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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 45, Iss. 31 — Nov. 1, 2006
  • pp: 8092–8101

Algebraic iterative algorithm for deflection tomography and its application to density flow fields in a hypersonic wind tunnel

Yang Song, Bin Zhang, and Anzhi He  »View Author Affiliations


Applied Optics, Vol. 45, Issue 31, pp. 8092-8101 (2006)
http://dx.doi.org/10.1364/AO.45.008092


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Abstract

A novel algebraic iterative algorithm based on deflection tomography is presented. This algorithm is derived from the essentials of deflection tomography with a linear expansion of the local basis functions. By use of this algorithm the tomographic problem is finally reduced to the solution of a set of linear equations. The algorithm is demonstrated by mapping a three-peak Gaussian simulative temperature field. Compared with reconstruction results obtained by other traditional deflection algorithms, its reconstruction results provide a significant improvement in reconstruction accuracy, especially in cases with noisy data added. In the density diagnosis of a hypersonic wind tunnel, this algorithm is adopted to reconstruct density distributions of an axial symmetry flow field. One cross section of the reconstruction results is selected to be compared with the inverse Abel transform algorithm. Results show that the novel algorithm can achieve an accuracy equivalent to the inverse Abel transform algorithm. However, the novel algorithm is more versatile because it is applicable to arbitrary kinds of distribution.

© 2006 Optical Society of America

OCIS Codes
(110.6960) Imaging systems : Tomography
(120.4120) Instrumentation, measurement, and metrology : Moire' techniques
(200.1130) Optics in computing : Algebraic optical processing

History
Original Manuscript: March 6, 2006
Revised Manuscript: June 7, 2006
Manuscript Accepted: June 16, 2006

Citation
Yang Song, Bin Zhang, and Anzhi 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)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-31-8092


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References

  1. G. P. Montgomery, Jr., and D. L. Reuss, "Effects of refraction on axisymmetric flame temperatures measured by holographic interferometry," Appl. Opt. 21, 1373-1380 (1982). [CrossRef] [PubMed]
  2. J. Stricker, E. Keren, and O. Kafri, "Axisymmetric density field measurements by moire deflectometry," AIAA J. 21, 1767-1769 (1983). [CrossRef]
  3. E. Bar-Ziv, S. Sgulim, O. Kafri, and E. Keren, "Temperature mapping in flames by moiré deflectometry," Appl. Opt. 22, 689-705 (1983). [CrossRef]
  4. G. W. Faris and R. L. Byer, "Three-dimensional beam-deflection optical tomography of a supersonic jet," Appl. Opt. 27, 5202-5212 (1988). [CrossRef] [PubMed]
  5. D. Wu and A. He, "Measurement of three-dimensional temperature fields with interferometric tomography," Appl. Opt. 38, 3468-3473 (1999). [CrossRef]
  6. 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] [PubMed]
  7. O. Sasaki and T. Kobayashi, "Beam-deflection optical tomography of the refractive-index distribution based on the Rytov approximation," Appl. Opt. 32, 746-751 (1993). [CrossRef] [PubMed]
  8. D. W. Sweeny and C. M. Vest, "Reconstruction of three-dimensional refractive index field from multi-direction interferometric data," Appl. Opt. 12, 2649-2664 (1973). [CrossRef]
  9. O. Kafri and I. Glatt, "Moiré deflectometry: a ray deflection approach to optical testing," Opt. Eng. 24, 944-960 (1985).
  10. Y. Song, B. Zhang, and A. He, "Bayesian approach to limited-projection reconstruction in moiré tomography," in ICO20: Optical Information Processing, Y. Sheng, S. Zhuang, and Y. Zhang, eds., Proc. SPIE 6027, 6027U (2006).
  11. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).
  12. R. M. Lewitt, "Reconstruction algorithms: transform methods," Proc. IEEE 71, 390-408 (1983). [CrossRef]
  13. R. Gordon, R. Bender, and G. T. Herman, "Algebraic reconstruction techniques (ART) for three dimensional electron microscopy and X-ray photography," J. Theor. Biol. 29, 471-481 (1970). [CrossRef] [PubMed]
  14. A. He, D. Yan, X. Ni, and H. Wang, "Design and application of real-time holographic large-aperture moire deflector with high sensitivity and high precision," Chin. J. Lasers 18, 827-831 (1991).
  15. D. Yan, A. He, and X. Ni, "New method of asymmetric flow field measurement in hypersonic shock tunnel," Appl. Opt. 30, 770-774 (1991). [CrossRef] [PubMed]
  16. J. Stricker, "Analysis of 3-D phase objects by moiré deflectometry," Appl. Opt. 23, 3657-3659 (1984). [CrossRef] [PubMed]
  17. Y.Song, B. Zhang, and A. He, "The filtered back-projection algorithm of deflection tomography and error analysis," Acta Opt. Sin. (to be published).
  18. G. W. Faris and R. L. Byer, "Beam-deflection optical tomography," Opt. Lett. 12, 72-74 (1987). [CrossRef] [PubMed]
  19. G. W. Faris and R. L. Byer, "Beam-deflection optical tomography of a flame," Opt. Lett. 12, 155-157 (1987). [CrossRef] [PubMed]
  20. A. K. Agrawal, N. K. Butuk, S. R. Gollahalli, and D. Griffin, "Three-dimensional rainbow schlieren tomography of a temperature field in gas flows," Appl. Opt. 37, 479-485 (1998). [CrossRef]
  21. R. Rangayyan, A. P. Dhawan, and R. Gordon, "Algorithms for limited-view computed tomography: an annotated bibliography and a challenge," Appl. Opt. 24, 4000-4012 (1985). [CrossRef] [PubMed]
  22. D. Yan, F. Liu, Z. Wang, and A. He, "Moiré tomography by ART," in Laser Interferometry: Applications, R. J. Pryputniewicz, G. M. Brown, and W. P. O. Jueptner, eds., Proc. SPIE 2861, 146-150 (1996). [CrossRef]
  23. 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]
  24. D. Zhu, Laser Metrology for Thermal Physics (Science, 1990).
  25. H. Thayyullathil, R. Langoju, R. Padmaram, R. Mohan Vasu, R. Kanjirodan, and L. Patnaik, "Three-dimensional optical tomographic imaging of supersonic jets through inversion of phase data obtained through the transport-of-intensity equation," Appl. Opt. 43, 4133-4141 (2004). [CrossRef]
  26. C. Soller, R. Wenskus, P. Middendorf, G. Meier, and F. Obermeier, "Interferometric tomography for flow visualization of density fields in supersonic jets and convective flow," Appl. Opt. 33, 2921-2932 (1994). [CrossRef] [PubMed]
  27. J. Stricker and O. Kafri, "A New Method for Density Gradient Measurements in Compressible Flows," AIAA J. 20, 820-823 (1982). [CrossRef]
  28. M. Anastasio and X. Pan, "Full- and minimal-scan reconstruction algorithms for fan-beam diffraction tomography," Appl. Opt. 40, 3334-3345 (2001). [CrossRef]
  29. A. H. Andersen and A. C. Kak, "Digital ray tracing in two-dimensional refractive fields," J. Acoust. Soc. Am. 72, 1593-1606 (1982). [CrossRef]

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