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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 20 — Sep. 28, 2009
  • pp: 17784–17791

Simultaneous measurement of displacement, strain and curvature in digital holographic interferometry using high-order instantaneous moments

Sai Siva Gorthi and Pramod Rastogi  »View Author Affiliations

Optics Express, Vol. 17, Issue 20, pp. 17784-17791 (2009)

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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

OCIS Codes
(120.2880) Instrumentation, measurement, and metrology : Holographic interferometry
(120.4290) Instrumentation, measurement, and metrology : Nondestructive testing
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(090.1995) Holography : Digital holography

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: July 29, 2009
Revised Manuscript: September 10, 2009
Manuscript Accepted: September 13, 2009
Published: September 18, 2009

Sai Siva Gorthi and Pramod Rastogi, "Simultaneous measurement of displacement, strain and curvature in digital holographic interferometry using high-order instantaneous moments," Opt. Express 17, 17784-17791 (2009)

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  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]
  2. Y. Y. Hung, "Shearography: A new optical method for strain measurement and nondestructive testing." Opt. Eng. 21, 391-395 (1982).
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  7. G. Subramanian and A. Subramanian, "Curvature contours of flexed plates by a multiple illumination moiré shearing interferometer," Strain 32, 59-62 (1996). [CrossRef]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  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]
  13. G. K. Bhat, "A Fourier transform technique to obtain phase derivatives in interferometry," Opt. Commun. 110, 279-286 (1994). [CrossRef]
  14. 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]
  15. 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]
  16. C. A. Sciammarella and T. Kim, "Frequency modulation interpretation of fringes and computation of strains," Exp. Mech. 45, 393-403 (2005). [CrossRef]
  17. A. T. Andonian and S. Danyluk, "Residual stresses of thin, short rectangular plates," J. Material Sci. 20, 4459- 4464 (1985). [CrossRef]
  18. 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]
  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]
  20. B. Ovryn, "Holographic interferometry," Critical Reviews in Biomedical Engineering 16, 269-322 (1989). [PubMed]
  21. 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]
  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]
  26. 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]
  27. Y. Zou, G. Pedrini, and H. Tiziani, "Derivatives obtained directly from displacement data," Opt. Commun. 111, 427-432 (1994). [CrossRef]
  28. 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]
  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).
  33. B. Porat, "Digital processing of random signals," Prentice-Hall (1994).
  34. S. Golden and B. Friedlander, "A modification of the discrete polynomial transform," IEEE Trans. Sig. Proc. 46, 1452-1455 (1998). [CrossRef]
  35. M. P. Rimmer, C. M. King, and D. G. Fox, "Computer program for the analysis of interferometric test data," Appl. Opt. 11, 2790-2796 (1972). [CrossRef] [PubMed]
  36. J. Y. Wang and D. E. Silva, "Wave-front interpretation with Zernike polynomials," Appl. Opt. 19, 1510-1518 (1980). [CrossRef] [PubMed]
  37. C. J. Kim, "Polynomial fit of interferograms," Appl. Opt. 21, 4521-4525 (1982). [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]

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