Abstract

A three-dimensional (3-D) residual stress detection technique is proposed to detect and evaluate the residual stress occurring in optical components due to repairs carried out at laser induced damage sites. It is possible with a cross-orthogonal reflective photo-elastic setup to obtain complete 3-D information of the residual shearing stress around the damage site. The damaged volume of the optical component is numerically sliced into multilayers for this purpose and reflected light intensity is recorded from each layer. The shearing stress from the reflected light intensity is then calculated based on photo-elasticity theory. The validity of the approach is also verified in experiments where it could measure 3-D residual stress with an axial resolution of 10 µm along the light path.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. E. I. Moses, “The national ignition campaign: status and progress,” Nucl. Fusion 53(10), 104020 (2013).
    [Crossref]
  2. A. J. Glass and A. H. Guenther, “Laser induced damage of optical elements—a status report,” Appl. Opt. 12(4), 637–649 (1973).
    [Crossref]
  3. M. Sozet, J. Neauport, E. Lavastre, E. Lavastre, N. Roquin, L. Gallais, and L. Lamaignere, “Laser damage growth with picosecond pulses,” Opt. Lett. 41(10), 2342–2345 (2016).
    [Crossref]
  4. P. Cormont, L. Gallais, L. Lamaignère, J. L. Rullier, P. Combis, and D. Hebert, “Impact of two CO2 laser heatings for damage repairing on fused silica surface,” Opt. Express 18(25), 26068–26076 (2010).
    [Crossref]
  5. E. Mendez, K. M. Nowak, H. J. Baker, F. Villarreal, and D. R. Hall, “Localized CO2 laser damage repair of fused silica optics,” Appl. Opt. 45(21), 5358–5367 (2006).
    [Crossref]
  6. F. Dahmani, J. C. Lambropoulos, A. W. Schmid, S. J. Burns, and C. Prat, “Nanoindentation technique for measuring residual stress field around a laser-induced crack in fused silica,” J. Mater. Sci. 33(19), 4677–4685 (1998).
    [Crossref]
  7. J. Neauport, C. Ambard, P. Cormont, N. Darbois, J. Destribats, C. Luitot, and O. Rondeau, “Subsurface damage measurement of ground fused silica parts by HF etching techniques,” Opt. Express 17(22), 20448–20456 (2009).
    [Crossref]
  8. S. Zhang, H. Xie, X. T. Zeng, and P. Hing, “Residual stress characterization of diamond-like carbon coatings by an X-ray diffraction method,” Surf. Coat. Technol. 122(2-3), 219–224 (1999).
    [Crossref]
  9. Y. Zhang, Y. Xu, C. You, D. Xu, J. Tang, P. Zhang, and S. Dai, “Raman gain and femtosecond laser induced damage of Ge-As-S chalcogenide glasses,” Opt. Express 25(8), 8886–8895 (2017).
    [Crossref]
  10. E. E. Gdoutos, Matrix theory of photoelasticity (Springer, 1979).
  11. C. S. Narayanamurthy, G. Pedrini, and W. Osten, “Digital holographic photoelasticity,” Appl. Opt. 56(13), F213–F217 (2017).
    [Crossref]
  12. A. Kuske and G. Robertson, Photoelastic Stress Analysis (Wiley, 1974).
  13. Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
    [Crossref]
  14. F. Wang, Y. Zhang, H. Wang, W. Xu, Y. Zhang, and C. Li, “Nondestructive evaluation of residual stress via digital holographic photoelasticity,” J. Opt. 47(4), 547–552 (2018).
    [Crossref]
  15. H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44(9), 093601 (2005).
    [Crossref]
  16. L. Gallais, P. Cormont, and J. Rullier, “Investigation of stress induced by CO2 laser processing of fused silica optics for laser damage growth mitigation,” Opt. Express 17(26), 23488–23501 (2009).
    [Crossref]
  17. T. Doualle, L. Gallais, P. Cormont, D. Hebert, P. Combis, and J. Rullier, “Thermo-mechanical simulations of CO2 laser-fused silica interactions,” J. Appl. Phys. 119(11), 113106 (2016).
    [Crossref]
  18. R. W. Boyd, Nonlinear Optics, Third Edition (Academic Press, 2009).
  19. M. Sakakura and M. Terazima, “Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass,” Appl. Phys. B 71(2), 024113 (2005).
    [Crossref]
  20. R. M. Vignes, T. F. Soules, J. S. Stolken, R. R. Settgast, S. Elhadj, and M. J. Matthews, “Thermomechanical modeling of laser-induced structural relaxation and deformation of glass: volume changes in fused silica at high temperatures,” J. Am. Ceram. Soc. 96(1), 137–145 (2013).
    [Crossref]

2018 (1)

F. Wang, Y. Zhang, H. Wang, W. Xu, Y. Zhang, and C. Li, “Nondestructive evaluation of residual stress via digital holographic photoelasticity,” J. Opt. 47(4), 547–552 (2018).
[Crossref]

2017 (2)

2016 (2)

T. Doualle, L. Gallais, P. Cormont, D. Hebert, P. Combis, and J. Rullier, “Thermo-mechanical simulations of CO2 laser-fused silica interactions,” J. Appl. Phys. 119(11), 113106 (2016).
[Crossref]

M. Sozet, J. Neauport, E. Lavastre, E. Lavastre, N. Roquin, L. Gallais, and L. Lamaignere, “Laser damage growth with picosecond pulses,” Opt. Lett. 41(10), 2342–2345 (2016).
[Crossref]

2013 (2)

E. I. Moses, “The national ignition campaign: status and progress,” Nucl. Fusion 53(10), 104020 (2013).
[Crossref]

R. M. Vignes, T. F. Soules, J. S. Stolken, R. R. Settgast, S. Elhadj, and M. J. Matthews, “Thermomechanical modeling of laser-induced structural relaxation and deformation of glass: volume changes in fused silica at high temperatures,” J. Am. Ceram. Soc. 96(1), 137–145 (2013).
[Crossref]

2012 (1)

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

2010 (1)

2009 (2)

2006 (1)

2005 (2)

M. Sakakura and M. Terazima, “Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass,” Appl. Phys. B 71(2), 024113 (2005).
[Crossref]

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44(9), 093601 (2005).
[Crossref]

1999 (1)

S. Zhang, H. Xie, X. T. Zeng, and P. Hing, “Residual stress characterization of diamond-like carbon coatings by an X-ray diffraction method,” Surf. Coat. Technol. 122(2-3), 219–224 (1999).
[Crossref]

1998 (1)

F. Dahmani, J. C. Lambropoulos, A. W. Schmid, S. J. Burns, and C. Prat, “Nanoindentation technique for measuring residual stress field around a laser-induced crack in fused silica,” J. Mater. Sci. 33(19), 4677–4685 (1998).
[Crossref]

1973 (1)

Aben, H.

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44(9), 093601 (2005).
[Crossref]

Ainola, L.

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44(9), 093601 (2005).
[Crossref]

Ambard, C.

Anton, J.

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44(9), 093601 (2005).
[Crossref]

Baker, H. J.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, Third Edition (Academic Press, 2009).

Burns, S. J.

F. Dahmani, J. C. Lambropoulos, A. W. Schmid, S. J. Burns, and C. Prat, “Nanoindentation technique for measuring residual stress field around a laser-induced crack in fused silica,” J. Mater. Sci. 33(19), 4677–4685 (1998).
[Crossref]

Cheng, X.

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

Combis, P.

T. Doualle, L. Gallais, P. Cormont, D. Hebert, P. Combis, and J. Rullier, “Thermo-mechanical simulations of CO2 laser-fused silica interactions,” J. Appl. Phys. 119(11), 113106 (2016).
[Crossref]

P. Cormont, L. Gallais, L. Lamaignère, J. L. Rullier, P. Combis, and D. Hebert, “Impact of two CO2 laser heatings for damage repairing on fused silica surface,” Opt. Express 18(25), 26068–26076 (2010).
[Crossref]

Cormont, P.

Dahmani, F.

F. Dahmani, J. C. Lambropoulos, A. W. Schmid, S. J. Burns, and C. Prat, “Nanoindentation technique for measuring residual stress field around a laser-induced crack in fused silica,” J. Mater. Sci. 33(19), 4677–4685 (1998).
[Crossref]

Dai, S.

Darbois, N.

Destribats, J.

Doualle, T.

T. Doualle, L. Gallais, P. Cormont, D. Hebert, P. Combis, and J. Rullier, “Thermo-mechanical simulations of CO2 laser-fused silica interactions,” J. Appl. Phys. 119(11), 113106 (2016).
[Crossref]

Elhadj, S.

R. M. Vignes, T. F. Soules, J. S. Stolken, R. R. Settgast, S. Elhadj, and M. J. Matthews, “Thermomechanical modeling of laser-induced structural relaxation and deformation of glass: volume changes in fused silica at high temperatures,” J. Am. Ceram. Soc. 96(1), 137–145 (2013).
[Crossref]

Errapart, A.

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44(9), 093601 (2005).
[Crossref]

Gallais, L.

Gdoutos, E. E.

E. E. Gdoutos, Matrix theory of photoelasticity (Springer, 1979).

Glass, A. J.

Guenther, A. H.

Hall, D. R.

Hebert, D.

T. Doualle, L. Gallais, P. Cormont, D. Hebert, P. Combis, and J. Rullier, “Thermo-mechanical simulations of CO2 laser-fused silica interactions,” J. Appl. Phys. 119(11), 113106 (2016).
[Crossref]

P. Cormont, L. Gallais, L. Lamaignère, J. L. Rullier, P. Combis, and D. Hebert, “Impact of two CO2 laser heatings for damage repairing on fused silica surface,” Opt. Express 18(25), 26068–26076 (2010).
[Crossref]

Hing, P.

S. Zhang, H. Xie, X. T. Zeng, and P. Hing, “Residual stress characterization of diamond-like carbon coatings by an X-ray diffraction method,” Surf. Coat. Technol. 122(2-3), 219–224 (1999).
[Crossref]

Huang, J.

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

Jiang, X.

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

Kuske, A.

A. Kuske and G. Robertson, Photoelastic Stress Analysis (Wiley, 1974).

Lamaignere, L.

Lamaignère, L.

Lambropoulos, J. C.

F. Dahmani, J. C. Lambropoulos, A. W. Schmid, S. J. Burns, and C. Prat, “Nanoindentation technique for measuring residual stress field around a laser-induced crack in fused silica,” J. Mater. Sci. 33(19), 4677–4685 (1998).
[Crossref]

Lavastre, E.

Li, C.

F. Wang, Y. Zhang, H. Wang, W. Xu, Y. Zhang, and C. Li, “Nondestructive evaluation of residual stress via digital holographic photoelasticity,” J. Opt. 47(4), 547–552 (2018).
[Crossref]

Liu, H.

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

Luitot, C.

Matthews, M. J.

R. M. Vignes, T. F. Soules, J. S. Stolken, R. R. Settgast, S. Elhadj, and M. J. Matthews, “Thermomechanical modeling of laser-induced structural relaxation and deformation of glass: volume changes in fused silica at high temperatures,” J. Am. Ceram. Soc. 96(1), 137–145 (2013).
[Crossref]

Mendez, E.

Moses, E. I.

E. I. Moses, “The national ignition campaign: status and progress,” Nucl. Fusion 53(10), 104020 (2013).
[Crossref]

Narayanamurthy, C. S.

Neauport, J.

Nowak, K. M.

Osten, W.

Pedrini, G.

Prat, C.

F. Dahmani, J. C. Lambropoulos, A. W. Schmid, S. J. Burns, and C. Prat, “Nanoindentation technique for measuring residual stress field around a laser-induced crack in fused silica,” J. Mater. Sci. 33(19), 4677–4685 (1998).
[Crossref]

Ren, D.

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

Robertson, G.

A. Kuske and G. Robertson, Photoelastic Stress Analysis (Wiley, 1974).

Rondeau, O.

Roquin, N.

Rullier, J.

T. Doualle, L. Gallais, P. Cormont, D. Hebert, P. Combis, and J. Rullier, “Thermo-mechanical simulations of CO2 laser-fused silica interactions,” J. Appl. Phys. 119(11), 113106 (2016).
[Crossref]

L. Gallais, P. Cormont, and J. Rullier, “Investigation of stress induced by CO2 laser processing of fused silica optics for laser damage growth mitigation,” Opt. Express 17(26), 23488–23501 (2009).
[Crossref]

Rullier, J. L.

Sakakura, M.

M. Sakakura and M. Terazima, “Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass,” Appl. Phys. B 71(2), 024113 (2005).
[Crossref]

Schmid, A. W.

F. Dahmani, J. C. Lambropoulos, A. W. Schmid, S. J. Burns, and C. Prat, “Nanoindentation technique for measuring residual stress field around a laser-induced crack in fused silica,” J. Mater. Sci. 33(19), 4677–4685 (1998).
[Crossref]

Settgast, R. R.

R. M. Vignes, T. F. Soules, J. S. Stolken, R. R. Settgast, S. Elhadj, and M. J. Matthews, “Thermomechanical modeling of laser-induced structural relaxation and deformation of glass: volume changes in fused silica at high temperatures,” J. Am. Ceram. Soc. 96(1), 137–145 (2013).
[Crossref]

Soules, T. F.

R. M. Vignes, T. F. Soules, J. S. Stolken, R. R. Settgast, S. Elhadj, and M. J. Matthews, “Thermomechanical modeling of laser-induced structural relaxation and deformation of glass: volume changes in fused silica at high temperatures,” J. Am. Ceram. Soc. 96(1), 137–145 (2013).
[Crossref]

Sozet, M.

Stolken, J. S.

R. M. Vignes, T. F. Soules, J. S. Stolken, R. R. Settgast, S. Elhadj, and M. J. Matthews, “Thermomechanical modeling of laser-induced structural relaxation and deformation of glass: volume changes in fused silica at high temperatures,” J. Am. Ceram. Soc. 96(1), 137–145 (2013).
[Crossref]

Tang, J.

Terazima, M.

M. Sakakura and M. Terazima, “Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass,” Appl. Phys. B 71(2), 024113 (2005).
[Crossref]

Vignes, R. M.

R. M. Vignes, T. F. Soules, J. S. Stolken, R. R. Settgast, S. Elhadj, and M. J. Matthews, “Thermomechanical modeling of laser-induced structural relaxation and deformation of glass: volume changes in fused silica at high temperatures,” J. Am. Ceram. Soc. 96(1), 137–145 (2013).
[Crossref]

Villarreal, F.

Wang, F.

F. Wang, Y. Zhang, H. Wang, W. Xu, Y. Zhang, and C. Li, “Nondestructive evaluation of residual stress via digital holographic photoelasticity,” J. Opt. 47(4), 547–552 (2018).
[Crossref]

Wang, H.

F. Wang, Y. Zhang, H. Wang, W. Xu, Y. Zhang, and C. Li, “Nondestructive evaluation of residual stress via digital holographic photoelasticity,” J. Opt. 47(4), 547–552 (2018).
[Crossref]

Wu, W.

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

Xie, H.

S. Zhang, H. Xie, X. T. Zeng, and P. Hing, “Residual stress characterization of diamond-like carbon coatings by an X-ray diffraction method,” Surf. Coat. Technol. 122(2-3), 219–224 (1999).
[Crossref]

Xu, D.

Xu, W.

F. Wang, Y. Zhang, H. Wang, W. Xu, Y. Zhang, and C. Li, “Nondestructive evaluation of residual stress via digital holographic photoelasticity,” J. Opt. 47(4), 547–552 (2018).
[Crossref]

Xu, Y.

You, C.

Zeng, X. T.

S. Zhang, H. Xie, X. T. Zeng, and P. Hing, “Residual stress characterization of diamond-like carbon coatings by an X-ray diffraction method,” Surf. Coat. Technol. 122(2-3), 219–224 (1999).
[Crossref]

Zhang, P.

Zhang, S.

S. Zhang, H. Xie, X. T. Zeng, and P. Hing, “Residual stress characterization of diamond-like carbon coatings by an X-ray diffraction method,” Surf. Coat. Technol. 122(2-3), 219–224 (1999).
[Crossref]

Zhang, Y.

F. Wang, Y. Zhang, H. Wang, W. Xu, Y. Zhang, and C. Li, “Nondestructive evaluation of residual stress via digital holographic photoelasticity,” J. Opt. 47(4), 547–552 (2018).
[Crossref]

F. Wang, Y. Zhang, H. Wang, W. Xu, Y. Zhang, and C. Li, “Nondestructive evaluation of residual stress via digital holographic photoelasticity,” J. Opt. 47(4), 547–552 (2018).
[Crossref]

Y. Zhang, Y. Xu, C. You, D. Xu, J. Tang, P. Zhang, and S. Dai, “Raman gain and femtosecond laser induced damage of Ge-As-S chalcogenide glasses,” Opt. Express 25(8), 8886–8895 (2017).
[Crossref]

Zhang, Z.

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

Zheng, W.

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

Zhou, X.

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

Appl. Opt. (3)

Appl. Phys. B (1)

M. Sakakura and M. Terazima, “Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass,” Appl. Phys. B 71(2), 024113 (2005).
[Crossref]

J. Am. Ceram. Soc. (1)

R. M. Vignes, T. F. Soules, J. S. Stolken, R. R. Settgast, S. Elhadj, and M. J. Matthews, “Thermomechanical modeling of laser-induced structural relaxation and deformation of glass: volume changes in fused silica at high temperatures,” J. Am. Ceram. Soc. 96(1), 137–145 (2013).
[Crossref]

J. Appl. Phys. (1)

T. Doualle, L. Gallais, P. Cormont, D. Hebert, P. Combis, and J. Rullier, “Thermo-mechanical simulations of CO2 laser-fused silica interactions,” J. Appl. Phys. 119(11), 113106 (2016).
[Crossref]

J. Mater. Sci. (1)

F. Dahmani, J. C. Lambropoulos, A. W. Schmid, S. J. Burns, and C. Prat, “Nanoindentation technique for measuring residual stress field around a laser-induced crack in fused silica,” J. Mater. Sci. 33(19), 4677–4685 (1998).
[Crossref]

J. Opt. (1)

F. Wang, Y. Zhang, H. Wang, W. Xu, Y. Zhang, and C. Li, “Nondestructive evaluation of residual stress via digital holographic photoelasticity,” J. Opt. 47(4), 547–552 (2018).
[Crossref]

Nucl. Fusion (1)

E. I. Moses, “The national ignition campaign: status and progress,” Nucl. Fusion 53(10), 104020 (2013).
[Crossref]

Opt. Eng. (2)

Z. Zhang, H. Liu, J. Huang, J. Huang, X. Zhou, D. Ren, X. Cheng, X. Jiang, W. Wu, and W. Zheng, “Residual stress near cracks of K and fused silica under 1064 nm nanosecond laser irradiation,” Opt. Eng. 51(11), 114201 (2012).
[Crossref]

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44(9), 093601 (2005).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Surf. Coat. Technol. (1)

S. Zhang, H. Xie, X. T. Zeng, and P. Hing, “Residual stress characterization of diamond-like carbon coatings by an X-ray diffraction method,” Surf. Coat. Technol. 122(2-3), 219–224 (1999).
[Crossref]

Other (3)

A. Kuske and G. Robertson, Photoelastic Stress Analysis (Wiley, 1974).

R. W. Boyd, Nonlinear Optics, Third Edition (Academic Press, 2009).

E. E. Gdoutos, Matrix theory of photoelasticity (Springer, 1979).

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Figures (7)

Fig. 1.
Fig. 1. (a) Two principal-stress axes around laser induced damage crack; (b) birefringence index distribution of numerical slices along z-direction.
Fig. 2.
Fig. 2. Determination of the sign of Δτk.
Fig. 3.
Fig. 3. Experimental setup for residual stress measurement on laser induced damage site.
Fig. 4.
Fig. 4. (a) Recorded interferograms, (b) reflect light intensity, (c) measured inner shear stress, and (d) simulated stress corresponding to various depths. White bars in (a), (b), (c) and (d) represent 1 mm.
Fig. 5.
Fig. 5. (a) 3-D plot of the measured residual stress around laser induced damage; (b) average stress distribution along radical direction; (c) average stress distribution along depth; (d) 3-D plot of the simulated residual stress around laser induced damage; (e) 3-D plot of the measured residual stress around laser induced damage after laser repairing.
Fig. 6.
Fig. 6. Comparison between the measurements obtained by traditional transmission photo-elastic method and suggested method. Rows (a), (b), (c) and (d) correspond to four samples, and the first six columns are the measured shearing stress at six depths, the 7th column is the integral of measured stress of all slices, and the 8th column is the measurement with common transmission photo-elastic method. The curves in the 9th column show quantitative comparisons between stress measured with the suggested method and common transmission method, where the red curves show the measurement of the suggested method, and the green curves show the measurement of the common transmission method.
Fig. 7.
Fig. 7. Experimental result on axial resolution.

Equations (7)

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

E k / / ( x , y ) = E 0 cos θ n k / / ( x , y ) n k + 1 / / ( x , y ) n k / / ( x , y ) + n k + 1 / / ( x , y ) exp [ 2 i 2 π λ 0 z k n / / ( x , y , z ) d z ] E k ( x , y ) = E 0 sin θ n k ( x , y ) n k + 1 ( x , y ) n k ( x , y ) + n k + 1 ( x , y ) exp [ 2 i 2 π λ 0 z k n ( x , y , z ) d z ]
E k ( x , y )  =  1 2 E 0 sin 2 θ { n k / / ( x , y ) n k + 1 / / ( x , y ) n k / / ( x , y ) + n k + 1 / / ( x , y ) exp [ 2 i 0 z k 2 π λ n / / ( x , y , z ) d z ] n k ( x , y ) n k + 1 ( x , y ) n k ( x , y ) + n k + 1 ( x , y ) exp [ 2 i 0 z k 2 π λ n ( x , y , z ) d z ] } .
I k ( x , y ) = 1 4 I 0 sin 2 2 θ { [ n k / / ( x , y ) n k + 1 / / ( x , y ) n k / / ( x , y ) + n k + 1 / / ( x , y ) ] 2 + [ n k ( x , y ) n k + 1 ( x , y ) n k ( x , y ) + n k + 1 ( x , y ) ] 2 2 n k / / ( x , y ) n k + 1 / / ( x , y ) n k / / ( x , y ) + n k + 1 / / ( x , y ) n k ( x , y ) n k + 1 ( x , y ) n k ( x , y ) + n k + 1 ( x , y ) + 4 n k / / ( x , y ) n k + 1 / / ( x , y ) n k / / ( x , y ) + n k + 1 / / ( x , y ) n k ( x , y ) n k + 1 ( x , y ) n k ( x , y ) + n k + 1 ( x , y ) sin 2 { 0 Z k [ n k / / ( x , y ) n k ( x , y ) ] d z } .
I k ( x , y ) 1 4 I 0 sin 2 2 θ [ n k / / ( x , y ) n k  +  1 / / ( x , y ) n k / / ( x , y ) + n k  +  1 / / ( x , y ) n k ( x , y ) n k + 1 ( x , y ) n k ( x , y ) + n k + 1 ( x , y ) ] 2 .
I k ( x , y ) 1 4 I 0 sin 2 2 θ [ n k / / ( x , y ) n k ( x , y ) 2 n 0 n k + 1 / / ( x , y ) n k + 1 ( x , y ) 2 n 0 ] 2 = 1 4 I 0 sin 2 2 θ [ δ n k ( x , y ) δ n k + 1 ( x , y ) 2 n 0 ] 2 .
I k ( x , y ) = C 2 16 n 0 2 E 0 2 sin 2 2 θ [ τ k ( x , y ) τ k + 1 ( x , y ) ] 2 .
Δ τ k ( x , y ) = 4 n 0 c I k ( x , y ) I 0 .