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Applied Optics

Applied Optics


  • Vol. 31, Iss. 9 — Mar. 20, 1992
  • pp: 1328–1343

Fiber-optic fan-beam absorption tomography

Edward J. Beiting  »View Author Affiliations

Applied Optics, Vol. 31, Issue 9, pp. 1328-1343 (1992)

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An absorption tomography instrument that is capable of acquiring 100 projections of 100 elements each in less than 200 ns is described. The instrument uses time-multiplexed, fiber-optic fan-beam sources that are sequentially activated in groups to reduce greatly the total number of detectors required for achieving a given resolution. The quantitative details required to tailor this instrument to a particular application are presented. A single-fiber prototype was used to verify the design and establish its sensitivity. The sensitivity is limited by laser-speckle noise. The fiber-optic fan-beam generator can produce an interdetector correlation of the projection noise, reducing the effect of this noise on the reconstruction. The noise is measured as a function of optic-fiber stability and size, laser bandwidth and mode stability, and detector size.

© 1992 Optical Society of America

Original Manuscript: April 9, 1991
Published: March 20, 1992

Edward J. Beiting, "Fiber-optic fan-beam absorption tomography," Appl. Opt. 31, 1328-1343 (1992)

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  1. E. J. Beiting, “Fast optical absorption tomography,” Opt. Lett. 16, 1280–1282, (1991). [CrossRef] [PubMed]
  2. R. Goulard, P. J. Emmerman, “Combustion diagnostics by multiangular absorption,” in Inverse Scattering Problems in Optics, H. P. Baltes, ed., Vol. 20 of Topics in Current Physics (Springer-Verlag, New York, 1980), p. 215. [CrossRef]
  3. R. Goulard, S. R. Ray, “Optical tomography in combustion,” in Advances in Remote Sensing Retrieval Methods, A. Deepak, H. E. Fleming, M. T. Chahine, eds. (Deepak, Hampton, Va., 1985).
  4. S. R. Ray, H. G. Semerjian, “Laser tomography for simultaneous concentration and temperature measurement in reacting flows,” presented at the AIAA 18th Thermophysics Conference, AIAA Publ. 83-1553 (1983).
  5. K. E. Bennett, G. W. Faris, R. L. Byer, “Experimental optical fan beam tomography,” Appl. Opt. 22, 2678–2685 (1984). [CrossRef]
  6. K. Bennett, R. L. Byer, “Optical tomography: experimental verification of noise theory,” Opt. Lett. 11, 270–272 (1984). [CrossRef]
  7. G. W. Faris, R. L. Byer, “Quantitative optical tomographic imaging of a supersonic jet,” Opt. Lett 7, 413–415 (1986). [CrossRef]
  8. R. Snyder, L. Hesselink, “High speed optical tomography for flow visualization,” Appl. Opt. 24, 4046–4051 (1985). [CrossRef] [PubMed]
  9. G. W. Faris, R. L. Byer, “Beam deflection optical tomography,” Opt. Lett. 12, 72–74 (1987). [CrossRef] [PubMed]
  10. G. W. Faris, R. L. Byer, “Beam deflection optical tomography of a flame,” Opt. Lett. 12, 155–157 (1987). [CrossRef] [PubMed]
  11. G. W. Faris, R. L. Byer, “Quantitative three-dimensional optical tomographic imaging of supersonic flows,” Science 238, 1700–1702 (1987). [CrossRef] [PubMed]
  12. G. W. Faris, R. L. Byer, “Beam deflection optical tomography facilitates flow analysis,” Laser Focus 23 (12), 145–147 (1987).
  13. R. Snyder, L. Hesselink, “Measurement of mixing fluid flows with optical tomography,” Opt. Lett. 13, 87–89 (1988). [CrossRef] [PubMed]
  14. H. M. Hertz, G. W. Faris, “Emission tomography of flame radicals,” Opt. Lett. 13, 351–353 (1988). [CrossRef] [PubMed]
  15. M. Hino, T. Aono, M. Nakajima, S. Yuta, “Light emission computed tomography system for plasma diagnostics,” Appl. Opt. 26, 4742–4746 (1987). [CrossRef] [PubMed]
  16. R. J. Hall, P. A. Bonczyk, “Sooting flame thermometry using emission/absorption tomography,” Appl. Opt. 29, 4590–4598 (1990). [CrossRef] [PubMed]
  17. L. Hesselink, “Digital image processing in flow visualization,” Ann. Rev. Fluid Mech. 20, 421–485 (1988). [CrossRef]
  18. L. Hesselink, “Optical tomography,” in Handbook of Flow Visualization, W.-J. Yang, ed. (Hemisphere, New York, 1989), pp. 307–329.
  19. See the special issue on computed tomography, Appl. Opt. 24(23), (1985). [PubMed]
  20. J. O. Hinze, Turbulence, 2nd. ed. (McGraw-Hill, Reading, Mass.1974).
  21. E. J. Beiting, “Application of fast optical tomography to flow tubes,” Tech. Rep. ATR-89(8455)-1 (Aerospace Corporation, Los Angeles, Calif., 1989), pp. 1–82.
  22. H. H. Barrett, W. Swindell, Radiological Imaging, Vol. 2 (Academic, New York, 1981), Vol. 2, Chap. 7.
  23. R. A. Brooks, G. H. Weiss, A. J. Talbert, “A new approach to interpolation in computed tomography,” J. Comput. Assist. Tomogr. 2, 577–585 (1978). [CrossRef] [PubMed]
  24. The problem of the minimum number of projections has been carefully studied. The minimum number of projections is determined by the necessity of avoiding streak artifacts that tend to appear at relatively large distances from high-contrast objects.25 Brooks and DiChiro26 argue heuristically that Nmin = πN/4 for parallel beam geometries in which views are collected over 180°. Snyder and Cox,27 using mathematically rigorous analysis for the same geometry, found that the minimum number of views required are given by Nmin = 2πrfνm, where νm is the maximum spatial frequency present. Joseph and Schulz28 calculated the minimum views for fan-beam geometries, using a filtered backprojection reconstruction algorithm in which views are collected over a 360°C field and foundNmin=4πνmrf1−sin(θfan/2),which reduces to the Snyder and Cox expression for θfan = 0 and equal angular ranges. Using the Brooks and DiChiro expression to define νm, the number of fans required to image an artifact-free region of radius rf isNf=πNd1−sin(θfan),which equals 4.2Nd for θfan = 30° and 6.3Nd for θfan = 60°. In practice, most medical CT scanners have values considerably far fewer fans, because serious streaks are produced only if the object is small and of high density. This situation is never the case for gaseous flows.
  25. O. J. Tretiak, “The point-spread function for the convolutional algorithm,” in Digest of Conference on Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences (Optical Society of America, Washington, D. C., 1975), pp. ThA5-1–ThA5-3.
  26. R. A. Brooks, G. DiChiro, “Principles of computer assisted tomography (CAT) in radiographic and radioisotopic imaging,” Phys. Med. Biol. 21, 689–732 (1976). [CrossRef] [PubMed]
  27. D. L. Snyder, J. R. Cox, Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine, M. M. Ter-Pogossian, M. E. Phelps, G. L. Brownell, J. R. Cox, D. O. David, R. G. Evens, eds. (University Park, Baltimore, Md., 1977), pp. 3–31.
  28. P. M. Joseph, R. A. Schulz, “View sampling requirements in fan beam computed tomography,” Med. Phys. 7, 692–702 (1980). [CrossRef] [PubMed]
  29. D. Marcuse, Light Transmission Optics (Van NostrandReinhold, New York, 1982).
  30. R. S. Taylor, K. E. Leopold, S. Mihailov, R. K. Brimacombe, “Damage measurements of fused silica fibres, using long optical pulse XeCl lasers,” Opt. Commun. 63, 26–31 (1987). [CrossRef]
  31. R. Pini, R. Salimbeni, M. Vannini, “Optical fiber transmission of high power excimer laser radiation,” Appl. Opt. 26, 4185–4189 (1987). [CrossRef] [PubMed]
  32. C. Whitehurst, M. R. Dickinson, T. A. King, “Ultraviolet pulse transmission in optical fibers,” J. Mod. Opt. 35, 371–385 (1988). [CrossRef]
  33. R. S. Taylor, K. E. Leopold, R. K. Brimacombe, S. Mihailov, “Dependence of the damage and transmission properties of fused silica fiber on the excimer laser wavelength,” Appl. Opt. 27, 3124–3134 (1988). [CrossRef] [PubMed]
  34. R. K. Brimacombe, R. S. Taylor, K. E. Leopold, “Dependence of the nonlinear transmission properties of fused silica fibers on excimer laser wavelength,” J. Appl. Phys. 66, 4035–4040 (1989). [CrossRef]
  35. I. Powell, “Design of a laser beam line expander,” Appl. Opt. 26, 3705–3709 (1987). [CrossRef] [PubMed]
  36. See, for example, EG&G FND100Q or Hamamatsu S1722-02.
  37. G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography (Academic, New York, 1980).
  38. United Detector Technology, PIN 6898.
  39. EG&G Judson #9085. This detector has the electrical and optical characteristics of the EG&G UV FFD detector.
  40. R. H. Huesman, G. T. Gullberg, W. L. Greenberg, T. F. Budinger, Donner Algorithms for Reconstruction Tomography (Lawrence Berkeley Laboratory, University of California, Berkeley, Berkeley, Calif., 1985).
  41. J. Radon, “Uber die Bestimmung von Funktionen Durch Ihre Integralwerte Langs Gewisser Mannigfaltigkeiten,” Ber. Verh. Saechs. Akad. Wiss. Leipzig Math. Phys. Kl. 69, 262–267 (1917).
  42. S. W. Rowland, “Computer implementation of image reconstruction formulas,” in Image Reconstruction from Projections: Implementation and Applications, G. T. Herman, ed. (Springer-Verlag, Berlin, 1979). [CrossRef]
  43. G. N. Ramachandran, A. V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sci. USA 68, 2236–2240 (1971). [CrossRef] [PubMed]
  44. K. E. Bennett, R. L. Byer, “Fan-beam-tomography noise theory,” J. Opt. Soc. Am. A 3, 624–633 (1986). [CrossRef]
  45. The number of speckles exiting a cylindrical fiber is approximately Ns = π[2af(NA)/λ]2 where NA is the numerical aperture and af is the radius of the fiber. The average area of the speckle grains expands quadratically from the fiber to the collimating lens to a beam with an area of AB=πfs2tan2(θNA) where fs is the focal length of the spherical lens and θNA = sin−1(NA). Thus the average speckle dimension in this beam iss=(1AB2¯Ns¯)1/2=λfstanθNA8af(NA),assuming that the speckles occupy one-half the area (100% contrast).
  46. The sample linear correlation coefficient rj(t) between two detectors dj and dj+t in a given projection isrj(t)=sj2(t)σjσj+t,where sj2(t) is the sample covariance and σj and σj+t are the standard deviations for detectors j and j + t. This is closely related to the correlation function defined in Ref. 44: f(t) = sj2(t)/σp2, where σp2 is the mean variance of the noise in the projection.
  47. A. Goldman, J. R. Gillis, “Spectral line parameters for the A2Σ–X2Π (0, 0) band of OH for atmospheric and high temperatures,” J. Quant. Spectrosc. Radiat. Transfer 25, 111–135 (1981). [CrossRef]

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