Abstract

This paper shows the optical setup of a radial in-plane digital speckle pattern interferometer which uses an axis-symmetrical diffractive optical element (DOE) to obtain double illumination. The application of the DOE gives in-plane sensitivity which only depends on the grating period of the DOE instead of the wavelength of the laser used as illumination source. A compact optical layout was built in order to have a portable optical strain sensor with a circular measurement area of about 5mm in diameter. In order to compare its performance with electrical strain sensors (strain gauges), mechanical loading was generated by a four-point bending device and simultaneously monitored by the optical strain sensor and by two-element strain gauge rosettes. Several mechanical stress levels were measured showing a good agreement between both sensors. Results showed that the optical sensor could measure applied mech anical strains with a mean uncertainty of about 5% and 4% for the maximum and minimum principal strains, respectively.

© 2011 Optical Society of America

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References

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  1. K. Hoffmann, An Introduction to Measurements Using Strain Gages (Hottinger Baldwin Messtechnik, 1989).
  2. R. Hooke, De Potentia Restitutiva (1678).
  3. N. E. Dowling, Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue (Prentice-Hall, 1993), p. 102.
  4. J. W. Dally and W. F. Riley, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).
  5. A. Albertazzi, Jr. and M. R. Viotti, “Radial speckle interferometry and applications,” in Advances in Speckle Metrology and Related Techniques, G.H.Kaufmann, ed. (Wiley, 2011), pp. 1–36.
  6. D. V. Nelson and J. T. McCrickerd, “Residual-stress determination through combined use of holographic interferometry and blind-hole drilling,” Exp. Mech. 26, 371–378 (1986).
    [CrossRef]
  7. M. Kujawinska and L. Salbut, “Recent development in instrumentation of automated grating interferometry,” Optica Applicata 25, 211–232 (1995).
  8. L. Salbut and M. Kujawinska, “Grating interferometer for local in-plane displacement/strain field analysis,” Proc. SPIE 3407, 490–494 (1998).
    [CrossRef]
  9. R. Czarnek, “High sensitivity moiré interferometry with compact achromatic interferometer,” Opt. Lasers Eng. 13, 99–115 (1990).
  10. M. Kujawinska and L. Salbut, “New generation of optical extensometers based on grating (moiré) interferometry,” Proc. SPIE 4101, 375 (2000).
  11. L. Salbut, “Waveguide grating (moiré) microinterferometer for inplane displacement/strain field investigation,” Opt. Eng. 41, 626–631 (2002).
    [CrossRef]
  12. P. K. Rastogi, “Measurement of static surface displacements, and three dimensional surface shapes - Examples of applications to non-destrucive testing,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 141–224.
  13. J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 59–140.
  14. S. Winther, “3D strain measurements using ESPI,” Opt. Lasers Eng. 8, 45–57 (1988).
    [CrossRef]
  15. A. Martínez, J. A. Rayas, R. Cordero, and K. Genovese, “Analysis of optical configurations for ESPI,” Opt. Lasers Eng. 46, 48–54 (2008).
    [CrossRef]
  16. J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E 3, 214–218 (1970).
    [CrossRef]
  17. 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]
  18. A. J. Moore and J. R. Tyrer, “Two-dimensional strain measurement with ESPI,” Opt. Lasers Eng. 24, 381–402(1996).
    [CrossRef]
  19. A. Albertazzi, Jr., M. R. Borges, and C. Kanda, “A radial in-plane interferometer for residual stresses measurement using ESPI,” in Proceedings of SEM IX International Congress on Experimental Mechanics (Society for Experimental Mechanics, 2000), pp. 108–111.
  20. A. Albertazzi, Jr., C. L. N. Veiga, and D. P. Willemann, “Evaluation of the optical rosette for translation, stresses, and stresses gradients measurement,” Proc. SPIE 5144, 533–544 (2003).
    [CrossRef]
  21. M. R. Viotti, A. Albertazzi, Jr., and W. A. 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]
  22. M. R. Viotti, W. A. Kapp, and A. Albertazzi, Jr., “A portable optical DSPI strain sensor with radial sensitivity using an axis-symmetrical DOE,” Proc. SPIE 7387, 73870B(2010).
    [CrossRef]
  23. M. R. Viotti, W. A. Kapp, and A. Albertazzi, Jr., “Achromatic digital speckle pattern interferometer with constant radial in-plane sensitivity by using a diffractive optical element,” Appl. Opt. 48, 2275–2281 (2009).
    [CrossRef]
  24. G. H. Kaufmann and A. Albertazzi, Jr., “Speckle interferometry for the measurement of residual stresses,” in New Directions in Holography and Speckle, H.J.Caulfield and C.S.Vikram, eds. (ASP, 2008), Section 9.

2010 (1)

M. R. Viotti, W. A. Kapp, and A. Albertazzi, Jr., “A portable optical DSPI strain sensor with radial sensitivity using an axis-symmetrical DOE,” Proc. SPIE 7387, 73870B(2010).
[CrossRef]

2009 (1)

2008 (2)

M. R. Viotti, A. Albertazzi, Jr., and W. A. 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]

A. Martínez, J. A. Rayas, R. Cordero, and K. Genovese, “Analysis of optical configurations for ESPI,” Opt. Lasers Eng. 46, 48–54 (2008).
[CrossRef]

2003 (1)

A. Albertazzi, Jr., C. L. N. Veiga, and D. P. Willemann, “Evaluation of the optical rosette for translation, stresses, and stresses gradients measurement,” Proc. SPIE 5144, 533–544 (2003).
[CrossRef]

2002 (1)

L. Salbut, “Waveguide grating (moiré) microinterferometer for inplane displacement/strain field investigation,” Opt. Eng. 41, 626–631 (2002).
[CrossRef]

2000 (1)

M. Kujawinska and L. Salbut, “New generation of optical extensometers based on grating (moiré) interferometry,” Proc. SPIE 4101, 375 (2000).

1998 (1)

L. Salbut and M. Kujawinska, “Grating interferometer for local in-plane displacement/strain field analysis,” Proc. SPIE 3407, 490–494 (1998).
[CrossRef]

1996 (1)

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

1995 (1)

M. Kujawinska and L. Salbut, “Recent development in instrumentation of automated grating interferometry,” Optica Applicata 25, 211–232 (1995).

1990 (2)

R. Czarnek, “High sensitivity moiré interferometry with compact achromatic interferometer,” Opt. Lasers Eng. 13, 99–115 (1990).

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]

1988 (1)

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

1986 (1)

D. V. Nelson and J. T. McCrickerd, “Residual-stress determination through combined use of holographic interferometry and blind-hole drilling,” Exp. Mech. 26, 371–378 (1986).
[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, W. A. Kapp, and A. Albertazzi, Jr., “A portable optical DSPI strain sensor with radial sensitivity using an axis-symmetrical DOE,” Proc. SPIE 7387, 73870B(2010).
[CrossRef]

M. R. Viotti, W. A. Kapp, and A. Albertazzi, Jr., “Achromatic digital speckle pattern interferometer with constant radial in-plane sensitivity by using a diffractive optical element,” Appl. Opt. 48, 2275–2281 (2009).
[CrossRef]

M. R. Viotti, A. Albertazzi, Jr., and W. A. 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]

A. Albertazzi, Jr., C. L. N. Veiga, and D. P. Willemann, “Evaluation of the optical rosette for translation, stresses, and stresses gradients measurement,” Proc. SPIE 5144, 533–544 (2003).
[CrossRef]

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

A. Albertazzi, Jr. and M. R. Viotti, “Radial speckle interferometry and applications,” in Advances in Speckle Metrology and Related Techniques, G.H.Kaufmann, ed. (Wiley, 2011), pp. 1–36.

G. H. Kaufmann and A. Albertazzi, Jr., “Speckle interferometry for the measurement of residual stresses,” in New Directions in Holography and Speckle, H.J.Caulfield and C.S.Vikram, eds. (ASP, 2008), Section 9.

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 SEM IX International Congress on Experimental Mechanics (Society for Experimental Mechanics, 2000), pp. 108–111.

Cordero, R.

A. Martínez, J. A. Rayas, R. Cordero, and K. Genovese, “Analysis of optical configurations for ESPI,” Opt. Lasers Eng. 46, 48–54 (2008).
[CrossRef]

Czarnek, R.

R. Czarnek, “High sensitivity moiré interferometry with compact achromatic interferometer,” Opt. Lasers Eng. 13, 99–115 (1990).

Dally, J. W.

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

Dowling, N. E.

N. E. Dowling, Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue (Prentice-Hall, 1993), p. 102.

Genovese, K.

A. Martínez, J. A. Rayas, R. Cordero, and K. Genovese, “Analysis of optical configurations for ESPI,” Opt. Lasers Eng. 46, 48–54 (2008).
[CrossRef]

Hoffmann, K.

K. Hoffmann, An Introduction to Measurements Using Strain Gages (Hottinger Baldwin Messtechnik, 1989).

Hooke, R.

R. Hooke, De Potentia Restitutiva (1678).

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. 59–140.

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 SEM IX International Congress on Experimental Mechanics (Society for Experimental Mechanics, 2000), pp. 108–111.

Kapp, W. A.

M. R. Viotti, W. A. Kapp, and A. Albertazzi, Jr., “A portable optical DSPI strain sensor with radial sensitivity using an axis-symmetrical DOE,” Proc. SPIE 7387, 73870B(2010).
[CrossRef]

M. R. Viotti, W. A. Kapp, and A. Albertazzi, Jr., “Achromatic digital speckle pattern interferometer with constant radial in-plane sensitivity by using a diffractive optical element,” Appl. Opt. 48, 2275–2281 (2009).
[CrossRef]

M. R. Viotti, A. Albertazzi, Jr., and W. A. 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]

Kaufmann, G. H.

G. H. Kaufmann and A. Albertazzi, Jr., “Speckle interferometry for the measurement of residual stresses,” in New Directions in Holography and Speckle, H.J.Caulfield and C.S.Vikram, eds. (ASP, 2008), Section 9.

Kujawinska, M.

M. Kujawinska and L. Salbut, “New generation of optical extensometers based on grating (moiré) interferometry,” Proc. SPIE 4101, 375 (2000).

L. Salbut and M. Kujawinska, “Grating interferometer for local in-plane displacement/strain field analysis,” Proc. SPIE 3407, 490–494 (1998).
[CrossRef]

M. Kujawinska and L. Salbut, “Recent development in instrumentation of automated grating interferometry,” Optica Applicata 25, 211–232 (1995).

Leendertz, J. A.

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

Martínez, A.

A. Martínez, J. A. Rayas, R. Cordero, and K. Genovese, “Analysis of optical configurations for ESPI,” Opt. Lasers Eng. 46, 48–54 (2008).
[CrossRef]

McCrickerd, J. T.

D. V. Nelson and J. T. McCrickerd, “Residual-stress determination through combined use of holographic interferometry and blind-hole drilling,” Exp. Mech. 26, 371–378 (1986).
[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]

Nelson, D. V.

D. V. Nelson and J. T. McCrickerd, “Residual-stress determination through combined use of holographic interferometry and blind-hole drilling,” Exp. Mech. 26, 371–378 (1986).
[CrossRef]

Rastogi, P. K.

P. K. Rastogi, “Measurement of static surface displacements, and three dimensional surface shapes - Examples of applications to non-destrucive testing,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 141–224.

Rayas, J. A.

A. Martínez, J. A. Rayas, R. Cordero, and K. Genovese, “Analysis of optical configurations for ESPI,” Opt. Lasers Eng. 46, 48–54 (2008).
[CrossRef]

Riley, W. F.

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

Salbut, L.

L. Salbut, “Waveguide grating (moiré) microinterferometer for inplane displacement/strain field investigation,” Opt. Eng. 41, 626–631 (2002).
[CrossRef]

M. Kujawinska and L. Salbut, “New generation of optical extensometers based on grating (moiré) interferometry,” Proc. SPIE 4101, 375 (2000).

L. Salbut and M. Kujawinska, “Grating interferometer for local in-plane displacement/strain field analysis,” Proc. SPIE 3407, 490–494 (1998).
[CrossRef]

M. Kujawinska and L. Salbut, “Recent development in instrumentation of automated grating interferometry,” Optica Applicata 25, 211–232 (1995).

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]

Veiga, C. L. N.

A. Albertazzi, Jr., C. L. N. Veiga, and D. P. Willemann, “Evaluation of the optical rosette for translation, stresses, and stresses gradients measurement,” Proc. SPIE 5144, 533–544 (2003).
[CrossRef]

Viotti, M. R.

M. R. Viotti, W. A. Kapp, and A. Albertazzi, Jr., “A portable optical DSPI strain sensor with radial sensitivity using an axis-symmetrical DOE,” Proc. SPIE 7387, 73870B(2010).
[CrossRef]

M. R. Viotti, W. A. Kapp, and A. Albertazzi, Jr., “Achromatic digital speckle pattern interferometer with constant radial in-plane sensitivity by using a diffractive optical element,” Appl. Opt. 48, 2275–2281 (2009).
[CrossRef]

M. R. Viotti, A. Albertazzi, Jr., and W. A. 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]

A. Albertazzi, Jr. and M. R. Viotti, “Radial speckle interferometry and applications,” in Advances in Speckle Metrology and Related Techniques, G.H.Kaufmann, ed. (Wiley, 2011), pp. 1–36.

Willemann, D. P.

A. Albertazzi, Jr., C. L. N. Veiga, and D. P. Willemann, “Evaluation of the optical rosette for translation, stresses, and stresses gradients measurement,” Proc. SPIE 5144, 533–544 (2003).
[CrossRef]

Winther, S.

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

Appl. Opt. (1)

Exp. Mech. (1)

D. V. Nelson and J. T. McCrickerd, “Residual-stress determination through combined use of holographic interferometry and blind-hole drilling,” Exp. Mech. 26, 371–378 (1986).
[CrossRef]

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)

L. Salbut, “Waveguide grating (moiré) microinterferometer for inplane displacement/strain field investigation,” Opt. Eng. 41, 626–631 (2002).
[CrossRef]

Opt. Lasers Eng. (5)

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

A. Martínez, J. A. Rayas, R. Cordero, and K. Genovese, “Analysis of optical configurations for ESPI,” Opt. Lasers Eng. 46, 48–54 (2008).
[CrossRef]

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

R. Czarnek, “High sensitivity moiré interferometry with compact achromatic interferometer,” Opt. Lasers Eng. 13, 99–115 (1990).

M. R. Viotti, A. Albertazzi, Jr., and W. A. 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]

Optica Applicata (1)

M. Kujawinska and L. Salbut, “Recent development in instrumentation of automated grating interferometry,” Optica Applicata 25, 211–232 (1995).

Proc. SPIE (4)

L. Salbut and M. Kujawinska, “Grating interferometer for local in-plane displacement/strain field analysis,” Proc. SPIE 3407, 490–494 (1998).
[CrossRef]

M. Kujawinska and L. Salbut, “New generation of optical extensometers based on grating (moiré) interferometry,” Proc. SPIE 4101, 375 (2000).

M. R. Viotti, W. A. Kapp, and A. Albertazzi, Jr., “A portable optical DSPI strain sensor with radial sensitivity using an axis-symmetrical DOE,” Proc. SPIE 7387, 73870B(2010).
[CrossRef]

A. Albertazzi, Jr., C. L. N. Veiga, and D. P. Willemann, “Evaluation of the optical rosette for translation, stresses, and stresses gradients measurement,” Proc. SPIE 5144, 533–544 (2003).
[CrossRef]

Other (9)

G. H. Kaufmann and A. Albertazzi, Jr., “Speckle interferometry for the measurement of residual stresses,” in New Directions in Holography and Speckle, H.J.Caulfield and C.S.Vikram, eds. (ASP, 2008), Section 9.

K. Hoffmann, An Introduction to Measurements Using Strain Gages (Hottinger Baldwin Messtechnik, 1989).

R. Hooke, De Potentia Restitutiva (1678).

N. E. Dowling, Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue (Prentice-Hall, 1993), p. 102.

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

A. Albertazzi, Jr. and M. R. Viotti, “Radial speckle interferometry and applications,” in Advances in Speckle Metrology and Related Techniques, G.H.Kaufmann, ed. (Wiley, 2011), pp. 1–36.

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

P. K. Rastogi, “Measurement of static surface displacements, and three dimensional surface shapes - Examples of applications to non-destrucive testing,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 141–224.

J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 59–140.

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Figures (7)

Fig. 1
Fig. 1

Radial in-plane illumination principle.

Fig. 2
Fig. 2

(a) Traditional optical arrangement of a radial in-plane interferometer with DOE (b) off-axis configuration.

Fig. 3
Fig. 3

Photograph of the compact strain sensor.

Fig. 4
Fig. 4

Photographs of clamping system: (a), (b) elastic legs and stiffness principle, (c) spring with different stiffness in two orthogonal directions.

Fig. 5
Fig. 5

Four-points bending device showing where the sensors were placed.

Fig. 6
Fig. 6

Wrapped phase maps for a reference strain of (a)  50 μm / m , (b)  400 μm / m , and (c)  800 μm / m .

Fig. 7
Fig. 7

Plots of the relative deviations for (a)  maximum and (b) minimum applied strains. (c) Plot of the measured stress field.

Tables (3)

Tables Icon

Table 1 Comparison among Mean Values of the Maximum Principal Strains Measured by Both Sensors

Tables Icon

Table 2 Comparison among Mean Values of the Minimum Principal Strains Measured by Both Sensors

Tables Icon

Table 3 Maximum and Minimum Measured Stress for Each Strain Increment

Equations (4)

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

u r ( r , θ ) = u t cos ( θ α ) ,
u r ( r , θ ) = r 2 [ ( ε 1 + ε 2 ) + ( ε 1 ε 2 ) cos ( 2 θ 2 β ) ] ,
u r ( r , θ ) = r 2 E [ ( 1 ν ) ( σ 1 + σ 2 ) + ( 1 + ν ) ( σ 1 σ 2 ) cos ( 2 θ 2 β ) ] ,
u r ( r , θ ) = ϕ ( r , θ ) p r 4 π ,

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