Abstract

Analysis of strain and the study of flexural moments of a deformed object is of utmost importance in non-destructive testing and evaluation. In digital holographic interferometry (DHI), this information is provided, respectively, by the first and second-order derivatives of the interference phase. This paper introduces high-order instantaneous moments based approach for the simultaneous measurement of displacement, strain and curvature distributions of a deformed object in DHI. Simulation and experimental results are presented to demonstrate the ability of the proposed method in accurately providing the direct estimation of the unwrapped distributions corresponding to the interference phase and its derivatives in a computationally efficient manner.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. B. Chen and C. Basaran, "Automatic full strain field moir’e interferometry measurement with nano-scale resolution," Exp. Mech. 48, 665-673 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. C. A. Sciammarella and T. Kim, "Frequency modulation interpretation of fringes and computation of strains," Exp. Mech. 45, 393-403 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. F. S. Chau, S. L. Toh, C. J. Tay, and H. M. Shang, "Some examples of nondestructive flaw detection by shearography," J. Nondestruct. Eval. 8, 225-234 (1989).
    [CrossRef]
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    [PubMed]
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    [CrossRef]
  22. T. J. Mackin, K. E. Perry, J. S. Epstein, C. Cady, and A. G. Evans, "Strain fields and damage around notches in ceramic-matrix composites," J. Am. Ceram. Soc. 79, 65-73 (1996).
    [CrossRef]
  23. M. R. Miller, I. Mohammed, P. S. Ho, and X. Dai, "Study of thermal deformation in underfilled flip-chip packages using high-resolution moire interferometry," American Society of Mechanical Engineers, EEP 26, 787-793 (1999).
  24. H. Xie, S. Kishimoto, J. Li, D. Zou, F. Dai, and N. Shinya, "Deformation analysis of laser processed grain oriented silicon steel sheet using moire interferometry," Materials Science Research International 5, 291-295 (1999).
  25. J. S. Ibrahim, J. N. Petzing, and J. R. Tyrer, "Deformation analysis of aircraft wheels using a speckle shearing interferometer," Proc. Inst. Mech. Eng., Part G: J. Aerospace Engg. 218, 287-295 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  29. C. Liu, "Simultaneous measurement of displacement and its spatial derivatives with a digital holographic method," Opt. Eng. 42, 3443-3446 (2003).
    [CrossRef]
  30. W. Chen, C. Quan, and C. J. Tay, "Measurement of curvature and twist of a deformed object using digital holography," Appl. Opt. 47, 2874-2881 (2008).
    [CrossRef] [PubMed]
  31. C. Quan, C. J. Tay, and W. Chen, "Determination of displacement derivative in digital holographic interferometry," Opt. Commun. 282, 809-815 (2009).
    [CrossRef]
  32. S. S. Gorthi and P. Rastogi, "Analysis of reconstructed interference fields in digital holographic interferometry using polynomial phase transform," Meas. Sci. Technol. 20(075307) (2009).
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    [CrossRef] [PubMed]
  38. A. Cordero-Davila, A. Cornejo-Rodriguez, and O. Cardona-Nunez, "Polynomial fitting of interferograms with Gaussian errors on fringe coordinates-I: Computer simulations," Appl. Opt. 33, 7339-7342 (1994).
    [CrossRef] [PubMed]
  39. J. Novak and A. Miks, "Least-squares fitting of wavefront using rational function," Opt. Laser Eng. 43, 40-51 (2005).
    [CrossRef]
  40. E. Aboutanios and B. Mulgrew, "Iterative frequency estimation by interpolation on Fourier coefficients," IEEE Trans. Sig. Proc. 53, 1237-1242 (2005).
    [CrossRef]
  41. U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
    [CrossRef]

2009 (2)

C. Quan, C. J. Tay, and W. Chen, "Determination of displacement derivative in digital holographic interferometry," Opt. Commun. 282, 809-815 (2009).
[CrossRef]

S. S. Gorthi and P. Rastogi, "Analysis of reconstructed interference fields in digital holographic interferometry using polynomial phase transform," Meas. Sci. Technol. 20(075307) (2009).

2008 (2)

B. Chen and C. Basaran, "Automatic full strain field moir’e interferometry measurement with nano-scale resolution," Exp. Mech. 48, 665-673 (2008).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, "Measurement of curvature and twist of a deformed object using digital holography," Appl. Opt. 47, 2874-2881 (2008).
[CrossRef] [PubMed]

2007 (1)

K. F. Wang, A. K. Tieu, and M. H. Gao, "Measurement of curvature distribution using digital speckle threeshearing aperture interferometry," Opt. Laser Technol. 39, 926-928 (2007).
[CrossRef]

2005 (3)

C. A. Sciammarella and T. Kim, "Frequency modulation interpretation of fringes and computation of strains," Exp. Mech. 45, 393-403 (2005).
[CrossRef]

J. Novak and A. Miks, "Least-squares fitting of wavefront using rational function," Opt. Laser Eng. 43, 40-51 (2005).
[CrossRef]

E. Aboutanios and B. Mulgrew, "Iterative frequency estimation by interpolation on Fourier coefficients," IEEE Trans. Sig. Proc. 53, 1237-1242 (2005).
[CrossRef]

2004 (1)

J. S. Ibrahim, J. N. Petzing, and J. R. Tyrer, "Deformation analysis of aircraft wheels using a speckle shearing interferometer," Proc. Inst. Mech. Eng., Part G: J. Aerospace Engg. 218, 287-295 (2004).
[CrossRef]

2003 (4)

C. Liu, "Simultaneous measurement of displacement and its spatial derivatives with a digital holographic method," Opt. Eng. 42, 3443-3446 (2003).
[CrossRef]

F. S. Chau and J. Zhou, "Direct measurement of curvature and twist of plates using digital shearography," Opt. Laser Eng. 39, 431-440 (2003).
[CrossRef]

Q. Kemao, S. H. Soon, and A. Asundi, "Phase-shifting windowed Fourier ridges for determination of phase derivatives," Opt. Lett. 28, 1657-1659 (2003).
[CrossRef]

Q. Kemao, S. H. Soon, and A. Asundi, "Instantaneous frequency and its application to strain extraction in moiré interferometry," Appl. Opt. 42, 6504-6513 (2003).
[CrossRef] [PubMed]

2002 (1)

U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

2001 (1)

2000 (1)

1999 (2)

M. R. Miller, I. Mohammed, P. S. Ho, and X. Dai, "Study of thermal deformation in underfilled flip-chip packages using high-resolution moire interferometry," American Society of Mechanical Engineers, EEP 26, 787-793 (1999).

H. Xie, S. Kishimoto, J. Li, D. Zou, F. Dai, and N. Shinya, "Deformation analysis of laser processed grain oriented silicon steel sheet using moire interferometry," Materials Science Research International 5, 291-295 (1999).

1998 (1)

S. Golden and B. Friedlander, "A modification of the discrete polynomial transform," IEEE Trans. Sig. Proc. 46, 1452-1455 (1998).
[CrossRef]

1996 (4)

A. Twitto, J. Shamir, A. Bekker, and A. Notea, "Detection of internal defects using phase shifting holographic interferometry," NDT and E International 29, 163-173 (1996).
[CrossRef]

T. J. Mackin, K. E. Perry, J. S. Epstein, C. Cady, and A. G. Evans, "Strain fields and damage around notches in ceramic-matrix composites," J. Am. Ceram. Soc. 79, 65-73 (1996).
[CrossRef]

G. Subramanian and A. Subramanian, "Curvature contours of flexed plates by a multiple illumination moiré shearing interferometer," Strain 32, 59-62 (1996).
[CrossRef]

P. K. Rastogi, "Measurement of curvature and twist of a deformed object by electronic speckle-shearing pattern interferometry," Opt. Lett. 21, 905-907 (1996).
[CrossRef] [PubMed]

1994 (6)

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, "Direct determination of second-order derivatives in plate bending using multiple-exposure shearography," Opt. Laser Technol. 26, 91-98 (1994).
[CrossRef]

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, "Coherent moire technique for obtaining slope and curvature of stress patterns," Opt. Eng. 33, 3359-3363 (1994).
[CrossRef]

G. K. Bhat, "A Fourier transform technique to obtain phase derivatives in interferometry," Opt. Commun. 110, 279-286 (1994).
[CrossRef]

Y. Zou, G. Pedrini, and H. Tiziani, "Derivatives obtained directly from displacement data," Opt. Commun. 111, 427-432 (1994).
[CrossRef]

U. Schnars and W. P. O. Juptner, "Digital recording and reconstruction of holograms in hologram interferometry and shearography," Appl. Opt. 33, 4373-4377 (1994).
[CrossRef] [PubMed]

A. Cordero-Davila, A. Cornejo-Rodriguez, and O. Cardona-Nunez, "Polynomial fitting of interferograms with Gaussian errors on fringe coordinates-I: Computer simulations," Appl. Opt. 33, 7339-7342 (1994).
[CrossRef] [PubMed]

1991 (1)

P. K. Rastogi, "Visualization and measurement of slope and curvature fields using holographic interferometry: an application to flaw detection," J. Mod. Opt. 38, 1251-1263 (1991).
[CrossRef]

1989 (2)

F. S. Chau, S. L. Toh, C. J. Tay, and H. M. Shang, "Some examples of nondestructive flaw detection by shearography," J. Nondestruct. Eval. 8, 225-234 (1989).
[CrossRef]

B. Ovryn, "Holographic interferometry," Critical Reviews in Biomedical Engineering 16, 269-322 (1989).
[PubMed]

1987 (1)

Y. Kwon, S. Danyluk, L. Bucciarelli, and J. P. Kalejs, "Residual stress measurement in silicon sheet by shadow moir’e interferometry," J. Cryst. Growth 82, 221-227 (1987).
[CrossRef]

1985 (1)

A. T. Andonian and S. Danyluk, "Residual stresses of thin, short rectangular plates," J. Material Sci. 20, 4459- 4464 (1985).
[CrossRef]

1984 (1)

1982 (2)

Y. Y. Hung, "Shearography: A new optical method for strain measurement and nondestructive testing." Opt. Eng. 21, 391-395 (1982).

C. J. Kim, "Polynomial fit of interferograms," Appl. Opt. 21, 4521-4525 (1982).
[CrossRef] [PubMed]

1980 (1)

1979 (1)

F. P. Chiang and T. Y. Kao, "An optical method of generating slope and curvature contours of bent plates," Int. J. Solids Struct. 15, 251-260 (1979).
[CrossRef]

1972 (1)

Aboutanios, E.

E. Aboutanios and B. Mulgrew, "Iterative frequency estimation by interpolation on Fourier coefficients," IEEE Trans. Sig. Proc. 53, 1237-1242 (2005).
[CrossRef]

Andonian, A. T.

A. T. Andonian and S. Danyluk, "Residual stresses of thin, short rectangular plates," J. Material Sci. 20, 4459- 4464 (1985).
[CrossRef]

Asundi, A.

Basaran, C.

B. Chen and C. Basaran, "Automatic full strain field moir’e interferometry measurement with nano-scale resolution," Exp. Mech. 48, 665-673 (2008).
[CrossRef]

Basuray, A.

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, "Coherent moire technique for obtaining slope and curvature of stress patterns," Opt. Eng. 33, 3359-3363 (1994).
[CrossRef]

Bekker, A.

A. Twitto, J. Shamir, A. Bekker, and A. Notea, "Detection of internal defects using phase shifting holographic interferometry," NDT and E International 29, 163-173 (1996).
[CrossRef]

Bhadra, S. K.

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, "Coherent moire technique for obtaining slope and curvature of stress patterns," Opt. Eng. 33, 3359-3363 (1994).
[CrossRef]

Bhat, G. K.

G. K. Bhat, "A Fourier transform technique to obtain phase derivatives in interferometry," Opt. Commun. 110, 279-286 (1994).
[CrossRef]

Bucciarelli, L.

Y. Kwon, S. Danyluk, L. Bucciarelli, and J. P. Kalejs, "Residual stress measurement in silicon sheet by shadow moir’e interferometry," J. Cryst. Growth 82, 221-227 (1987).
[CrossRef]

Cady, C.

T. J. Mackin, K. E. Perry, J. S. Epstein, C. Cady, and A. G. Evans, "Strain fields and damage around notches in ceramic-matrix composites," J. Am. Ceram. Soc. 79, 65-73 (1996).
[CrossRef]

Cardona-Nunez, O.

Chakraborty, R. N.

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, "Coherent moire technique for obtaining slope and curvature of stress patterns," Opt. Eng. 33, 3359-3363 (1994).
[CrossRef]

Chau, F. S.

F. S. Chau and J. Zhou, "Direct measurement of curvature and twist of plates using digital shearography," Opt. Laser Eng. 39, 431-440 (2003).
[CrossRef]

F. S. Chau, S. L. Toh, C. J. Tay, and H. M. Shang, "Some examples of nondestructive flaw detection by shearography," J. Nondestruct. Eval. 8, 225-234 (1989).
[CrossRef]

Chen, B.

B. Chen and C. Basaran, "Automatic full strain field moir’e interferometry measurement with nano-scale resolution," Exp. Mech. 48, 665-673 (2008).
[CrossRef]

Chen, W.

C. Quan, C. J. Tay, and W. Chen, "Determination of displacement derivative in digital holographic interferometry," Opt. Commun. 282, 809-815 (2009).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, "Measurement of curvature and twist of a deformed object using digital holography," Appl. Opt. 47, 2874-2881 (2008).
[CrossRef] [PubMed]

Chiang, F. P.

F. P. Chiang and T. Y. Kao, "An optical method of generating slope and curvature contours of bent plates," Int. J. Solids Struct. 15, 251-260 (1979).
[CrossRef]

Cordero-Davila, A.

Cornejo-Rodriguez, A.

Dai, F.

H. Xie, S. Kishimoto, J. Li, D. Zou, F. Dai, and N. Shinya, "Deformation analysis of laser processed grain oriented silicon steel sheet using moire interferometry," Materials Science Research International 5, 291-295 (1999).

Dai, X.

M. R. Miller, I. Mohammed, P. S. Ho, and X. Dai, "Study of thermal deformation in underfilled flip-chip packages using high-resolution moire interferometry," American Society of Mechanical Engineers, EEP 26, 787-793 (1999).

Danyluk, S.

Y. Kwon, S. Danyluk, L. Bucciarelli, and J. P. Kalejs, "Residual stress measurement in silicon sheet by shadow moir’e interferometry," J. Cryst. Growth 82, 221-227 (1987).
[CrossRef]

A. T. Andonian and S. Danyluk, "Residual stresses of thin, short rectangular plates," J. Material Sci. 20, 4459- 4464 (1985).
[CrossRef]

Epstein, J. S.

T. J. Mackin, K. E. Perry, J. S. Epstein, C. Cady, and A. G. Evans, "Strain fields and damage around notches in ceramic-matrix composites," J. Am. Ceram. Soc. 79, 65-73 (1996).
[CrossRef]

Evans, A. G.

T. J. Mackin, K. E. Perry, J. S. Epstein, C. Cady, and A. G. Evans, "Strain fields and damage around notches in ceramic-matrix composites," J. Am. Ceram. Soc. 79, 65-73 (1996).
[CrossRef]

Fox, D. G.

Friedlander, B.

S. Golden and B. Friedlander, "A modification of the discrete polynomial transform," IEEE Trans. Sig. Proc. 46, 1452-1455 (1998).
[CrossRef]

Gao, M. H.

K. F. Wang, A. K. Tieu, and M. H. Gao, "Measurement of curvature distribution using digital speckle threeshearing aperture interferometry," Opt. Laser Technol. 39, 926-928 (2007).
[CrossRef]

Golden, S.

S. Golden and B. Friedlander, "A modification of the discrete polynomial transform," IEEE Trans. Sig. Proc. 46, 1452-1455 (1998).
[CrossRef]

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, "Analysis of reconstructed interference fields in digital holographic interferometry using polynomial phase transform," Meas. Sci. Technol. 20(075307) (2009).

Ho, P. S.

M. R. Miller, I. Mohammed, P. S. Ho, and X. Dai, "Study of thermal deformation in underfilled flip-chip packages using high-resolution moire interferometry," American Society of Mechanical Engineers, EEP 26, 787-793 (1999).

Hung, M. Y. Y.

Hung, Y. Y.

Y. Y. Hung, "Shearography: A new optical method for strain measurement and nondestructive testing." Opt. Eng. 21, 391-395 (1982).

Ibrahim, J. S.

J. S. Ibrahim, J. N. Petzing, and J. R. Tyrer, "Deformation analysis of aircraft wheels using a speckle shearing interferometer," Proc. Inst. Mech. Eng., Part G: J. Aerospace Engg. 218, 287-295 (2004).
[CrossRef]

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

U. Schnars and W. P. O. Juptner, "Digital recording and reconstruction of holograms in hologram interferometry and shearography," Appl. Opt. 33, 4373-4377 (1994).
[CrossRef] [PubMed]

Kalejs, J. P.

Y. Kwon, S. Danyluk, L. Bucciarelli, and J. P. Kalejs, "Residual stress measurement in silicon sheet by shadow moir’e interferometry," J. Cryst. Growth 82, 221-227 (1987).
[CrossRef]

Kao, T. Y.

F. P. Chiang and T. Y. Kao, "An optical method of generating slope and curvature contours of bent plates," Int. J. Solids Struct. 15, 251-260 (1979).
[CrossRef]

Kemao, Q.

Kiet Tieu, A.

Kim, C. J.

Kim, T.

C. A. Sciammarella and T. Kim, "Frequency modulation interpretation of fringes and computation of strains," Exp. Mech. 45, 393-403 (2005).
[CrossRef]

King, C. M.

Kishimoto, S.

H. Xie, S. Kishimoto, J. Li, D. Zou, F. Dai, and N. Shinya, "Deformation analysis of laser processed grain oriented silicon steel sheet using moire interferometry," Materials Science Research International 5, 291-295 (1999).

Kothiyal, M. P.

Kwon, Y.

Y. Kwon, S. Danyluk, L. Bucciarelli, and J. P. Kalejs, "Residual stress measurement in silicon sheet by shadow moir’e interferometry," J. Cryst. Growth 82, 221-227 (1987).
[CrossRef]

Li, E. B.

Li, J.

H. Xie, S. Kishimoto, J. Li, D. Zou, F. Dai, and N. Shinya, "Deformation analysis of laser processed grain oriented silicon steel sheet using moire interferometry," Materials Science Research International 5, 291-295 (1999).

Lin, L.

Lin, Q. Y.

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, "Direct determination of second-order derivatives in plate bending using multiple-exposure shearography," Opt. Laser Technol. 26, 91-98 (1994).
[CrossRef]

Liu, C.

C. Liu, "Simultaneous measurement of displacement and its spatial derivatives with a digital holographic method," Opt. Eng. 42, 3443-3446 (2003).
[CrossRef]

Mackin, T. J.

T. J. Mackin, K. E. Perry, J. S. Epstein, C. Cady, and A. G. Evans, "Strain fields and damage around notches in ceramic-matrix composites," J. Am. Ceram. Soc. 79, 65-73 (1996).
[CrossRef]

Miks, A.

J. Novak and A. Miks, "Least-squares fitting of wavefront using rational function," Opt. Laser Eng. 43, 40-51 (2005).
[CrossRef]

Miller, M. R.

M. R. Miller, I. Mohammed, P. S. Ho, and X. Dai, "Study of thermal deformation in underfilled flip-chip packages using high-resolution moire interferometry," American Society of Mechanical Engineers, EEP 26, 787-793 (1999).

Mohammed, I.

M. R. Miller, I. Mohammed, P. S. Ho, and X. Dai, "Study of thermal deformation in underfilled flip-chip packages using high-resolution moire interferometry," American Society of Mechanical Engineers, EEP 26, 787-793 (1999).

Mulgrew, B.

E. Aboutanios and B. Mulgrew, "Iterative frequency estimation by interpolation on Fourier coefficients," IEEE Trans. Sig. Proc. 53, 1237-1242 (2005).
[CrossRef]

Notea, A.

A. Twitto, J. Shamir, A. Bekker, and A. Notea, "Detection of internal defects using phase shifting holographic interferometry," NDT and E International 29, 163-173 (1996).
[CrossRef]

Novak, J.

J. Novak and A. Miks, "Least-squares fitting of wavefront using rational function," Opt. Laser Eng. 43, 40-51 (2005).
[CrossRef]

Ovryn, B.

B. Ovryn, "Holographic interferometry," Critical Reviews in Biomedical Engineering 16, 269-322 (1989).
[PubMed]

Pedrini, G.

Y. Zou, G. Pedrini, and H. Tiziani, "Derivatives obtained directly from displacement data," Opt. Commun. 111, 427-432 (1994).
[CrossRef]

Perry, K. E.

T. J. Mackin, K. E. Perry, J. S. Epstein, C. Cady, and A. G. Evans, "Strain fields and damage around notches in ceramic-matrix composites," J. Am. Ceram. Soc. 79, 65-73 (1996).
[CrossRef]

Petzing, J. N.

J. S. Ibrahim, J. N. Petzing, and J. R. Tyrer, "Deformation analysis of aircraft wheels using a speckle shearing interferometer," Proc. Inst. Mech. Eng., Part G: J. Aerospace Engg. 218, 287-295 (2004).
[CrossRef]

Quan, C.

C. Quan, C. J. Tay, and W. Chen, "Determination of displacement derivative in digital holographic interferometry," Opt. Commun. 282, 809-815 (2009).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, "Measurement of curvature and twist of a deformed object using digital holography," Appl. Opt. 47, 2874-2881 (2008).
[CrossRef] [PubMed]

Rastogi, P.

S. S. Gorthi and P. Rastogi, "Analysis of reconstructed interference fields in digital holographic interferometry using polynomial phase transform," Meas. Sci. Technol. 20(075307) (2009).

Rastogi, P. K.

P. K. Rastogi, "Measurement of curvature and twist of a deformed object by electronic speckle-shearing pattern interferometry," Opt. Lett. 21, 905-907 (1996).
[CrossRef] [PubMed]

P. K. Rastogi, "Visualization and measurement of slope and curvature fields using holographic interferometry: an application to flaw detection," J. Mod. Opt. 38, 1251-1263 (1991).
[CrossRef]

Rimmer, M. P.

Sarkar, S. K.

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, "Coherent moire technique for obtaining slope and curvature of stress patterns," Opt. Eng. 33, 3359-3363 (1994).
[CrossRef]

Schnars, U.

U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

U. Schnars and W. P. O. Juptner, "Digital recording and reconstruction of holograms in hologram interferometry and shearography," Appl. Opt. 33, 4373-4377 (1994).
[CrossRef] [PubMed]

Sciammarella, C. A.

C. A. Sciammarella and T. Kim, "Frequency modulation interpretation of fringes and computation of strains," Exp. Mech. 45, 393-403 (2005).
[CrossRef]

Shamir, J.

A. Twitto, J. Shamir, A. Bekker, and A. Notea, "Detection of internal defects using phase shifting holographic interferometry," NDT and E International 29, 163-173 (1996).
[CrossRef]

Shang, H. M.

M. Y. Y. Hung, L. Lin, and H. M. Shang, "Simple method for direct determination of bending strains by use of digital holography," Appl. Opt. 40, 4514-4518 (2001).
[CrossRef]

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, "Direct determination of second-order derivatives in plate bending using multiple-exposure shearography," Opt. Laser Technol. 26, 91-98 (1994).
[CrossRef]

F. S. Chau, S. L. Toh, C. J. Tay, and H. M. Shang, "Some examples of nondestructive flaw detection by shearography," J. Nondestruct. Eval. 8, 225-234 (1989).
[CrossRef]

Sharma, D. K.

Shinya, N.

H. Xie, S. Kishimoto, J. Li, D. Zou, F. Dai, and N. Shinya, "Deformation analysis of laser processed grain oriented silicon steel sheet using moire interferometry," Materials Science Research International 5, 291-295 (1999).

Silva, D. E.

Sirohi, R. S.

Soon, S. H.

Subramanian, A.

G. Subramanian and A. Subramanian, "Curvature contours of flexed plates by a multiple illumination moiré shearing interferometer," Strain 32, 59-62 (1996).
[CrossRef]

Subramanian, G.

G. Subramanian and A. Subramanian, "Curvature contours of flexed plates by a multiple illumination moiré shearing interferometer," Strain 32, 59-62 (1996).
[CrossRef]

Tay, C. J.

C. Quan, C. J. Tay, and W. Chen, "Determination of displacement derivative in digital holographic interferometry," Opt. Commun. 282, 809-815 (2009).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, "Measurement of curvature and twist of a deformed object using digital holography," Appl. Opt. 47, 2874-2881 (2008).
[CrossRef] [PubMed]

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, "Direct determination of second-order derivatives in plate bending using multiple-exposure shearography," Opt. Laser Technol. 26, 91-98 (1994).
[CrossRef]

F. S. Chau, S. L. Toh, C. J. Tay, and H. M. Shang, "Some examples of nondestructive flaw detection by shearography," J. Nondestruct. Eval. 8, 225-234 (1989).
[CrossRef]

Tieu, A. K.

K. F. Wang, A. K. Tieu, and M. H. Gao, "Measurement of curvature distribution using digital speckle threeshearing aperture interferometry," Opt. Laser Technol. 39, 926-928 (2007).
[CrossRef]

Tiziani, H.

Y. Zou, G. Pedrini, and H. Tiziani, "Derivatives obtained directly from displacement data," Opt. Commun. 111, 427-432 (1994).
[CrossRef]

Toh, S. L.

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, "Direct determination of second-order derivatives in plate bending using multiple-exposure shearography," Opt. Laser Technol. 26, 91-98 (1994).
[CrossRef]

F. S. Chau, S. L. Toh, C. J. Tay, and H. M. Shang, "Some examples of nondestructive flaw detection by shearography," J. Nondestruct. Eval. 8, 225-234 (1989).
[CrossRef]

Twitto, A.

A. Twitto, J. Shamir, A. Bekker, and A. Notea, "Detection of internal defects using phase shifting holographic interferometry," NDT and E International 29, 163-173 (1996).
[CrossRef]

Tyrer, J. R.

J. S. Ibrahim, J. N. Petzing, and J. R. Tyrer, "Deformation analysis of aircraft wheels using a speckle shearing interferometer," Proc. Inst. Mech. Eng., Part G: J. Aerospace Engg. 218, 287-295 (2004).
[CrossRef]

Wang, J. Y.

Wang, K. F.

K. F. Wang, A. K. Tieu, and M. H. Gao, "Measurement of curvature distribution using digital speckle threeshearing aperture interferometry," Opt. Laser Technol. 39, 926-928 (2007).
[CrossRef]

K. F. Wang, A. Kiet Tieu, and E. B. Li, "Simultaneous measurement of pure curvature and twist distribution fields by a five-aperture shearing and two-Fourier filtering technique," Appl. Opt. 39, 2577-2583 (2000).
[CrossRef]

Xie, H.

H. Xie, S. Kishimoto, J. Li, D. Zou, F. Dai, and N. Shinya, "Deformation analysis of laser processed grain oriented silicon steel sheet using moire interferometry," Materials Science Research International 5, 291-295 (1999).

Zhou, J.

F. S. Chau and J. Zhou, "Direct measurement of curvature and twist of plates using digital shearography," Opt. Laser Eng. 39, 431-440 (2003).
[CrossRef]

Zou, D.

H. Xie, S. Kishimoto, J. Li, D. Zou, F. Dai, and N. Shinya, "Deformation analysis of laser processed grain oriented silicon steel sheet using moire interferometry," Materials Science Research International 5, 291-295 (1999).

Zou, Y.

Y. Zou, G. Pedrini, and H. Tiziani, "Derivatives obtained directly from displacement data," Opt. Commun. 111, 427-432 (1994).
[CrossRef]

American Society of Mechanical Engineers, EEP (1)

M. R. Miller, I. Mohammed, P. S. Ho, and X. Dai, "Study of thermal deformation in underfilled flip-chip packages using high-resolution moire interferometry," American Society of Mechanical Engineers, EEP 26, 787-793 (1999).

Appl. Opt. (10)

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C. J. Kim, "Polynomial fit of interferograms," Appl. Opt. 21, 4521-4525 (1982).
[CrossRef] [PubMed]

D. K. Sharma, R. S. Sirohi, and M. P. Kothiyal, "Simultaneous measurement of slope and curvature with a three-aperture speckle shearing interferometr." Appl. Opt. 23, 1542-1546 (1984).
[CrossRef] [PubMed]

U. Schnars and W. P. O. Juptner, "Digital recording and reconstruction of holograms in hologram interferometry and shearography," Appl. Opt. 33, 4373-4377 (1994).
[CrossRef] [PubMed]

A. Cordero-Davila, A. Cornejo-Rodriguez, and O. Cardona-Nunez, "Polynomial fitting of interferograms with Gaussian errors on fringe coordinates-I: Computer simulations," Appl. Opt. 33, 7339-7342 (1994).
[CrossRef] [PubMed]

K. F. Wang, A. Kiet Tieu, and E. B. Li, "Simultaneous measurement of pure curvature and twist distribution fields by a five-aperture shearing and two-Fourier filtering technique," Appl. Opt. 39, 2577-2583 (2000).
[CrossRef]

M. Y. Y. Hung, L. Lin, and H. M. Shang, "Simple method for direct determination of bending strains by use of digital holography," Appl. Opt. 40, 4514-4518 (2001).
[CrossRef]

Q. Kemao, S. H. Soon, and A. Asundi, "Instantaneous frequency and its application to strain extraction in moiré interferometry," Appl. Opt. 42, 6504-6513 (2003).
[CrossRef] [PubMed]

W. Chen, C. Quan, and C. J. Tay, "Measurement of curvature and twist of a deformed object using digital holography," Appl. Opt. 47, 2874-2881 (2008).
[CrossRef] [PubMed]

Critical Reviews in Biomedical Engineering (1)

B. Ovryn, "Holographic interferometry," Critical Reviews in Biomedical Engineering 16, 269-322 (1989).
[PubMed]

Exp. Mech. (2)

C. A. Sciammarella and T. Kim, "Frequency modulation interpretation of fringes and computation of strains," Exp. Mech. 45, 393-403 (2005).
[CrossRef]

B. Chen and C. Basaran, "Automatic full strain field moir’e interferometry measurement with nano-scale resolution," Exp. Mech. 48, 665-673 (2008).
[CrossRef]

IEEE Trans. Sig. Proc. (2)

E. Aboutanios and B. Mulgrew, "Iterative frequency estimation by interpolation on Fourier coefficients," IEEE Trans. Sig. Proc. 53, 1237-1242 (2005).
[CrossRef]

S. Golden and B. Friedlander, "A modification of the discrete polynomial transform," IEEE Trans. Sig. Proc. 46, 1452-1455 (1998).
[CrossRef]

Int. J. Solids Struct. (1)

F. P. Chiang and T. Y. Kao, "An optical method of generating slope and curvature contours of bent plates," Int. J. Solids Struct. 15, 251-260 (1979).
[CrossRef]

J. Am. Ceram. Soc. (1)

T. J. Mackin, K. E. Perry, J. S. Epstein, C. Cady, and A. G. Evans, "Strain fields and damage around notches in ceramic-matrix composites," J. Am. Ceram. Soc. 79, 65-73 (1996).
[CrossRef]

J. Cryst. Growth (1)

Y. Kwon, S. Danyluk, L. Bucciarelli, and J. P. Kalejs, "Residual stress measurement in silicon sheet by shadow moir’e interferometry," J. Cryst. Growth 82, 221-227 (1987).
[CrossRef]

J. Material Sci. (1)

A. T. Andonian and S. Danyluk, "Residual stresses of thin, short rectangular plates," J. Material Sci. 20, 4459- 4464 (1985).
[CrossRef]

J. Mod. Opt. (1)

P. K. Rastogi, "Visualization and measurement of slope and curvature fields using holographic interferometry: an application to flaw detection," J. Mod. Opt. 38, 1251-1263 (1991).
[CrossRef]

J. Nondestruct. Eval. (1)

F. S. Chau, S. L. Toh, C. J. Tay, and H. M. Shang, "Some examples of nondestructive flaw detection by shearography," J. Nondestruct. Eval. 8, 225-234 (1989).
[CrossRef]

Materials Science Research International (1)

H. Xie, S. Kishimoto, J. Li, D. Zou, F. Dai, and N. Shinya, "Deformation analysis of laser processed grain oriented silicon steel sheet using moire interferometry," Materials Science Research International 5, 291-295 (1999).

Meas. Sci. Technol. (2)

S. S. Gorthi and P. Rastogi, "Analysis of reconstructed interference fields in digital holographic interferometry using polynomial phase transform," Meas. Sci. Technol. 20(075307) (2009).

U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

NDT and E International (1)

A. Twitto, J. Shamir, A. Bekker, and A. Notea, "Detection of internal defects using phase shifting holographic interferometry," NDT and E International 29, 163-173 (1996).
[CrossRef]

Opt. Commun. (3)

G. K. Bhat, "A Fourier transform technique to obtain phase derivatives in interferometry," Opt. Commun. 110, 279-286 (1994).
[CrossRef]

C. Quan, C. J. Tay, and W. Chen, "Determination of displacement derivative in digital holographic interferometry," Opt. Commun. 282, 809-815 (2009).
[CrossRef]

Y. Zou, G. Pedrini, and H. Tiziani, "Derivatives obtained directly from displacement data," Opt. Commun. 111, 427-432 (1994).
[CrossRef]

Opt. Eng. (3)

C. Liu, "Simultaneous measurement of displacement and its spatial derivatives with a digital holographic method," Opt. Eng. 42, 3443-3446 (2003).
[CrossRef]

Y. Y. Hung, "Shearography: A new optical method for strain measurement and nondestructive testing." Opt. Eng. 21, 391-395 (1982).

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, "Coherent moire technique for obtaining slope and curvature of stress patterns," Opt. Eng. 33, 3359-3363 (1994).
[CrossRef]

Opt. Laser Eng. (2)

F. S. Chau and J. Zhou, "Direct measurement of curvature and twist of plates using digital shearography," Opt. Laser Eng. 39, 431-440 (2003).
[CrossRef]

J. Novak and A. Miks, "Least-squares fitting of wavefront using rational function," Opt. Laser Eng. 43, 40-51 (2005).
[CrossRef]

Opt. Laser Technol. (2)

K. F. Wang, A. K. Tieu, and M. H. Gao, "Measurement of curvature distribution using digital speckle threeshearing aperture interferometry," Opt. Laser Technol. 39, 926-928 (2007).
[CrossRef]

C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, "Direct determination of second-order derivatives in plate bending using multiple-exposure shearography," Opt. Laser Technol. 26, 91-98 (1994).
[CrossRef]

Opt. Lett. (2)

Part G: J. Aerospace Engg. (1)

J. S. Ibrahim, J. N. Petzing, and J. R. Tyrer, "Deformation analysis of aircraft wheels using a speckle shearing interferometer," Proc. Inst. Mech. Eng., Part G: J. Aerospace Engg. 218, 287-295 (2004).
[CrossRef]

Strain (1)

G. Subramanian and A. Subramanian, "Curvature contours of flexed plates by a multiple illumination moiré shearing interferometer," Strain 32, 59-62 (1996).
[CrossRef]

Other (1)

B. Porat, "Digital processing of random signals," Prentice-Hall (1994).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Simulated fringe pattern using the peaks function in MATLAB (SNR=30dB, 256×256), (b) 3D mesh plot of the estimated phase distribution using the HIMs based method (c) Error in phase estimation.

Fig. 2.
Fig. 2.

Patterns analyzed with the proposed method for estimating phase and their derivatives (a) Simulated fringe pattern (SNR=30 dB, 256×256) (b) Fringe pattern obtained in a DHI experiment corresponding to the central loading of a circularly clamped object (256×256).

Fig. 3.
Fig. 3.

3D mesh plots of the estimated distributions from Fig. 2(a) with the proposed method corresponding to (a) interference phase, (b) first-order derivative of phase (c) second-order derivative of phase, (d), (e), (f) wrapped phase maps generated for the purpose of illustration corresponding to (a), (b) and (c) respectively.

Fig. 4.
Fig. 4.

3D mesh plots of the estimated distributions from Fig. 2(b) with the proposed method corresponding to (a) out-of-plane displacement, (b) slope, (c) curvature, (d), (e), (f) wrapped maps generated for the purpose of illustration corresponding to (a), (b) and (c) respectively, (g), (h), (i) phase and its derivatives calculated using conventional direct differentiation approach shown for the purpose of comparison.

Equations (8)

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

A(x,y)=b(x,y)exp[jΔϕ(x,y)]+η(x,y)
Ayi=byiexp(jΔϕyi)+ηyi
g(x)=b(x)exp[j(q=0Maqxq)]+η(x)
Δϕ(x)=a0+a1x+a2x2++aMxM
Δϕx=a1+2a2x+3a3x2++MaMxM1
2Δϕx2=2a2+6a3x+12a4x2++M(M1)aMxM2
HIMM[g(x),τq]=q=0M1[gq(xqτq)](M1q)
âM=ω0M!γ

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