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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 8 — Aug. 1, 2013
  • pp: 1535–1543

Theoretical analysis and experimental verification of six-step spatial phase-shifting shearing interferometry by double gratings

Zhen-yan Guo, Yang Song, Jia Wang, Zhen-hua Li, and An-zhi He  »View Author Affiliations

JOSA A, Vol. 30, Issue 8, pp. 1535-1543 (2013)

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In order to measure the phase projection in moiré tomography, in this paper we present a new spatial phase-shifting shearing interferometry that consists only of a crossed grating and a linear grating. With it, six phase-shifted interferograms can be acquired simultaneously. The intensity distributions of these six interferograms are derived based on the scalar diffraction theory. Analytical results indicate that phase shifts are symmetrically and consistently distributed in the vertical and horizontal directions. Moreover, phase-shift values depend primarily on the parameters of the optical structure. And a six-step phase-shifting algorithm with arbitrary phase-shift values in two perpendicular directions is proposed to extract the phase information. The phase retrieval results of the spherical wave have verified the validity of the proposed method. Finally, an experiment with a plane incident wave is performed to measure the first-order derivative of the phase projection of a propane flame.

© 2013 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(050.5080) Diffraction and gratings : Phase shift
(100.5070) Image processing : Phase retrieval
(100.6950) Image processing : Tomographic image processing
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry

ToC Category:
Diffraction and Gratings

Original Manuscript: March 11, 2013
Manuscript Accepted: June 4, 2013
Published: July 15, 2013

Zhen-yan Guo, Yang Song, Jia Wang, Zhen-hua Li, and An-zhi He, "Theoretical analysis and experimental verification of six-step spatial phase-shifting shearing interferometry by double gratings," J. Opt. Soc. Am. A 30, 1535-1543 (2013)

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  1. O. Kafri, “Noncoherent method for mapping phase objects,” Opt. Lett. 5, 555–557 (1980). [CrossRef]
  2. E. Keren, E. Bar-Ziv, I. Glatt, and O. Kafri, “Measurements of temperature distribution of flames by moiré deflectometry,” Appl. Opt. 20, 4263–4266 (1981). [CrossRef]
  3. Y. Song, B. Zhang, and A. He, “Algebraic iterative algorithm for deflection tomography and its application to density flow fields in a hypersonic wind tunnel,” Appl. Opt. 45, 8092–8101 (2006). [CrossRef]
  4. Y. Chen, Y. Song, A. He, and Z. Li, “Applicability of moiré deflection tomography for diagnosing arc plasmas,” Appl. Opt. 48, 489–496 (2009). [CrossRef]
  5. Y. Chen, S. Yang, Z. Li, and A. He, “A model for arc plasma’s optical diagnosis by the measurement of the refractive index,” Opt. Commun. 284, 2648–2652 (2011). [CrossRef]
  6. N. Sun, Y. Song, J. Wang, Z. Li, and A. He, “Volume moiré tomography based on double cross gratings for real three-dimension flow field diagnosis,” Appl. Opt. 51, 8081–8089 (2012). [CrossRef]
  7. B. Zhang, Y. Song, and A. He, “New reconstruction algorithm for moiré tomography in flow field measurements,” Opt. Eng. 45, 117002 (2006). [CrossRef]
  8. J. Stricker, E. Keren, and O. Kafri, “Axisymmetric density field measurements by moiré deflectometry,” AIAA J. 21, 1767–1769 (1983). [CrossRef]
  9. V. Vlad, D. Popa, and I. Apostol, “Computer moiré deflectometry using the Talbot effect,” Opt. Eng. 30, 300–306 (1991). [CrossRef]
  10. M. Servin, R. Rodriguez-Vera, M. Carpio, and A. Morale, “Automatic fringe detection algorithm used for moiré deflectometry,” Appl. Opt. 29, 3266–3270 (1990). [CrossRef]
  11. J. Zhong and M. Wang, “Fourier transform moiré deflectometry for the automatic measurement of phase objects,” Proc. SPIE 2899, 311–318 (1996). [CrossRef]
  12. J. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999). [CrossRef]
  13. C. Koliopoulos, “Phase shifting techniques applied to unique applications,” Proc. SPIE 2861, 86–93 (1996). [CrossRef]
  14. C. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1991). [CrossRef]
  15. O. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9, 59–61 (1984). [CrossRef]
  16. H. Bruning, D. Herriott, J. Gallagher, D. Rosenfeld, A. White, and D. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef]
  17. H. Schreiber and J. Schwider, “Lateral shearing interferometer based on two Ronchi phase gratings in series,” Appl. Opt. 36, 5321–5324 (1997). [CrossRef]
  18. R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 234361 (1984). [CrossRef]
  19. L. Deck, “Vibration-resistant phase-shifting interometry,” Appl. Opt. 35, 6655–6662 (1996). [CrossRef]
  20. S. Wolfling and E. Lanzmann, “Wavefront reconstruction by spatial-phase-shift imaging interometry,” Appl. Opt. 45, 2586–2596 (2006). [CrossRef]
  21. B. Ngoi, K. Venkatakrishnan, and N. Sivakumar, “Phase-shifting interferometry immune to vibration,” Appl. Opt. 40, 3211–3214 (2001). [CrossRef]
  22. M. Kujawinska, L. Salbut, and K. Patorski, “Three-channel phase stepped system for moire interferometry,” Appl. Opt. 30, 1633–1637 (1991). [CrossRef]
  23. N. I. Toto-Arellano, A. Martínez-García, G. Rodríguez-Zurita, J. Rayas-Álvarez, and A. Montes-Perez, “Slope measurement of a phase object using a polarizing phase-shifting high-frequency Ronchi grating interferometer,” Appl. Opt. 49, 6402–6408 (2010). [CrossRef]
  24. Y. Song, Y. Chen, A. He, and Z. Zhao, “Spatial phase-shifting characteristic of double grating interferometer,” Opt. Express 17, 20415–20429 (2009). [CrossRef]
  25. Y. Song, Y. Chen, J. Wang, N. Sun, and A. He, “Four-step spatial phase-shifting shearing interferometry from moire configuration by triple gratings,” Opt. Lett. 37, 1922–1924 (2012). [CrossRef]
  26. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  27. M. D. Pritt, “Phase unwrapping by means of multigrid techniques for interferometric SAR,” IEEE Trans. Geosci. Remote Sens. 34, 728–738 (1996). [CrossRef]

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