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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 8 — Aug. 1, 2012
  • pp: 1686–1693

Theoretical analysis for moiré effect of circular gratings for volume optical computerized tomography

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

JOSA A, Vol. 29, Issue 8, pp. 1686-1693 (2012)

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Obtaining the radial derivatives of wavefronts in projections is a critical step for volume optical computerized tomography. In this paper, the moiré effect of two identical circular gratings in acquiring the first-order radial derivative of a wavefront is analyzed. Based on scalar diffraction theory, the formation mechanism of circular gratings’ moiré fringes is derived. A more explicit analytical relation between moiré fringes of different diffraction orders and tested wavefront is obtained. The involved results will be useful for extracting the projection information that is used in three-dimensional reconstruction by volume OCT.

© 2012 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(050.5080) Diffraction and gratings : Phase shift
(110.6960) Imaging systems : Tomography
(120.4120) Instrumentation, measurement, and metrology : Moire' techniques

ToC Category:
Imaging Systems

Original Manuscript: April 23, 2012
Revised Manuscript: June 4, 2012
Manuscript Accepted: June 4, 2012
Published: July 26, 2012

Virtual Issues
Vol. 7, Iss. 10 Virtual Journal for Biomedical Optics

Jia Wang, Yang Song, Zhen-hua Li, Nan Sun, and An-zhi He, "Theoretical analysis for moiré effect of circular gratings for volume optical computerized tomography," J. Opt. Soc. Am. A 29, 1686-1693 (2012)

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  1. J. D. Posner and D. Dunn-Rankin, “Temperature field measurements of small, nonpremixed flames with use of an Abel inversion of holographic interferograms,” Appl. Opt. 42, 952–959 (2003). [CrossRef]
  2. D. A. Feikema, “Quantitative rainbow schlieren deflectometry as a temperature diagnostic for nonsooting spherical flames,” Appl. Opt. 45, 4826–4832 (2006). [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. H. Thayyullathil, R. M. Vasu, and R. Kanhirodan, “Quantitative flow visualization in supersonic jets through tomographic inversion of wavefronts estimated through shadow casting,” Appl. Opt. 45, 5010–5019 (2006). [CrossRef]
  5. X. Wan, S. Yu, G. Cai, Y. Gao, and J. Yi, “Three-dimensional plasma field reconstruction with multiobjective optimization emission spectral tomography,” J. Opt. Soc. Am. A 21, 1161–1171 (2004). [CrossRef]
  6. Y.-y. Chen, S. Yang, Z.-h. Li, and A.-z. He, “A model for arc plasma’s optical diagnosis by the measurement of the refractive index,” Opt. Commun. 284, 2648–2652 (2011). [CrossRef]
  7. T. M. Buzug, “Three-dimensional fourier-based reconstruction methods,” in Computed Tomography (Springer, 2008), pp. 303–401.
  8. O. Bryngdahl, “Reversed-radial-shearing interferometry,” J. Opt. Soc. Am. 60, 915–917 (1970). [CrossRef]
  9. A. W. Lohmann and D. E. Silva, “A Talbot interferometer with circular gratings,” Opt. Commun. 4, 326–328 (1972). [CrossRef]
  10. D. E. Silva, “Talbot interferometer for radial and lateral derivatives,” Appl. Opt. 11, 2613–2624 (1972). [CrossRef]
  11. Q. Ru, N. Ohyama, and T. Honda, “Fringe scanning radial shearing interferometry with circular gratings,” Opt. Commun. 69, 189–192 (1989). [CrossRef]
  12. Q. Ru, N. Ohyama, T. Honda, and J. Tsujiuchi, “Constant radial shearing interferometry with circular gratings,” Appl. Opt. 28, 3350–3353 (1989). [CrossRef]
  13. C. Colautti, L. M. Zerbino, E. E. Sicre, and M. Garavaglia, “Lau effect using circular gratings,” Appl. Opt. 26, 2061–2062 (1987). [CrossRef]
  14. I. Glatt and O. Kafri, “Beam direction determination by moire deflectometry using circular gratings,” Appl. Opt. 26, 4051–4053 (1987). [CrossRef]
  15. C. Shakher and A. J. Pramila Daniel, “Talbot interferometer with circular gratings for the measurement of temperature in axisymmetric gaseous flames,” Appl. Opt. 33, 6068–6072 (1994). [CrossRef]
  16. M. Thakur, A. L. Vyas, and C. Shakher, “Measurement of temperature profile of a gaseous flame with a Lau phase interferometer that has circular gratings,” Appl. Opt. 41, 654–657 (2002). [CrossRef]
  17. Y. Park and S. Kim, “Determination of two-dimensional planar displacement by moiré fringes of concentric circle,” Appl. Opt. 33, 5171–5176 (1994). [CrossRef]
  18. Y. L. Lay and W. Y. Chen, “Rotation measurement using a circular moiré grating,” Opt. Laser Technol. 30, 539–544(1998). [CrossRef]
  19. Joseph W. Goodman, Introduction to Fourier Optics(Publishing House of Electronics Industry, Beijing, 2006).

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