Abstract

An optical setup that can be switched to produce in-plane and out-of-plane sensitivity interferometers was designed for three-dimensional deformation measuring by electronic speckle pattern interferometry. Divergent illumination is considered in the evaluation of sensitivity vectors to measure both in-plane and out-of-plane displacement components. The combination of these interferometers presents the advantage of greater sensitivity in directions u, v, and w than a typical interferometer with three illumination beams provides. The system and its basic operation are described, and results with an elastic target that is exposed to a mechanical load are reported.

© 2004 Optical Society of America

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References

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  1. W. Jüptner, W. Osten, eds., Holographic Interferometry (Akademie Verlag, New York, 1996), pp. 259–266, pp. 171–173, pp. 125–149.
  2. R. S. Sirohi, F. S. Chau, Optical Methods of Measurement: Whole Field Techniques (Marcel Dekker, New York, 1999), Chap. 6, pp. 174–176.
  3. A. Asundi, “Moiré interferometry for deformation measurement,” Opt. Lasers Eng. 11, 281–292 (1989).
    [CrossRef]
  4. J. Schmit, K. Patorski, K. Creath, “Simultaneous registration of in- and out-of-plane displacements in modified grating interferometry,” Opt. Eng. 36, 2240–2248 (1997).
    [CrossRef]
  5. A. Martínez, R. Rodríguez-Vera, J. A. Rayas, J. F. Vázquez, “Influence of object roughness on specimen gratings for moiré interferometry,” Opt. Eng. 40, 1978–1983 (2001).
    [CrossRef]
  6. J. A. Rayas, A. Martínez, R. Rodríguez-Vera, S. Calixto, “Development in situ for gratings recorded in photoresist,” Appl. Opt. 42, 6877–6879 (2003).
    [CrossRef] [PubMed]
  7. S. Winther, “3D strain measurements using ESPI,” Opt. Lasers Eng. 8, 45–57 (1988).
    [CrossRef]
  8. R. Krupka, T. Walz, A. Ettemeyer, “Fast and full-field measurement of brake squeal using pulsed ESPI technique,” Opt. Eng. 42, 1354–1358 (2003).
    [CrossRef]
  9. Dantec Ettemeyer, http://www.ettemeyer.com/espi_ndt_shearography_Win.html .
  10. E. Kolenovic, W. Osten, R. Klattenhoff, S. Lai, Ch. Von Kopylow, W. Jüptner, “Miniaturized digital holography sensor for distal three-dimensional endoscopy,” Appl. Opt. 42, 5167–5172 (2003).
    [CrossRef] [PubMed]
  11. A. Davila, G. H. Kaufmann, C. Pérez-López, “Transient deformation analysis by a carrier method of pulsed electronic speckle-shearing pattern interferometry,” Appl. Opt. 37, 4116–4122 (1998).
    [CrossRef]
  12. H. J. Puga, R. Rodríguez-Vera, A. Martínez, “General model to predict and correct errors in phase map interpretation and measurement for out-of-plane ESPI interferometers,” Opt. Laser Technol. 34, 81–92 (2002).
    [CrossRef]
  13. A. Martínez, R. Rodríguez-Vera, J. A. Rayas, H. J. Puga, “Error in the measurement due to the divergence of the object illumination wavefront for in-plane interferometers,” Opt. Commun. 223, 239–246 (2003).
    [CrossRef]

2003 (4)

R. Krupka, T. Walz, A. Ettemeyer, “Fast and full-field measurement of brake squeal using pulsed ESPI technique,” Opt. Eng. 42, 1354–1358 (2003).
[CrossRef]

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, H. J. Puga, “Error in the measurement due to the divergence of the object illumination wavefront for in-plane interferometers,” Opt. Commun. 223, 239–246 (2003).
[CrossRef]

E. Kolenovic, W. Osten, R. Klattenhoff, S. Lai, Ch. Von Kopylow, W. Jüptner, “Miniaturized digital holography sensor for distal three-dimensional endoscopy,” Appl. Opt. 42, 5167–5172 (2003).
[CrossRef] [PubMed]

J. A. Rayas, A. Martínez, R. Rodríguez-Vera, S. Calixto, “Development in situ for gratings recorded in photoresist,” Appl. Opt. 42, 6877–6879 (2003).
[CrossRef] [PubMed]

2002 (1)

H. J. Puga, R. Rodríguez-Vera, A. Martínez, “General model to predict and correct errors in phase map interpretation and measurement for out-of-plane ESPI interferometers,” Opt. Laser Technol. 34, 81–92 (2002).
[CrossRef]

2001 (1)

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, J. F. Vázquez, “Influence of object roughness on specimen gratings for moiré interferometry,” Opt. Eng. 40, 1978–1983 (2001).
[CrossRef]

1998 (1)

1997 (1)

J. Schmit, K. Patorski, K. Creath, “Simultaneous registration of in- and out-of-plane displacements in modified grating interferometry,” Opt. Eng. 36, 2240–2248 (1997).
[CrossRef]

1989 (1)

A. Asundi, “Moiré interferometry for deformation measurement,” Opt. Lasers Eng. 11, 281–292 (1989).
[CrossRef]

1988 (1)

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

Asundi, A.

A. Asundi, “Moiré interferometry for deformation measurement,” Opt. Lasers Eng. 11, 281–292 (1989).
[CrossRef]

Calixto, S.

Chau, F. S.

R. S. Sirohi, F. S. Chau, Optical Methods of Measurement: Whole Field Techniques (Marcel Dekker, New York, 1999), Chap. 6, pp. 174–176.

Creath, K.

J. Schmit, K. Patorski, K. Creath, “Simultaneous registration of in- and out-of-plane displacements in modified grating interferometry,” Opt. Eng. 36, 2240–2248 (1997).
[CrossRef]

Davila, A.

Ettemeyer, A.

R. Krupka, T. Walz, A. Ettemeyer, “Fast and full-field measurement of brake squeal using pulsed ESPI technique,” Opt. Eng. 42, 1354–1358 (2003).
[CrossRef]

Jüptner, W.

Kaufmann, G. H.

Klattenhoff, R.

Kolenovic, E.

Krupka, R.

R. Krupka, T. Walz, A. Ettemeyer, “Fast and full-field measurement of brake squeal using pulsed ESPI technique,” Opt. Eng. 42, 1354–1358 (2003).
[CrossRef]

Lai, S.

Martínez, A.

J. A. Rayas, A. Martínez, R. Rodríguez-Vera, S. Calixto, “Development in situ for gratings recorded in photoresist,” Appl. Opt. 42, 6877–6879 (2003).
[CrossRef] [PubMed]

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, H. J. Puga, “Error in the measurement due to the divergence of the object illumination wavefront for in-plane interferometers,” Opt. Commun. 223, 239–246 (2003).
[CrossRef]

H. J. Puga, R. Rodríguez-Vera, A. Martínez, “General model to predict and correct errors in phase map interpretation and measurement for out-of-plane ESPI interferometers,” Opt. Laser Technol. 34, 81–92 (2002).
[CrossRef]

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, J. F. Vázquez, “Influence of object roughness on specimen gratings for moiré interferometry,” Opt. Eng. 40, 1978–1983 (2001).
[CrossRef]

Osten, W.

Patorski, K.

J. Schmit, K. Patorski, K. Creath, “Simultaneous registration of in- and out-of-plane displacements in modified grating interferometry,” Opt. Eng. 36, 2240–2248 (1997).
[CrossRef]

Pérez-López, C.

Puga, H. J.

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, H. J. Puga, “Error in the measurement due to the divergence of the object illumination wavefront for in-plane interferometers,” Opt. Commun. 223, 239–246 (2003).
[CrossRef]

H. J. Puga, R. Rodríguez-Vera, A. Martínez, “General model to predict and correct errors in phase map interpretation and measurement for out-of-plane ESPI interferometers,” Opt. Laser Technol. 34, 81–92 (2002).
[CrossRef]

Rayas, J. A.

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, H. J. Puga, “Error in the measurement due to the divergence of the object illumination wavefront for in-plane interferometers,” Opt. Commun. 223, 239–246 (2003).
[CrossRef]

J. A. Rayas, A. Martínez, R. Rodríguez-Vera, S. Calixto, “Development in situ for gratings recorded in photoresist,” Appl. Opt. 42, 6877–6879 (2003).
[CrossRef] [PubMed]

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, J. F. Vázquez, “Influence of object roughness on specimen gratings for moiré interferometry,” Opt. Eng. 40, 1978–1983 (2001).
[CrossRef]

Rodríguez-Vera, R.

J. A. Rayas, A. Martínez, R. Rodríguez-Vera, S. Calixto, “Development in situ for gratings recorded in photoresist,” Appl. Opt. 42, 6877–6879 (2003).
[CrossRef] [PubMed]

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, H. J. Puga, “Error in the measurement due to the divergence of the object illumination wavefront for in-plane interferometers,” Opt. Commun. 223, 239–246 (2003).
[CrossRef]

H. J. Puga, R. Rodríguez-Vera, A. Martínez, “General model to predict and correct errors in phase map interpretation and measurement for out-of-plane ESPI interferometers,” Opt. Laser Technol. 34, 81–92 (2002).
[CrossRef]

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, J. F. Vázquez, “Influence of object roughness on specimen gratings for moiré interferometry,” Opt. Eng. 40, 1978–1983 (2001).
[CrossRef]

Schmit, J.

J. Schmit, K. Patorski, K. Creath, “Simultaneous registration of in- and out-of-plane displacements in modified grating interferometry,” Opt. Eng. 36, 2240–2248 (1997).
[CrossRef]

Sirohi, R. S.

R. S. Sirohi, F. S. Chau, Optical Methods of Measurement: Whole Field Techniques (Marcel Dekker, New York, 1999), Chap. 6, pp. 174–176.

Vázquez, J. F.

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, J. F. Vázquez, “Influence of object roughness on specimen gratings for moiré interferometry,” Opt. Eng. 40, 1978–1983 (2001).
[CrossRef]

Von Kopylow, Ch.

Walz, T.

R. Krupka, T. Walz, A. Ettemeyer, “Fast and full-field measurement of brake squeal using pulsed ESPI technique,” Opt. Eng. 42, 1354–1358 (2003).
[CrossRef]

Winther, S.

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

Appl. Opt. (3)

Opt. Commun. (1)

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, H. J. Puga, “Error in the measurement due to the divergence of the object illumination wavefront for in-plane interferometers,” Opt. Commun. 223, 239–246 (2003).
[CrossRef]

Opt. Eng. (3)

J. Schmit, K. Patorski, K. Creath, “Simultaneous registration of in- and out-of-plane displacements in modified grating interferometry,” Opt. Eng. 36, 2240–2248 (1997).
[CrossRef]

A. Martínez, R. Rodríguez-Vera, J. A. Rayas, J. F. Vázquez, “Influence of object roughness on specimen gratings for moiré interferometry,” Opt. Eng. 40, 1978–1983 (2001).
[CrossRef]

R. Krupka, T. Walz, A. Ettemeyer, “Fast and full-field measurement of brake squeal using pulsed ESPI technique,” Opt. Eng. 42, 1354–1358 (2003).
[CrossRef]

Opt. Laser Technol. (1)

H. J. Puga, R. Rodríguez-Vera, A. Martínez, “General model to predict and correct errors in phase map interpretation and measurement for out-of-plane ESPI interferometers,” Opt. Laser Technol. 34, 81–92 (2002).
[CrossRef]

Opt. Lasers Eng. (2)

A. Asundi, “Moiré interferometry for deformation measurement,” Opt. Lasers Eng. 11, 281–292 (1989).
[CrossRef]

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

Other (3)

W. Jüptner, W. Osten, eds., Holographic Interferometry (Akademie Verlag, New York, 1996), pp. 259–266, pp. 171–173, pp. 125–149.

R. S. Sirohi, F. S. Chau, Optical Methods of Measurement: Whole Field Techniques (Marcel Dekker, New York, 1999), Chap. 6, pp. 174–176.

Dantec Ettemeyer, http://www.ettemeyer.com/espi_ndt_shearography_Win.html .

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Figures (11)

Fig. 1
Fig. 1

Schematic of the sensitivity vector to one divergent illumination beam.

Fig. 2
Fig. 2

Schematic of the sensitivity vector to dual divergent illumination.

Fig. 3
Fig. 3

Schematic of the combined setup for 3D measuring: PZT, piezoelectric transducer.

Fig. 4
Fig. 4

Top to bottom, for u-direction deformation: recorded-fringes pattern, wrapped phase, and 3D plot.

Fig. 5
Fig. 5

Top to bottom for v-direction deformation: recorded-fringes pattern, wrapped phase, and 3D plot.

Fig. 6
Fig. 6

Top to bottom for w-direction deformation: recorded-fringes pattern, wrapped phase, and 3D plot.

Fig. 7
Fig. 7

Plot of combined shape and deformation data.

Fig. 8
Fig. 8

Percentage of each sensitivity vector components in a system with the three illumination sources, P s1 = (0 cm, 0 cm, -167 cm).

Fig. 9
Fig. 9

Percentage of each sensitivity vector components in a system with the three illumination sources, P s2 = (-161.3 cm, 0 cm, -43.2 cm).

Fig. 10
Fig. 10

Percentage of each sensitivity vector components in a system with the three illumination sources, P s3 = (0 cm, 161.3 cm, -43.2 cm).

Fig. 11
Fig. 11

Percentage of each sensitivity vector components in an in-plane system, P s1 = (-161.3 cm, 0 cm, -43.2 cm) and P s2 = (161.3 cm, 0 cm, -43.2 cm).

Equations (12)

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

I1x, y=i1+i2+2i1i2cos φ,
I2x, y=i1+i2+2i1i2cosφ+Δϕ.
|I1x, y-I2x, y|=4i1i2× sinφ+ Δϕ2sinΔϕ2.
ΔϕP=dPeP,
eP= 2πλbˆP-nˆP,
ex= 2πλx0-xpx0-xp2+y0-yp2+z0-zp21/2- xp-xsxp-xs2+yp-ys2+zp-zs21/2,
ey= 2πλy0-ypx0-xp2+y0-yp2+z0-zp21/2- yp-ysxp-xs2+yp-ys2+zp-zs21/2,
ez= 2πλz0-zpx0-xp2+y0-yp2+z0-zp21/2- zp-zsxp-xs2+yp-ys2+zp-zs21/2,
eP= 2πλnˆ1P-nˆ2P,
ex= 2πλxp-xs1xp-xs12+yp-ys12+zp-zs121/2- xp-xs2xp-xs22+yp-ys22+zp-zs221/2,
ey= 2πλyp-ys1xp-xs12+yp-ys12+zp-zs121/2- yp-ys2xp-xs22+yp-ys22+zp-zs221/2,
ez= 2πλzp-zs1xp-xs12+yp-ys12+zp-zs121/2- zp-zs2xp-xs22+yp-ys22+zp-zs221/2,

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