Abstract

We present the simultaneous measurement of three-dimensional deformations by electronic speckle pattern interferometry using five object beams and three colors. Each color, corresponding to an orthogonal direction of displacement, is separated through dichroic filtering before being recorded by a separate CCD camera. Carrier fringes are introduced by tilting the beam path in one arm of each of the three interferometers. The measured deformation modulates these carrier fringes and is extracted using the Fourier-transform method to achieve high displacement sensitivity. The field of view is on the order of a millimeter, making the system suitable for study of microstructural deformations. We compare experimental results with calculated values to validate out-of-plane and in-plane deformation measurements and demonstrate sensitivity on the order of 10  nm.

© 2006 Optical Society of America

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  1. G. L. Cloud, Optical Methods of Engineering Analysis (Cambridge U. Press, 1995).
    [CrossRef]
  2. R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, 1989).
  3. K. Creath, "Phase-shifting speckle interferometry," Appl. Opt. 24, 3053-3058 (1985).
    [CrossRef] [PubMed]
  4. M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982).
    [CrossRef]
  5. A. J. Moore and C. Pérez-López, "Fringe carrier methods in double-pulsed addition ESPI," Opt. Commun. 141, 203-212 (1997).
    [CrossRef]
  6. D. I. Farrant, G. H. Kaufmann, J. N. Petzing, J. R. Tyrer, B. F. Oreb, and D. Kerr, "Measurement of transient deformations with dual-pulse addition electronic speckle-pattern interferometry," Appl. Opt. 37, 7259-7267 (1998).
    [CrossRef]
  7. A. Fernández, J. Blanco-García, A. F. Doval, J. Bugarín, B. V. Dorrío, C. López, J. M. Alén, M. Pérez-Amor, and J. L. Fernández, "Transient deformation measurement by double-pulsed-subtraction TV holography and the Fourier transform method," Appl. Opt. 37, 3440-3446 (1998).
    [CrossRef]
  8. S. Winther, "3D strain measurements using ESPI," Opt. Lasers Eng. 8, 45-57 (1988).
    [CrossRef]
  9. L. S. Wang, K. Jambunathan, B. N. Dobbins, and S. P. He, "Measurement of three-dimensional surface shape and deformations using phase stepping speckle interferometry," Opt. Eng. 35, 2333-2340 (1996).
    [CrossRef]
  10. A. Martínez, J. A. Rayas, R. Rodríguez-Vera, and H. J. Puga, "Three-dimensional deformation measurement from the combination of in-plane and out-of-plane electronic speckle pattern interferometers," Appl. Opt. 43, 4652-4658 (2004).
    [CrossRef] [PubMed]
  11. G. Pedrini and H. J. Tiziani, "Double-pulse electronic speckle interferometry for vibration analysis," Appl. Opt. 33, 7857-7863 (1994).
    [CrossRef] [PubMed]
  12. A. J. Moore and J. R. Tyrer, "An electronic speckle pattern interferometer for complete in-plane displacement measurement," Meas. Sci. Technol. 1, 1024-1030 (1990).
    [CrossRef]
  13. T. Takatsuji, B. F. Oreb, D. I. Farrant, and P. S. Fairman, "Simultaneous measurement of vector components of displacements by ESPI and FFT techniques," in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, and M. Takeda, eds., Proc. SPIE 2544, 309-316 (1995).
  14. T. Takatsuji, B. F. Oreb, I. Farrant, and J. R. Tyrer, "Simultaneous measurement of three orthogonal components of displacement by electronic speckle-pattern interferometry and the Fourier transform method," Appl. Opt. 36, 1438-1445 (1997).
    [CrossRef] [PubMed]
  15. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  16. J. B. Hurtado-Ramos, J. Blanco-García, A. Fernández, and F. Ribas, "An ESPI system for determining in-plane deformations. Three-dimensional analysis of the carrier fringes and a proposal for analysis of transient in-plane deformations," Meas. Sci. Technol. 12, 644-651 (2001).
    [CrossRef]
  17. T. Yoshimura, M. Zhou, K. Yamahai, and Z. Liyan, "Optimum determination of speckle size to be used in electronic speckle pattern interferometry," Appl. Opt. 34, 87-91 (1995).
    [CrossRef] [PubMed]
  18. Y. Arai and S. Yokozeki, "Electronic speckle pattern interferometry based on spatial fringe analysis method," in Optical Measurement Systems for Industrial Inspection II: Application in Industrial Design, W.Osten, W.P. O.Jueptner, and M.Kujawinska, eds., Proc. SPIE 4398, 14-22 (2001).
  19. C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Speckle interferometry with temporal phase evaluation for measuring large-object deformation," Appl. Opt. 37, 2608-2614 (1998).
    [CrossRef]

2004 (1)

2001 (1)

J. B. Hurtado-Ramos, J. Blanco-García, A. Fernández, and F. Ribas, "An ESPI system for determining in-plane deformations. Three-dimensional analysis of the carrier fringes and a proposal for analysis of transient in-plane deformations," Meas. Sci. Technol. 12, 644-651 (2001).
[CrossRef]

1998 (3)

1997 (2)

1996 (1)

L. S. Wang, K. Jambunathan, B. N. Dobbins, and S. P. He, "Measurement of three-dimensional surface shape and deformations using phase stepping speckle interferometry," Opt. Eng. 35, 2333-2340 (1996).
[CrossRef]

1995 (2)

T. Takatsuji, B. F. Oreb, D. I. Farrant, and P. S. Fairman, "Simultaneous measurement of vector components of displacements by ESPI and FFT techniques," in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, and M. Takeda, eds., Proc. SPIE 2544, 309-316 (1995).

T. Yoshimura, M. Zhou, K. Yamahai, and Z. Liyan, "Optimum determination of speckle size to be used in electronic speckle pattern interferometry," Appl. Opt. 34, 87-91 (1995).
[CrossRef] [PubMed]

1994 (1)

1990 (1)

A. J. Moore and J. R. Tyrer, "An electronic speckle pattern interferometer for complete in-plane displacement measurement," Meas. Sci. Technol. 1, 1024-1030 (1990).
[CrossRef]

1988 (1)

S. Winther, "3D strain measurements using ESPI," Opt. Lasers Eng. 8, 45-57 (1988).
[CrossRef]

1985 (1)

1982 (1)

Alén, J. M.

Arai, Y.

Y. Arai and S. Yokozeki, "Electronic speckle pattern interferometry based on spatial fringe analysis method," in Optical Measurement Systems for Industrial Inspection II: Application in Industrial Design, W.Osten, W.P. O.Jueptner, and M.Kujawinska, eds., Proc. SPIE 4398, 14-22 (2001).

Blanco-García, J.

J. B. Hurtado-Ramos, J. Blanco-García, A. Fernández, and F. Ribas, "An ESPI system for determining in-plane deformations. Three-dimensional analysis of the carrier fringes and a proposal for analysis of transient in-plane deformations," Meas. Sci. Technol. 12, 644-651 (2001).
[CrossRef]

A. Fernández, J. Blanco-García, A. F. Doval, J. Bugarín, B. V. Dorrío, C. López, J. M. Alén, M. Pérez-Amor, and J. L. Fernández, "Transient deformation measurement by double-pulsed-subtraction TV holography and the Fourier transform method," Appl. Opt. 37, 3440-3446 (1998).
[CrossRef]

Bugarín, J.

Cloud, G. L.

G. L. Cloud, Optical Methods of Engineering Analysis (Cambridge U. Press, 1995).
[CrossRef]

Creath, K.

Dobbins, B. N.

L. S. Wang, K. Jambunathan, B. N. Dobbins, and S. P. He, "Measurement of three-dimensional surface shape and deformations using phase stepping speckle interferometry," Opt. Eng. 35, 2333-2340 (1996).
[CrossRef]

Dorrío, B. V.

Doval, A. F.

Fairman, P. S.

T. Takatsuji, B. F. Oreb, D. I. Farrant, and P. S. Fairman, "Simultaneous measurement of vector components of displacements by ESPI and FFT techniques," in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, and M. Takeda, eds., Proc. SPIE 2544, 309-316 (1995).

Farrant, D. I.

D. I. Farrant, G. H. Kaufmann, J. N. Petzing, J. R. Tyrer, B. F. Oreb, and D. Kerr, "Measurement of transient deformations with dual-pulse addition electronic speckle-pattern interferometry," Appl. Opt. 37, 7259-7267 (1998).
[CrossRef]

T. Takatsuji, B. F. Oreb, D. I. Farrant, and P. S. Fairman, "Simultaneous measurement of vector components of displacements by ESPI and FFT techniques," in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, and M. Takeda, eds., Proc. SPIE 2544, 309-316 (1995).

Farrant, I.

Fernández, A.

J. B. Hurtado-Ramos, J. Blanco-García, A. Fernández, and F. Ribas, "An ESPI system for determining in-plane deformations. Three-dimensional analysis of the carrier fringes and a proposal for analysis of transient in-plane deformations," Meas. Sci. Technol. 12, 644-651 (2001).
[CrossRef]

A. Fernández, J. Blanco-García, A. F. Doval, J. Bugarín, B. V. Dorrío, C. López, J. M. Alén, M. Pérez-Amor, and J. L. Fernández, "Transient deformation measurement by double-pulsed-subtraction TV holography and the Fourier transform method," Appl. Opt. 37, 3440-3446 (1998).
[CrossRef]

Fernández, J. L.

Franze, B.

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Haible, P.

He, S. P.

L. S. Wang, K. Jambunathan, B. N. Dobbins, and S. P. He, "Measurement of three-dimensional surface shape and deformations using phase stepping speckle interferometry," Opt. Eng. 35, 2333-2340 (1996).
[CrossRef]

Hurtado-Ramos, J. B.

J. B. Hurtado-Ramos, J. Blanco-García, A. Fernández, and F. Ribas, "An ESPI system for determining in-plane deformations. Three-dimensional analysis of the carrier fringes and a proposal for analysis of transient in-plane deformations," Meas. Sci. Technol. 12, 644-651 (2001).
[CrossRef]

Ina, H.

Jambunathan, K.

L. S. Wang, K. Jambunathan, B. N. Dobbins, and S. P. He, "Measurement of three-dimensional surface shape and deformations using phase stepping speckle interferometry," Opt. Eng. 35, 2333-2340 (1996).
[CrossRef]

Joenathan, C.

Jones, R.

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, 1989).

Kaufmann, G. H.

Kerr, D.

Kobayashi, S.

Liyan, Z.

López, C.

Martínez, A.

Moore, A. J.

A. J. Moore and C. Pérez-López, "Fringe carrier methods in double-pulsed addition ESPI," Opt. Commun. 141, 203-212 (1997).
[CrossRef]

A. J. Moore and J. R. Tyrer, "An electronic speckle pattern interferometer for complete in-plane displacement measurement," Meas. Sci. Technol. 1, 1024-1030 (1990).
[CrossRef]

Oreb, B. F.

Pedrini, G.

Pérez-Amor, M.

Pérez-López, C.

A. J. Moore and C. Pérez-López, "Fringe carrier methods in double-pulsed addition ESPI," Opt. Commun. 141, 203-212 (1997).
[CrossRef]

Petzing, J. N.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Puga, H. J.

Rayas, J. A.

Ribas, F.

J. B. Hurtado-Ramos, J. Blanco-García, A. Fernández, and F. Ribas, "An ESPI system for determining in-plane deformations. Three-dimensional analysis of the carrier fringes and a proposal for analysis of transient in-plane deformations," Meas. Sci. Technol. 12, 644-651 (2001).
[CrossRef]

Rodríguez-Vera, R.

Takatsuji, T.

T. Takatsuji, B. F. Oreb, I. Farrant, and J. R. Tyrer, "Simultaneous measurement of three orthogonal components of displacement by electronic speckle-pattern interferometry and the Fourier transform method," Appl. Opt. 36, 1438-1445 (1997).
[CrossRef] [PubMed]

T. Takatsuji, B. F. Oreb, D. I. Farrant, and P. S. Fairman, "Simultaneous measurement of vector components of displacements by ESPI and FFT techniques," in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, and M. Takeda, eds., Proc. SPIE 2544, 309-316 (1995).

Takeda, M.

Tiziani, H. J.

Tyrer, J. R.

Wang, L. S.

L. S. Wang, K. Jambunathan, B. N. Dobbins, and S. P. He, "Measurement of three-dimensional surface shape and deformations using phase stepping speckle interferometry," Opt. Eng. 35, 2333-2340 (1996).
[CrossRef]

Winther, S.

S. Winther, "3D strain measurements using ESPI," Opt. Lasers Eng. 8, 45-57 (1988).
[CrossRef]

Wykes, C.

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, 1989).

Yamahai, K.

Yokozeki, S.

Y. Arai and S. Yokozeki, "Electronic speckle pattern interferometry based on spatial fringe analysis method," in Optical Measurement Systems for Industrial Inspection II: Application in Industrial Design, W.Osten, W.P. O.Jueptner, and M.Kujawinska, eds., Proc. SPIE 4398, 14-22 (2001).

Yoshimura, T.

Zhou, M.

Appl. Opt. (8)

K. Creath, "Phase-shifting speckle interferometry," Appl. Opt. 24, 3053-3058 (1985).
[CrossRef] [PubMed]

A. Martínez, J. A. Rayas, R. Rodríguez-Vera, and H. J. Puga, "Three-dimensional deformation measurement from the combination of in-plane and out-of-plane electronic speckle pattern interferometers," Appl. Opt. 43, 4652-4658 (2004).
[CrossRef] [PubMed]

G. Pedrini and H. J. Tiziani, "Double-pulse electronic speckle interferometry for vibration analysis," Appl. Opt. 33, 7857-7863 (1994).
[CrossRef] [PubMed]

D. I. Farrant, G. H. Kaufmann, J. N. Petzing, J. R. Tyrer, B. F. Oreb, and D. Kerr, "Measurement of transient deformations with dual-pulse addition electronic speckle-pattern interferometry," Appl. Opt. 37, 7259-7267 (1998).
[CrossRef]

A. Fernández, J. Blanco-García, A. F. Doval, J. Bugarín, B. V. Dorrío, C. López, J. M. Alén, M. Pérez-Amor, and J. L. Fernández, "Transient deformation measurement by double-pulsed-subtraction TV holography and the Fourier transform method," Appl. Opt. 37, 3440-3446 (1998).
[CrossRef]

T. Takatsuji, B. F. Oreb, I. Farrant, and J. R. Tyrer, "Simultaneous measurement of three orthogonal components of displacement by electronic speckle-pattern interferometry and the Fourier transform method," Appl. Opt. 36, 1438-1445 (1997).
[CrossRef] [PubMed]

T. Yoshimura, M. Zhou, K. Yamahai, and Z. Liyan, "Optimum determination of speckle size to be used in electronic speckle pattern interferometry," Appl. Opt. 34, 87-91 (1995).
[CrossRef] [PubMed]

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Speckle interferometry with temporal phase evaluation for measuring large-object deformation," Appl. Opt. 37, 2608-2614 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (2)

A. J. Moore and J. R. Tyrer, "An electronic speckle pattern interferometer for complete in-plane displacement measurement," Meas. Sci. Technol. 1, 1024-1030 (1990).
[CrossRef]

J. B. Hurtado-Ramos, J. Blanco-García, A. Fernández, and F. Ribas, "An ESPI system for determining in-plane deformations. Three-dimensional analysis of the carrier fringes and a proposal for analysis of transient in-plane deformations," Meas. Sci. Technol. 12, 644-651 (2001).
[CrossRef]

Opt. Commun. (1)

A. J. Moore and C. Pérez-López, "Fringe carrier methods in double-pulsed addition ESPI," Opt. Commun. 141, 203-212 (1997).
[CrossRef]

Opt. Eng. (1)

L. S. Wang, K. Jambunathan, B. N. Dobbins, and S. P. He, "Measurement of three-dimensional surface shape and deformations using phase stepping speckle interferometry," Opt. Eng. 35, 2333-2340 (1996).
[CrossRef]

Opt. Lasers Eng. (1)

S. Winther, "3D strain measurements using ESPI," Opt. Lasers Eng. 8, 45-57 (1988).
[CrossRef]

Proc. SPIE (1)

T. Takatsuji, B. F. Oreb, D. I. Farrant, and P. S. Fairman, "Simultaneous measurement of vector components of displacements by ESPI and FFT techniques," in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, and M. Takeda, eds., Proc. SPIE 2544, 309-316 (1995).

Other (4)

G. L. Cloud, Optical Methods of Engineering Analysis (Cambridge U. Press, 1995).
[CrossRef]

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, 1989).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Y. Arai and S. Yokozeki, "Electronic speckle pattern interferometry based on spatial fringe analysis method," in Optical Measurement Systems for Industrial Inspection II: Application in Industrial Design, W.Osten, W.P. O.Jueptner, and M.Kujawinska, eds., Proc. SPIE 4398, 14-22 (2001).

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Figures (9)

Fig. 1
Fig. 1

Illumination of the sample by one OOP, two HIP, and two VIP beams. The dashed lines show the beams after the mirrors have been tilted and translated (exaggerated in figure). The mirror tilt in the OOP interferometer is made in the reference arm (not shown). All of the light collected by the imaging lens (not shown) and directed to the CCDs is that which is scattered near normal to the sample surface. Acronyms defined in text.

Fig. 2
Fig. 2

Schematic of the color separation system showing light of all three wavelengths scattered normal to the sample: solid line, 543 nm OOP; dotted line, 405 nm HIP; dashed line, 633 nm VIP. Thin lines indicate low transmission or reflection from filters 1 and 2. All key elements of the OOP interferometer are included to show the lenses in the incoming beam and the reference arm that ensure that the conjugacy condition is met. Acronyms defined in text.

Fig. 3
Fig. 3

Carrier fringes in the OOP interferograms (a) before the sample tilt deformation (image 2 minus image 1) and (b) after the sample tilt deformation (image 3 minus image 1). Note that there is a change in frequency of the fringes after deformation [approximately one less fringe in (b)].

Fig. 4
Fig. 4

Carrier fringes after the rotation deformation in the (a) HIP and (b) VIP image 3 minus image 1 interferograms. The fringes were initially vertical and horizontal, respectively, in the image 2 minus image 1 interferograms.

Fig. 5
Fig. 5

Central 125 × 125 pixels of the 2D Fourier transform of the interferogram in Fig. 3(a). The circle around the peak at the positive carrier frequency (f 0) illustrates a mask for the data near the peak.

Fig. 6
Fig. 6

Unwrapped phase map corresponding to OOP displacement for the sample tilt deformation. Phase changes shown are relative.

Fig. 7
Fig. 7

Vector plot showing the combined results of the HIP and VIP interferometers for the rotation test. A vector is shown for every 30th pixel in each direction on the 768 × 512 pixel field: black, experimental; gray, analytical. The sample was rotated 0.023°.

Fig. 8
Fig. 8

Speckle intensity averaged over rows for the undeformed HIP carrier fringes corresponding to those in Fig. 4(a) and a sinusoidal fit for determination of depth of modulation.

Fig. 9
Fig. 9

Depth of modulation for the sample with a rms roughness of 0.95 μm for the (a) OOP and (b) IP interferometers. In (b) the dotted trend lines correspond to the HIP data.

Tables (2)

Tables Icon

Table 1 Percentage of Each Wavelength on Each CCD

Tables Icon

Table 2 Sensitivity Measurements (in nm)a

Equations (2)

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Δ d OOP = λ 4 π Δ φ ,
Δ d IP = λ 4 π Δ φ sin θ ,

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