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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 15 — May. 20, 2008
  • pp: 2874–2881

Measurement of curvature and twist of a deformed object using digital holography

Wen Chen, Chenggen Quan, and Cho Jui Tay  »View Author Affiliations

Applied Optics, Vol. 47, Issue 15, pp. 2874-2881 (2008)

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Measurement of curvature and twist is an important aspect in the study of object deformation. In recent years, several methods have been proposed to determine curvature and twist of a deformed object using digital shearography. Here we propose a novel method to determine the curvature and twist of a deformed object using digital holography and a complex phasor. A sine/cosine transformation method and two-dimensional short time Fourier transform are proposed subsequently to process the wrapped phase maps. It is shown that high-quality phase maps corresponding to curvature and twist can be obtained. An experiment is conducted to demonstrate the validity of the proposed method.

© 2008 Optical Society of America

OCIS Codes
(090.2880) Holography : Holographic interferometry
(100.5070) Image processing : Phase retrieval
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(090.1995) Holography : Digital holography

ToC Category:

Original Manuscript: February 28, 2008
Revised Manuscript: April 23, 2008
Manuscript Accepted: April 25, 2008
Published: May 15, 2008

Wen Chen, Chenggen Quan, and Cho Jui Tay, "Measurement of curvature and twist of a deformed object using digital holography," Appl. Opt. 47, 2874-2881 (2008)

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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. F. S. Chau and J. Zhou, “Direct measurement of curvature and twist of plates using digital shearography,” Opt. Lasers Eng. 39, 431-440 (2003). [CrossRef]
  3. Y. Y. Hung and C. Y. Liang, “Image-shearing camera for direct measurement of surface strains,” Appl. Opt. 18, 1046-1051(1979). [CrossRef] [PubMed]
  4. D. K. Sharma, R. S. Sirohi, and M. P. Kothiyal, “Simultaneous measurement of slope and curvature with a three-aperture speckle shearing interferometer,” Appl. Opt. 23, 1542-1546(1984). [CrossRef] [PubMed]
  5. D. K. Sharma, N. K. Mohan, and R. S. Sirohi, “A holographic speckle shearing technique for the measurement of out-of-plane displacement, slope and curvature,” Opt. Commun. 57, 230-235 (1986). [CrossRef]
  6. K. V. Sriram, M. P. Kothiyal, and R. S. Sirohi, “Talbot interferometry in noncollimated illumination for curvature and focal length measurements,” Appl. Opt. 31, 75-79 (1992). [CrossRef] [PubMed]
  7. 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]
  8. 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]
  9. C. J. Tay, S. L. Toh, H. M. Shang, and Q. Y. Lin, “Multiple-image shearography: a direct method to determine curvatures,” Appl. Opt. 34, 2202-2206 (1995). [CrossRef] [PubMed]
  10. 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]
  11. K. F. Wang, A. K. 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]
  12. S. Grilli, P. Ferraro, S. D. Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294-302 (2001). [CrossRef] [PubMed]
  13. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997). [CrossRef] [PubMed]
  14. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291-293 (1999). [CrossRef]
  15. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156-160 (1982). [CrossRef]
  16. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed.(Academic, 1999).
  17. M. M. Hossain, D. S. Mehta, and C. Shakher, “Information reduction using lensless Fourier transform digital composite holography,” Opt. Laser Technol. 40, 120-128 (2008). [CrossRef]
  18. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).
  19. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007). [CrossRef]
  20. B. Ströbel, “Processing of interferometric phase maps as complex-valued phasor images,” Appl. Opt. 35, 2192-2198(1996). [CrossRef] [PubMed]
  21. C. Liu, “Simultaneous measurement of displacement and its spatial derivatives with a digital holographic method,” Opt. Eng. 42, 3443-3446 (2003). [CrossRef]

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