, derivatives of displacements and three dimensional surface shape. Examples of applications to non-destructive testing,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 142–224.

2011 (1)

L. P. Tendela, A. Federico, and G. H. Kaufmann, “Evaluation of the piezoelectric behavior produced by a thick-film transducer using digital speckle pattern interferometry,” Opt. Lasers Eng. 49, 281–284 (2011).
[CrossRef]

1999 (1)

B. V. Dorrío and J. L. Fernández, “Phase-evaluation methods in whole-field optical measurement techniques,” Meas. Sci. Technol. 10, R33–R55 (1999).
[CrossRef]

1998 (1)

J. M. Huntley, “Automated analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105–125 (1998).
[CrossRef]

1997 (1)

1994 (1)

Aswendt, P.

R. Höfling and P. Aswendt, “Speckle metrology for microsystem inspection,” in Optical Inspection of Microsystems, W.Osten, ed. (Taylor & Francis, 2007), pp. 427–458.

Dávila, A.

Dobson, J. D.

J. D. Dobson, Applied Multivariate Data Analysis Volume I: Regression and Experimental Design (Springer-Verlag, 1991).

Dorrío, B. V.

B. V. Dorrío and J. L. Fernández, “Phase-evaluation methods in whole-field optical measurement techniques,” Meas. Sci. Technol. 10, R33–R55 (1999).
[CrossRef]

Federico, A.

L. P. Tendela, A. Federico, and G. H. Kaufmann, “Evaluation of the piezoelectric behavior produced by a thick-film transducer using digital speckle pattern interferometry,” Opt. Lasers Eng. 49, 281–284 (2011).
[CrossRef]

Fernández, J. L.

B. V. Dorrío and J. L. Fernández, “Phase-evaluation methods in whole-field optical measurement techniques,” Meas. Sci. Technol. 10, R33–R55 (1999).
[CrossRef]

Höfling, R.

R. Höfling and P. Aswendt, “Speckle metrology for microsystem inspection,” in Optical Inspection of Microsystems, W.Osten, ed. (Taylor & Francis, 2007), pp. 427–458.

Hunt, R. W.

Huntley, J. M.

J. M. Huntley, “Automated analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105–125 (1998).
[CrossRef]

J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 59–139.

Jones, R.

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge Univ. Press, 1983).

Kaufmann, G. H.

L. P. Tendela, A. Federico, and G. H. Kaufmann, “Evaluation of the piezoelectric behavior produced by a thick-film transducer using digital speckle pattern interferometry,” Opt. Lasers Eng. 49, 281–284 (2011).
[CrossRef]

G. H. Kaufmann, A. Dávila, and D. Kerr, “Digital processing of ESPI addition fringes,” Appl. Opt. 33, 5964–5969 (1994).
[CrossRef] [PubMed]

Kerr, D.

Rastogi, P. K.

P. K. Rastogi, “Measurement of static surface displacements, derivatives of displacements and three dimensional surface shape. Examples of applications to non-destructive testing,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 142–224.

Schmitt, D. R.

Tendela, L. P.

L. P. Tendela, A. Federico, and G. H. Kaufmann, “Evaluation of the piezoelectric behavior produced by a thick-film transducer using digital speckle pattern interferometry,” Opt. Lasers Eng. 49, 281–284 (2011).
[CrossRef]

Wykes, C.

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge Univ. Press, 1983).

Appl. Opt. (2)

J. Strain Anal. (1)

J. M. Huntley, “Automated analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105–125 (1998).
[CrossRef]

Meas. Sci. Technol. (1)

B. V. Dorrío and J. L. Fernández, “Phase-evaluation methods in whole-field optical measurement techniques,” Meas. Sci. Technol. 10, R33–R55 (1999).
[CrossRef]

Opt. Lasers Eng. (1)

L. P. Tendela, A. Federico, and G. H. Kaufmann, “Evaluation of the piezoelectric behavior produced by a thick-film transducer using digital speckle pattern interferometry,” Opt. Lasers Eng. 49, 281–284 (2011).
[CrossRef]

Other (8)

P. K. Rastogi, “Measurement of static surface displacements, derivatives of displacements and three dimensional surface shape. Examples of applications to non-destructive testing,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 142–224.

J. D. Dobson, Applied Multivariate Data Analysis Volume I: Regression and Experimental Design (Springer-Verlag, 1991).

Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1989).

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge Univ. Press, 1983).

Optical Inspection of Microsystems, W.Osten, ed. (Taylor & Francis, 2007).

Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001).

R. Höfling and P. Aswendt, “Speckle metrology for microsystem inspection,” in Optical Inspection of Microsystems, W.Osten, ed. (Taylor & Francis, 2007), pp. 427–458.

J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 59–139.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Comparison between the original phase change (thin curve) with the retrieved phase maps obtained using the proposed approach (bold curve) and the Carré phase-shifting technique (solid circles) for a simulated out-of-plane tilt displacement.

Fig. 2
Fig. 2

Comparison between the original phase change (thin curve) with the retrieved phase maps obtained using the proposed approach (bold curve) and the Carré phase-shifting technique (solid circles) for a simulated out-of-plane parabolic displacement.

Fig. 3
Fig. 3

Comparison between the original phase change (thin curve) with the retrieved phase maps obtained using the proposed approach (bold curve) and the Carré phase-shifting technique (solid circles) for a simulated out-of-plane generic displacement.

Fig. 4
Fig. 4

Optical arrangement of the out-of-plane digital speckle pattern interferometer: Nd:Yag laser; M, mirrors; PT, piezoelectric transducer; L, microscope objectives; BS, beam splitters; PH, pin holes; CL, camera lens.

Fig. 5
Fig. 5

Out-of-plane displacement component w along a line crossing the center of the steel plate obtained using the proposed approach (bold curve), with its linear fit (thin curve) and the Carré phase-shifting technique (solid circles).

Equations (21)

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

I = I 1 + I 2 + 2 I 1 I 2 cos ( ϕ 1 ϕ 2 ) = I 0 + I M cos ϕ ,
I a = I a 0 + I a M cos ϕ a = I a 0 + I a M cos ϕ s , I b = I b 0 + I b M cos ϕ b = I b 0 + I b M cos ( ϕ s + Δ ϕ ) ,
C ( p , q ) = ( p p ) ( q q ) [ ( p 2 p 2 ) ( q 2 q 2 ) ] 1 / 2 ,
C = ( I a I a 0 I a I a 0 ) ( I b I b 0 I b I b 0 ) [ ( ( I a I a 0 ) 2 I a I a 0 2 ) ( ( I b I b 0 ) 2 I b I b 0 2 ) ] 1 / 2 = ( I a M cos ϕ a I a M cos ϕ a ) ( I b M cos ϕ b I b M cos ϕ b ) [ ( I a M 2 cos 2 ϕ a I a M cos ϕ a 2 ) ( I b M 2 cos 2 ϕ b I b M cos ϕ b 2 ) ] 1 / 2 ,
N a b = ( I a M cos ϕ a I a M cos ϕ a ) ( I b M cos ϕ b I b M cos ϕ b ) = ( I a M cos ϕ s I a M cos ϕ s ) ( I b M cos ϕ s I b M cos ϕ s ) cos Δ ϕ ( I a M cos ϕ s I a M cos ϕ s ) ( I b M sin ϕ s I b M sin ϕ s ) sin Δ ϕ .
I M cos ϕ s = I M cos ϕ s , I M sin ϕ s = I M sin ϕ s , I M 2 sin 2 ϕ s = I M 2 cos 2 ϕ s , sin ϕ s = cos ϕ s 0 , sin ϕ s cos ϕ s 0.
N a b I a M I b M cos 2 ϕ s cos Δ ϕ .
D a b = [ ( I a M 2 cos 2 ϕ a I a M cos ϕ a 2 ) ( I b M 2 cos 2 ϕ b I b M cos ϕ b 2 ) ] 1 / 2 = { ( I a M 2 cos 2 ϕ s I a M cos ϕ s 2 ) [ I b M 2 ( cos ϕ s cos Δ ϕ sin ϕ s sin Δ ϕ ) 2 I b M ( cos ϕ s cos Δ ϕ sin ϕ s sin Δ ϕ ) 2 ] } 1 / 2 .
D a b [ I a M 2 cos 2 ϕ s ( I b M 2 cos 2 ϕ s cos 2 Δ ϕ + I b M 2 sin 2 ϕ s sin 2 Δ ϕ ) ] 1 / 2 = [ I a M 2 cos 2 ϕ s I b M 2 cos 2 ϕ s ] 1 / 2 .
C ( I a I a 0 , I b I b 0 ) I a M I b M cos 2 ϕ s cos Δ ϕ [ I a M 2 cos 2 ϕ s I b M 2 cos 2 ϕ s ] 1 / 2 .
C ( I a I a 0 , I b I b 0 ) = I a M I b M I a M 2 I b M 2 cos Δ ϕ .
Δ ϕ = acos [ C ( I a I a 0 , I b I b 0 ) I a M 2 I b M 2 I a M I b M ] ,
I a = | R exp ( j α ) + F 1 H F [ exp ( j ϕ s ) ] | 2 ,
H ( ρ ) = { 1 ρ D / 2 0 ρ > D / 2 ,
I b = | R exp ( j α ) + F 1 H F { exp [ j ( ϕ s + Δ ϕ o ) ] } | 2 ,
σ = { 1 L m = 1 L n = 1 L [ e ( m , n ) e ] 2 } 1 / 2 ,
e ( m , n ) = | Δ ϕ ( m , n ) Δ ϕ o ( m , n ) | ,
I a k = | R + F 1 H F { exp [ j ( ϕ s + γ k ) ] } | 2 ,
I b k = | R + F 1 H F { exp [ j ( ϕ s + Δ ϕ o + γ k ) ] } | 2 .
γ 1 = 0 , γ 2 = γ ( 1 + ε ) , γ 3 = 2 γ ( 1 ε ) , γ 4 = 3 γ ( 1 + ε ) .
w = λ 4 π Δ ϕ ,

Metrics