Abstract

We report on a digital speckle pattern interferometer that applies a binary diffractive optical element (DOE) to generate double illumination and radial in-plane sensitivity. The application of the DOE ensures independence on the wavelength of the laser used as an illumination source. Furthermore, in-plane sensitivity only depends on the grating period of the DOE. An experimental setup was built allowing the measurement of a set of radial in-plane displacement fields either using a red laser as a light source or a green one. When displacement fields computed from the measured optical phase maps obtained with a red or a green laser were compared, two main results were observed: (a) deviations between mean values ranged only up to 7nm and (b) phase maps presented the same amount of fringes. In addition, phase maps measured with the red laser were processed as they were obtained with green light. For this case, deviations have ranged only up to 0.5nm. On the other hand, a set of measurements performed changing the DOE by a conical mirror showed clearly that radial in-plane sensitivity increased when the red laser was changed by the green one.

© 2009 Optical Society of America

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References

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  1. J. W. Dally and W. F. Riley, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).
  2. P. K. Rastogi, “Measurement of static surface displacements, derivatives of displacements, and three-dimensional surface shapes--examples of applications to non-destructive testing,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001).
  3. 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.
  4. J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E 3, 214-218 (1970).
    [CrossRef]
  5. A. J. Moore and J. R. Tyrer, “An electronic speckle pattern interferometer for complete in-plane measurement,” Meas. Sci. Technol. 1, 1024-1030 (1990).
    [CrossRef]
  6. A. J. Moore and J. R. Tyrer, “Two-dimensional strain measurement with ESPI,” Opt. Lasers Eng. 24, 381-402 (1996).
    [CrossRef]
  7. A. Albertazzi, Jr., M. R. Borges, and C. Kanda, “A radial in-plane interferometer for residual stresses measurement using ESPI,” in Proceedings of the Society of Experimental Mechanics IX International Congress on Experimental Mechanics (Society for Experimental Mechanics, 2000), pp. 108-111.
  8. M. R. Viotti, A. Albertazzi Jr., and G. H. Kaufmann, “Measurement of residual stresses using local heating and a radial in-plane speckle interferometer,” Opt. Eng. 44, 093606(2005).
    [CrossRef]
  9. D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, “Diffractive Optics: Design, Fabrication, and Test,” Vol. TT62 of Tutorial Texts in OE (SPIE, 2003).
  10. M. R. Viotti, A. Albertazzi Jr., and W. Kapp, “Experimental comparison between a portable DSPI device with diffractive optical element and a hole drilling strain gage combined system,” Opt. Lasers Eng. 46, 835-841 (2008).
    [CrossRef]
  11. E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974).
  12. “Standard test method for determining residual stresses by the hole-drilling strain-gage method,” ASTM E837-01e1, Annual Book of ASTM Standards (American Society for Testing and Materials, 2001), Vol 03.01.

2008 (1)

M. R. Viotti, A. Albertazzi Jr., and W. Kapp, “Experimental comparison between a portable DSPI device with diffractive optical element and a hole drilling strain gage combined system,” Opt. Lasers Eng. 46, 835-841 (2008).
[CrossRef]

2005 (1)

M. R. Viotti, A. Albertazzi Jr., and G. H. Kaufmann, “Measurement of residual stresses using local heating and a radial in-plane speckle interferometer,” Opt. Eng. 44, 093606(2005).
[CrossRef]

1996 (1)

A. J. Moore and J. R. Tyrer, “Two-dimensional strain measurement with ESPI,” Opt. Lasers Eng. 24, 381-402 (1996).
[CrossRef]

1990 (1)

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

1970 (1)

J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E 3, 214-218 (1970).
[CrossRef]

Albertazzi, A.

M. R. Viotti, A. Albertazzi Jr., and W. Kapp, “Experimental comparison between a portable DSPI device with diffractive optical element and a hole drilling strain gage combined system,” Opt. Lasers Eng. 46, 835-841 (2008).
[CrossRef]

M. R. Viotti, A. Albertazzi Jr., and G. H. Kaufmann, “Measurement of residual stresses using local heating and a radial in-plane speckle interferometer,” Opt. Eng. 44, 093606(2005).
[CrossRef]

A. Albertazzi, Jr., M. R. Borges, and C. Kanda, “A radial in-plane interferometer for residual stresses measurement using ESPI,” in Proceedings of the Society of Experimental Mechanics IX International Congress on Experimental Mechanics (Society for Experimental Mechanics, 2000), pp. 108-111.

Borges, M. R.

A. Albertazzi, Jr., M. R. Borges, and C. Kanda, “A radial in-plane interferometer for residual stresses measurement using ESPI,” in Proceedings of the Society of Experimental Mechanics IX International Congress on Experimental Mechanics (Society for Experimental Mechanics, 2000), pp. 108-111.

Dally, J. W.

J. W. Dally and W. F. Riley, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).

Hecht, E.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974).

Huntley, J. M.

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.

Kanda, C.

A. Albertazzi, Jr., M. R. Borges, and C. Kanda, “A radial in-plane interferometer for residual stresses measurement using ESPI,” in Proceedings of the Society of Experimental Mechanics IX International Congress on Experimental Mechanics (Society for Experimental Mechanics, 2000), pp. 108-111.

Kapp, W.

M. R. Viotti, A. Albertazzi Jr., and W. Kapp, “Experimental comparison between a portable DSPI device with diffractive optical element and a hole drilling strain gage combined system,” Opt. Lasers Eng. 46, 835-841 (2008).
[CrossRef]

Kathman, A. D.

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, “Diffractive Optics: Design, Fabrication, and Test,” Vol. TT62 of Tutorial Texts in OE (SPIE, 2003).

Kaufmann, G. H.

M. R. Viotti, A. Albertazzi Jr., and G. H. Kaufmann, “Measurement of residual stresses using local heating and a radial in-plane speckle interferometer,” Opt. Eng. 44, 093606(2005).
[CrossRef]

Leendertz, J. A.

J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E 3, 214-218 (1970).
[CrossRef]

Moore, A. J.

A. J. Moore and J. R. Tyrer, “Two-dimensional strain measurement with ESPI,” Opt. Lasers Eng. 24, 381-402 (1996).
[CrossRef]

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

O'Shea, D. C.

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, “Diffractive Optics: Design, Fabrication, and Test,” Vol. TT62 of Tutorial Texts in OE (SPIE, 2003).

Prather, D. W.

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, “Diffractive Optics: Design, Fabrication, and Test,” Vol. TT62 of Tutorial Texts in OE (SPIE, 2003).

Rastogi, P. K.

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

Riley, W. F.

J. W. Dally and W. F. Riley, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).

Suleski, T. J.

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, “Diffractive Optics: Design, Fabrication, and Test,” Vol. TT62 of Tutorial Texts in OE (SPIE, 2003).

Tyrer, J. R.

A. J. Moore and J. R. Tyrer, “Two-dimensional strain measurement with ESPI,” Opt. Lasers Eng. 24, 381-402 (1996).
[CrossRef]

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

Viotti, M. R.

M. R. Viotti, A. Albertazzi Jr., and W. Kapp, “Experimental comparison between a portable DSPI device with diffractive optical element and a hole drilling strain gage combined system,” Opt. Lasers Eng. 46, 835-841 (2008).
[CrossRef]

M. R. Viotti, A. Albertazzi Jr., and G. H. Kaufmann, “Measurement of residual stresses using local heating and a radial in-plane speckle interferometer,” Opt. Eng. 44, 093606(2005).
[CrossRef]

Zajac, A.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974).

J. Phys. E (1)

J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E 3, 214-218 (1970).
[CrossRef]

Meas. Sci. Technol. (1)

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

Opt. Eng. (1)

M. R. Viotti, A. Albertazzi Jr., and G. H. Kaufmann, “Measurement of residual stresses using local heating and a radial in-plane speckle interferometer,” Opt. Eng. 44, 093606(2005).
[CrossRef]

Opt. Lasers Eng. (2)

A. J. Moore and J. R. Tyrer, “Two-dimensional strain measurement with ESPI,” Opt. Lasers Eng. 24, 381-402 (1996).
[CrossRef]

M. R. Viotti, A. Albertazzi Jr., and W. Kapp, “Experimental comparison between a portable DSPI device with diffractive optical element and a hole drilling strain gage combined system,” Opt. Lasers Eng. 46, 835-841 (2008).
[CrossRef]

Other (7)

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974).

“Standard test method for determining residual stresses by the hole-drilling strain-gage method,” ASTM E837-01e1, Annual Book of ASTM Standards (American Society for Testing and Materials, 2001), Vol 03.01.

A. Albertazzi, Jr., M. R. Borges, and C. Kanda, “A radial in-plane interferometer for residual stresses measurement using ESPI,” in Proceedings of the Society of Experimental Mechanics IX International Congress on Experimental Mechanics (Society for Experimental Mechanics, 2000), pp. 108-111.

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, “Diffractive Optics: Design, Fabrication, and Test,” Vol. TT62 of Tutorial Texts in OE (SPIE, 2003).

J. W. Dally and W. F. Riley, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).

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

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.

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Figures (6)

Fig. 1
Fig. 1

Cross section of the diffractive optical element showing radial in-plane sensitivity.

Fig. 2
Fig. 2

Photograph of the portable device showing the measurement module (MM) and the universal base (UB).

Fig. 3
Fig. 3

Rigid body wrapped phase maps obtained by using the radial in-plane interferometer with DOE for a wavelength light source of (a)  658 nm and (b)  532 nm .

Fig. 4
Fig. 4

Optical arrangement for the radial in-plane interfero meter with conical mirror.

Fig. 5
Fig. 5

Module 2 π phase maps measured by means of a radial in-plane interferometer with conical mirror for (a) red and (b) green light sources.

Fig. 6
Fig. 6

Cantilever beam: unloaded and loaded states generated by using a height gauge block.

Tables (3)

Tables Icon

Table 1 Radial In-Plane Displacements Measured with the Diffractive Optical Element

Tables Icon

Table 2 Radial In-Plane Displacements Measured with Conical Mirror

Tables Icon

Table 3 Radial In-Plane Displacements Measured with a Red Light Source, but Processed with Green Light Sensitivity

Equations (5)

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p r sin ξ = m λ sin ξ = m λ p r ,
u r ( r , θ ) = ϕ ( r , θ ) λ 4 π sin γ ,
u r ( r , θ ) = λ 2 sin γ .
u r ( r , θ ) = ϕ ( r , θ ) λ 4 π λ p r = ϕ ( r , θ ) p r 4 π .
u r ( r , θ ) = p r 2 .

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