Abstract

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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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]

1991 (1)

1990 (1)

R. J. Hall, P. A. Bonczyk, “Sooting flame thermometry using emission/absorption tomography,” Appl. Opt. 29, 4590–4598 (1990).
[CrossRef] [PubMed]

1989 (1)

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]

1988 (5)

1987 (8)

I. Powell, “Design of a laser beam line expander,” Appl. Opt. 26, 3705–3709 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Beam deflection optical tomography,” Opt. Lett. 12, 72–74 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Beam deflection optical tomography of a flame,” Opt. Lett. 12, 155–157 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Quantitative three-dimensional optical tomographic imaging of supersonic flows,” Science 238, 1700–1702 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Beam deflection optical tomography facilitates flow analysis,” Laser Focus 23 (12), 145–147 (1987).

M. Hino, T. Aono, M. Nakajima, S. Yuta, “Light emission computed tomography system for plasma diagnostics,” Appl. Opt. 26, 4742–4746 (1987).
[CrossRef] [PubMed]

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]

R. Pini, R. Salimbeni, M. Vannini, “Optical fiber transmission of high power excimer laser radiation,” Appl. Opt. 26, 4185–4189 (1987).
[CrossRef] [PubMed]

1986 (2)

G. W. Faris, R. L. Byer, “Quantitative optical tomographic imaging of a supersonic jet,” Opt. Lett 7, 413–415 (1986).
[CrossRef]

K. E. Bennett, R. L. Byer, “Fan-beam-tomography noise theory,” J. Opt. Soc. Am. A 3, 624–633 (1986).
[CrossRef]

1985 (2)

1984 (2)

K. E. Bennett, G. W. Faris, R. L. Byer, “Experimental optical fan beam tomography,” Appl. Opt. 22, 2678–2685 (1984).
[CrossRef]

K. Bennett, R. L. Byer, “Optical tomography: experimental verification of noise theory,” Opt. Lett. 11, 270–272 (1984).
[CrossRef]

1981 (1)

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]

1980 (1)

P. M. Joseph, R. A. Schulz, “View sampling requirements in fan beam computed tomography,” Med. Phys. 7, 692–702 (1980).
[CrossRef] [PubMed]

1978 (1)

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]

1976 (1)

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]

1971 (1)

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]

1917 (1)

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).

Aono, T.

M. Hino, T. Aono, M. Nakajima, S. Yuta, “Light emission computed tomography system for plasma diagnostics,” Appl. Opt. 26, 4742–4746 (1987).
[CrossRef] [PubMed]

Barrett, H. H.

H. H. Barrett, W. Swindell, Radiological Imaging, Vol. 2 (Academic, New York, 1981), Vol. 2, Chap. 7.

Beiting, E. J.

E. J. Beiting, “Fast optical absorption tomography,” Opt. Lett. 16, 1280–1282, (1991).
[CrossRef] [PubMed]

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.

Bennett, K.

K. Bennett, R. L. Byer, “Optical tomography: experimental verification of noise theory,” Opt. Lett. 11, 270–272 (1984).
[CrossRef]

Bennett, K. E.

K. E. Bennett, R. L. Byer, “Fan-beam-tomography noise theory,” J. Opt. Soc. Am. A 3, 624–633 (1986).
[CrossRef]

K. E. Bennett, G. W. Faris, R. L. Byer, “Experimental optical fan beam tomography,” Appl. Opt. 22, 2678–2685 (1984).
[CrossRef]

Bonczyk, P. A.

R. J. Hall, P. A. Bonczyk, “Sooting flame thermometry using emission/absorption tomography,” Appl. Opt. 29, 4590–4598 (1990).
[CrossRef] [PubMed]

Brimacombe, R. K.

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]

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]

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]

Brooks, R. A.

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]

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]

Budinger, T. F.

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).

Byer, R. L.

G. W. Faris, R. L. Byer, “Beam deflection optical tomography of a flame,” Opt. Lett. 12, 155–157 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Quantitative three-dimensional optical tomographic imaging of supersonic flows,” Science 238, 1700–1702 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Beam deflection optical tomography facilitates flow analysis,” Laser Focus 23 (12), 145–147 (1987).

G. W. Faris, R. L. Byer, “Beam deflection optical tomography,” Opt. Lett. 12, 72–74 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Quantitative optical tomographic imaging of a supersonic jet,” Opt. Lett 7, 413–415 (1986).
[CrossRef]

K. E. Bennett, R. L. Byer, “Fan-beam-tomography noise theory,” J. Opt. Soc. Am. A 3, 624–633 (1986).
[CrossRef]

K. Bennett, R. L. Byer, “Optical tomography: experimental verification of noise theory,” Opt. Lett. 11, 270–272 (1984).
[CrossRef]

K. E. Bennett, G. W. Faris, R. L. Byer, “Experimental optical fan beam tomography,” Appl. Opt. 22, 2678–2685 (1984).
[CrossRef]

Cox, J. R.

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.

DiChiro, G.

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]

Dickinson, M. R.

C. Whitehurst, M. R. Dickinson, T. A. King, “Ultraviolet pulse transmission in optical fibers,” J. Mod. Opt. 35, 371–385 (1988).
[CrossRef]

Emmerman, P. J.

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]

Faris, G. W.

H. M. Hertz, G. W. Faris, “Emission tomography of flame radicals,” Opt. Lett. 13, 351–353 (1988).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Beam deflection optical tomography,” Opt. Lett. 12, 72–74 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Beam deflection optical tomography facilitates flow analysis,” Laser Focus 23 (12), 145–147 (1987).

G. W. Faris, R. L. Byer, “Quantitative three-dimensional optical tomographic imaging of supersonic flows,” Science 238, 1700–1702 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Beam deflection optical tomography of a flame,” Opt. Lett. 12, 155–157 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Quantitative optical tomographic imaging of a supersonic jet,” Opt. Lett 7, 413–415 (1986).
[CrossRef]

K. E. Bennett, G. W. Faris, R. L. Byer, “Experimental optical fan beam tomography,” Appl. Opt. 22, 2678–2685 (1984).
[CrossRef]

Gillis, J. R.

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]

Goldman, A.

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]

Goulard, R.

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]

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).

Greenberg, W. L.

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).

Gullberg, G. T.

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).

Hall, R. J.

R. J. Hall, P. A. Bonczyk, “Sooting flame thermometry using emission/absorption tomography,” Appl. Opt. 29, 4590–4598 (1990).
[CrossRef] [PubMed]

Herman, G. T.

G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography (Academic, New York, 1980).

Hertz, H. M.

Hesselink, L.

R. Snyder, L. Hesselink, “Measurement of mixing fluid flows with optical tomography,” Opt. Lett. 13, 87–89 (1988).
[CrossRef] [PubMed]

L. Hesselink, “Digital image processing in flow visualization,” Ann. Rev. Fluid Mech. 20, 421–485 (1988).
[CrossRef]

R. Snyder, L. Hesselink, “High speed optical tomography for flow visualization,” Appl. Opt. 24, 4046–4051 (1985).
[CrossRef] [PubMed]

L. Hesselink, “Optical tomography,” in Handbook of Flow Visualization, W.-J. Yang, ed. (Hemisphere, New York, 1989), pp. 307–329.

Hino, M.

M. Hino, T. Aono, M. Nakajima, S. Yuta, “Light emission computed tomography system for plasma diagnostics,” Appl. Opt. 26, 4742–4746 (1987).
[CrossRef] [PubMed]

Hinze, J. O.

J. O. Hinze, Turbulence, 2nd. ed. (McGraw-Hill, Reading, Mass.1974).

Huesman, R. H.

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).

Joseph, P. M.

P. M. Joseph, R. A. Schulz, “View sampling requirements in fan beam computed tomography,” Med. Phys. 7, 692–702 (1980).
[CrossRef] [PubMed]

King, T. A.

C. Whitehurst, M. R. Dickinson, T. A. King, “Ultraviolet pulse transmission in optical fibers,” J. Mod. Opt. 35, 371–385 (1988).
[CrossRef]

Lakshminarayanan, A. V.

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]

Leopold, K. E.

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]

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]

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]

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van NostrandReinhold, New York, 1982).

Mihailov, S.

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]

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]

Nakajima, M.

M. Hino, T. Aono, M. Nakajima, S. Yuta, “Light emission computed tomography system for plasma diagnostics,” Appl. Opt. 26, 4742–4746 (1987).
[CrossRef] [PubMed]

Pini, R.

R. Pini, R. Salimbeni, M. Vannini, “Optical fiber transmission of high power excimer laser radiation,” Appl. Opt. 26, 4185–4189 (1987).
[CrossRef] [PubMed]

Powell, I.

Radon, J.

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).

Ramachandran, G. N.

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]

Ray, S. R.

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).

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).

Rowland, S. W.

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]

Salimbeni, R.

R. Pini, R. Salimbeni, M. Vannini, “Optical fiber transmission of high power excimer laser radiation,” Appl. Opt. 26, 4185–4189 (1987).
[CrossRef] [PubMed]

Schulz, R. A.

P. M. Joseph, R. A. Schulz, “View sampling requirements in fan beam computed tomography,” Med. Phys. 7, 692–702 (1980).
[CrossRef] [PubMed]

Semerjian, H. G.

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).

Snyder, D. L.

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.

Snyder, R.

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging, Vol. 2 (Academic, New York, 1981), Vol. 2, Chap. 7.

Talbert, A. J.

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]

Taylor, R. S.

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]

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]

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]

Tretiak, O. J.

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.

Vannini, M.

R. Pini, R. Salimbeni, M. Vannini, “Optical fiber transmission of high power excimer laser radiation,” Appl. Opt. 26, 4185–4189 (1987).
[CrossRef] [PubMed]

Weiss, G. H.

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]

Whitehurst, C.

C. Whitehurst, M. R. Dickinson, T. A. King, “Ultraviolet pulse transmission in optical fibers,” J. Mod. Opt. 35, 371–385 (1988).
[CrossRef]

Yuta, S.

M. Hino, T. Aono, M. Nakajima, S. Yuta, “Light emission computed tomography system for plasma diagnostics,” Appl. Opt. 26, 4742–4746 (1987).
[CrossRef] [PubMed]

Ann. Rev. Fluid Mech. (1)

L. Hesselink, “Digital image processing in flow visualization,” Ann. Rev. Fluid Mech. 20, 421–485 (1988).
[CrossRef]

Appl. Opt. (3)

M. Hino, T. Aono, M. Nakajima, S. Yuta, “Light emission computed tomography system for plasma diagnostics,” Appl. Opt. 26, 4742–4746 (1987).
[CrossRef] [PubMed]

R. J. Hall, P. A. Bonczyk, “Sooting flame thermometry using emission/absorption tomography,” Appl. Opt. 29, 4590–4598 (1990).
[CrossRef] [PubMed]

R. Pini, R. Salimbeni, M. Vannini, “Optical fiber transmission of high power excimer laser radiation,” Appl. Opt. 26, 4185–4189 (1987).
[CrossRef] [PubMed]

Appl. Opt. (5)

Ber. Verh. Saechs. Akad. Wiss. Leipzig Math. Phys. Kl. (1)

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).

J. Appl. Phys. (1)

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]

J. Comput. Assist. Tomogr. (1)

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]

J. Mod. Opt. (1)

C. Whitehurst, M. R. Dickinson, T. A. King, “Ultraviolet pulse transmission in optical fibers,” J. Mod. Opt. 35, 371–385 (1988).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

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]

Laser Focus (1)

G. W. Faris, R. L. Byer, “Beam deflection optical tomography facilitates flow analysis,” Laser Focus 23 (12), 145–147 (1987).

Med. Phys. (1)

P. M. Joseph, R. A. Schulz, “View sampling requirements in fan beam computed tomography,” Med. Phys. 7, 692–702 (1980).
[CrossRef] [PubMed]

Opt. Lett (1)

G. W. Faris, R. L. Byer, “Quantitative optical tomographic imaging of a supersonic jet,” Opt. Lett 7, 413–415 (1986).
[CrossRef]

Opt. Lett. (1)

K. Bennett, R. L. Byer, “Optical tomography: experimental verification of noise theory,” Opt. Lett. 11, 270–272 (1984).
[CrossRef]

Opt. Commun. (1)

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]

Opt. Lett. (5)

Phys. Med. Biol. (1)

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]

Proc. Natl. Acad. Sci. USA (1)

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]

Science (1)

G. W. Faris, R. L. Byer, “Quantitative three-dimensional optical tomographic imaging of supersonic flows,” Science 238, 1700–1702 (1987).
[CrossRef] [PubMed]

Other (19)

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]

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).

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.

D. Marcuse, Light Transmission Optics (Van NostrandReinhold, New York, 1982).

See, for example, EG&G FND100Q or Hamamatsu S1722-02.

G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography (Academic, New York, 1980).

United Detector Technology, PIN 6898.

EG&G Judson #9085. This detector has the electrical and optical characteristics of the EG&G UV FFD detector.

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).

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.

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.

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.

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]

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).

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).

J. O. Hinze, Turbulence, 2nd. ed. (McGraw-Hill, Reading, Mass.1974).

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.

H. H. Barrett, W. Swindell, Radiological Imaging, Vol. 2 (Academic, New York, 1981), Vol. 2, Chap. 7.

L. Hesselink, “Optical tomography,” in Handbook of Flow Visualization, W.-J. Yang, ed. (Hemisphere, New York, 1989), pp. 307–329.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Geometry of a 96-fiber absorption tomography instrument with 16× multiplexing. All fans radiating from positions marked t1 are activated concurrently. The ratio of the diameter of the source-detector ring to the diameter of the fully sampled reconstruction zone is 3.86.

Fig. 2
Fig. 2

Ray passing through a region with an index of refraction gradient is refracted as shown if the index increases with radial distance. The deviation θ(yi) is a function of the distance yi.

Fig. 3
Fig. 3

Deviation of rays as they pass through a cylindrically symmetric hot gas flow as a function of the ray angle in a fan. The results are given for five index variations, assuming a center temperature of 1000 K and an ambient edge temperature.

Fig. 4
Fig. 4

Exit energies for three fiber diameters and two wavelengths as a function of entrance energy calculated for the conditions given in the text.

Fig. 5
Fig. 5

Geometry of the fiber-optic fan-beam generator. The focal length of the spherical lens is given by fs and that of the cylindrical lens by fc.

Fig. 6
Fig. 6

Measured profiles of fan-beam intensity as a function of ray angle when the collimated beam between lenses is apertured (squares) and unapertured (circles). The profile of a fan-beam design that allows for maximum dynamic range is shown by the dashed curve.

Fig. 7
Fig. 7

Experimental configuration comprising a fiber-optic fan-beam generator and fast photodiodes that was used to acquire projections. The detectors have a 100% fill factor. Two reference detectors were used to measure noise in the system not attributable to speckle noise.

Fig. 8
Fig. 8

Definitions of the coordinates used in Eqs. (12)(18).

Fig. 9
Fig. 9

Linear correlation coefficient for broadband 532-nm radiation. (a) Steady fiber, 30° fan. Note that the profile is peaked. (b) Steady fiber, 60° fan. (c) Dynamic fiber, 60° fan.

Fig. 10
Fig. 10

Linear correlation coefficients for dye laser radiation for (a) steady fiber and (b) moving fiber. Note that the value of the correlation coefficient remains high, even when the fiber is moved between projections.

Fig. 11
Fig. 11

Reconstruction of a 2.5-cm-diameter plume of diacetyl located near the edge of the 10-cm-diameter reconstruction zone. Each of the 96 projections was taken by using a single pulse of radiation at 444 nm. The noise levels are due principally to the flow source and are not indicative of the instrument sensitivity. (a) No smoothing to the projection; resolution ≈1 mm. (b) Projections smoothed with a triangle function with a FWHM of two detector spacings, degrading the resolution by a factor of 2 and reducing the noise by a factor of 1.8.

Tables (4)

Tables Icon

Table I Instrument Parametersa

Tables Icon

Table II Fused Silica Fiber Characteristics (2-m length, 5-ns pulse)

Tables Icon

Table III Null Tomogram Noise Study (400-μm diam fiber, 60° fan)

Tables Icon

Table IV Ratio of Reconstruction Noise in Unsmoothed Data to that in Smoothed Data

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

R = r f [ 2 / ( 1 cos θ fan ) ] 1 / 2 F r f ,
θ fan = π F M N f .
N d = 2 π r f F w 4 r r N f w F M ,
N a n d = π θ fan [ 2 ( 1 cos θ fan ) ] 1 / 2 .
d d s ( n d r d s ) = n ,
θ ( y i ) = 1 n 0 δ y d x ,
θ ( y i ) = 2 y i n 0 y i R δ ( r ) r ( r 2 y i 2 ) 1 / 2 d r .
δ ( r ) = C ( T m k r n ) 1 ,
1 I d I d x = α 0 + I α 1 ,
E p ( I 0 ) = A t p I 0 exp ( α 0 l ) + [ exp ( α 0 l ) 1 ] α 0 α 1 I 0 ,
f c = K d f tan ( θ fiber / 2 ) tan ( π 2 N a ) ,
p ( s , θ ) = R ρ ( x , y ) = ρ ( s cos θ u sin θ , s sin θ + u cos θ ) d u ,
ρ ( x , y ) = 1 2 π B ( H { D s [ p ( s , θ ) ] } ) ,
B h ( s , θ ) = 0 π h ( x cos θ + y sin θ , θ ) d θ .
ρ ( x , y ) = B ( F 1 abs ) * p ( s , θ ) ,
ρ ( x n , y n ) = B N { I b [ K M * p M ( s M , θ N ) ] } ,
ρ ¯ ( x n , y n ) = B N ( I b { K M * M [ f M * p M ( s M , θ N ) ] } ) .
ρ ¯ ( x n , y n ) = B N { I b [ ( f M * K M ) * p M ( s M , θ N ) ] } .
σ 2 ( r ) = σ p 2 π 2 3 18 M a 2 R 2 w ( r ) .
w ( r ) = 1 + 1 2 r ( 1 r 2 ) 3 ,
n 0 H = Q ( T ) g J exp ( E J / k T ) σ noise q eff l = 5 . 36 × 10 16 σ noise ( cm 3 ) ,
r j ( t ) = s j 2 ( t ) σ j σ j + t ,

Metrics