Abstract

X-ray scattering, including coherent, incoherent, and resonance (fluorescent) phenomena, is of fundamental importance in contemporary science as a tool to probe the structure of matter at an atomic level. This elevated status is in sharp contrast to the role of x-ray scatter in medical and industrial radiography, where it is generally regarded as an unmitigated nuisance to be corrected for or, preferably, eliminated. We introduce a novel x-radiographic technique [x-ray diffraction computed tomography (CT)] based on measurement of coherent scatter. The physical background to coherent scattering is described in a simple, classical way, and its importance in conventional radiography is demonstrated by using Monte Carlo analysis. Some diffraction patterns of plastics and animal tissues are presented to illustrate the relevance of coherent scattering to material characterization and diagnosis in industrial and medical radiology. An experimental first-generation (single-pencil-beam) CT system has been constructed to demonstrate the feasiblity of x-ray diffraction CT. Some diffraction CT and coherent scatter projection images of simple objects are presented. Possibilities for improving the ratio of image contrast to noise and increasing the momentum resolution of the technique are illustrated.

© 1987 Optical Society of America

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  1. A. H. Compton, “X-rays as a branch of optics,” J. Opt. Soc. Am./Rev. Sci. Instrum. 16, 71–87 (1928).
    [Crossref]
  2. W. Heitler, The Quantum Theory of Radiation, 3rd ed. (Clarendon, Oxford, 1954), pp. 34–38.
  3. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 370–386.
  4. D. C. Champeney, Fourier Transforms and Their Physical Applications (Academic, London, 1973), Chap. 13, pp. 181–197.
  5. J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, R. J. Howerton, “Atomic form factors, incoherent scattering functions and photon scattering cross-sections,”J. Phys. Chem. Ref. Data 4, 471–538 (1975); Errata 6, 615–616 (1977).
    [Crossref]
  6. D. W. L. Hukins, X-Ray Diffraction by Disordered and Ordered Systems (Pergamon, Oxford, 1981), pp. 19–24.
  7. J. M. Kosanetzky, B. Knoerr, G. Harding, U. Neitzel, “X-ray diffraction measurements of some plastic materials and body tissues,” Med. Phys. (to be published).
    [PubMed]
  8. D. E. Cashwell, C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon, London, 1959).
  9. U. Neitzel, J. Kosanetzky, G. Harding, “Coherent scatter in radiographic imaging: a Monte Carlo simulation study,” Phys. Med. Biol. 30, 1289–1296 (1985).
    [Crossref] [PubMed]
  10. L. R. M. Morin, “Molecular form factors and photon coherent scattering cross-sections of water,”J. Phys. Chem. Ref. Data 11, 1091–1098 (1982).
    [Crossref]
  11. M. J. Cooper, “Compton scattering and electron momentum determination,” Rep. Prog. Phys. 48, 415–481 (1985).
    [Crossref]
  12. G. Alm Carlsson, C. A. Carlsson, K. F. Berggren, R. Ribberfors, “Calculation of scattering cross-sections for increased accuracy in diagnostic radiology. I. Energy broadening of Compton scattered photons,” Med. Phys. 9, 868–879 (1982).
    [Crossref]
  13. J. Bednar, “Electronic excitations in condensed biological matter,” Int. J. Radiat. Biol. 48, 147–166 (1985).
    [Crossref]
  14. W. H. McMaster, N. Kerr del Grande, J. H. Mallett, J. H. Hubbell, “Compilation of x-ray cross-sections,” (Lawrence Livermore Radiation Laboratory, Livermore, Calif., 1969), Sec. 2, Rev. 1.
  15. J. H. Hubbell, “Photon cross-sections, attenuation coefficients and energy absorption coefficients from 10 keV to 100 GeV,” (National Bureau of Standards, Gaithersburg, Md., 1969).
  16. P. C. Johns, M. J. Yaffe, “Coherent scatter in diagnostic radiology,” Med. Phys. 10, 40–50 (1983).
    [Crossref] [PubMed]
  17. E. P. Muntz, T. Fewell, R. Jennings, H. Bernstein, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
    [Crossref] [PubMed]
  18. L. R. M. Morin, A. Berroir, “Calculation of x-ray single scattering in diagnostic radiology,” Phys. Med. Biol. 28, 789–797 (1983).
    [Crossref] [PubMed]
  19. G. Harding, J. Kosanetzky, U. Neitzel, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
    [Crossref] [PubMed]
  20. G. Harding, J. Kosanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. (to be published).
  21. G. Harding, R. Tischler, “Dual energy Compton scatter tomography,” Phys. Med. Biol. 31, 477–489, 1986.
    [Crossref] [PubMed]
  22. J. Kosanetzky, G. Harding, U. Neitzel, “Energy-resolved x-ray diffraction CT,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.
  23. N. A. Mullani, J. Markham, M. Ter Pogossian, “Feasibility of time of flight positron emission tomography,”J. Nucl. Med. 21, 1095–1097 (1980).
    [PubMed]
  24. D. L. Snyder, L. J. Thomas, M. Ter Pogossian, “A mathematical model for positron emission tomography systems having time of flight measurements,” IEEE Trans. Nucl. Sci. NS-28, 3575–3583 (1981).
    [Crossref]
  25. H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, p. 470.
  26. M. Singh, “An electronically collimated gamma camera. Part 1: Theoretical considerations and design criteria for single photon emission computed tomography,” Med. Phys. 10, 421–435 (1983).
    [Crossref] [PubMed]
  27. M. Singh, D. Doria, “An electronically collimated gamma camera for single photon emission computed tomography. Part 2: Image reconstruction and preliminary experimental measurements,” Med. Phys. 10, 428–435 (1983).
    [Crossref] [PubMed]

1986 (1)

G. Harding, R. Tischler, “Dual energy Compton scatter tomography,” Phys. Med. Biol. 31, 477–489, 1986.
[Crossref] [PubMed]

1985 (4)

M. J. Cooper, “Compton scattering and electron momentum determination,” Rep. Prog. Phys. 48, 415–481 (1985).
[Crossref]

G. Harding, J. Kosanetzky, U. Neitzel, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
[Crossref] [PubMed]

U. Neitzel, J. Kosanetzky, G. Harding, “Coherent scatter in radiographic imaging: a Monte Carlo simulation study,” Phys. Med. Biol. 30, 1289–1296 (1985).
[Crossref] [PubMed]

J. Bednar, “Electronic excitations in condensed biological matter,” Int. J. Radiat. Biol. 48, 147–166 (1985).
[Crossref]

1983 (5)

P. C. Johns, M. J. Yaffe, “Coherent scatter in diagnostic radiology,” Med. Phys. 10, 40–50 (1983).
[Crossref] [PubMed]

E. P. Muntz, T. Fewell, R. Jennings, H. Bernstein, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
[Crossref] [PubMed]

L. R. M. Morin, A. Berroir, “Calculation of x-ray single scattering in diagnostic radiology,” Phys. Med. Biol. 28, 789–797 (1983).
[Crossref] [PubMed]

M. Singh, “An electronically collimated gamma camera. Part 1: Theoretical considerations and design criteria for single photon emission computed tomography,” Med. Phys. 10, 421–435 (1983).
[Crossref] [PubMed]

M. Singh, D. Doria, “An electronically collimated gamma camera for single photon emission computed tomography. Part 2: Image reconstruction and preliminary experimental measurements,” Med. Phys. 10, 428–435 (1983).
[Crossref] [PubMed]

1982 (2)

G. Alm Carlsson, C. A. Carlsson, K. F. Berggren, R. Ribberfors, “Calculation of scattering cross-sections for increased accuracy in diagnostic radiology. I. Energy broadening of Compton scattered photons,” Med. Phys. 9, 868–879 (1982).
[Crossref]

L. R. M. Morin, “Molecular form factors and photon coherent scattering cross-sections of water,”J. Phys. Chem. Ref. Data 11, 1091–1098 (1982).
[Crossref]

1981 (1)

D. L. Snyder, L. J. Thomas, M. Ter Pogossian, “A mathematical model for positron emission tomography systems having time of flight measurements,” IEEE Trans. Nucl. Sci. NS-28, 3575–3583 (1981).
[Crossref]

1980 (1)

N. A. Mullani, J. Markham, M. Ter Pogossian, “Feasibility of time of flight positron emission tomography,”J. Nucl. Med. 21, 1095–1097 (1980).
[PubMed]

1975 (1)

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, R. J. Howerton, “Atomic form factors, incoherent scattering functions and photon scattering cross-sections,”J. Phys. Chem. Ref. Data 4, 471–538 (1975); Errata 6, 615–616 (1977).
[Crossref]

1928 (1)

A. H. Compton, “X-rays as a branch of optics,” J. Opt. Soc. Am./Rev. Sci. Instrum. 16, 71–87 (1928).
[Crossref]

Alm Carlsson, G.

G. Alm Carlsson, C. A. Carlsson, K. F. Berggren, R. Ribberfors, “Calculation of scattering cross-sections for increased accuracy in diagnostic radiology. I. Energy broadening of Compton scattered photons,” Med. Phys. 9, 868–879 (1982).
[Crossref]

Barrett, H. H.

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, p. 470.

Bednar, J.

J. Bednar, “Electronic excitations in condensed biological matter,” Int. J. Radiat. Biol. 48, 147–166 (1985).
[Crossref]

Berggren, K. F.

G. Alm Carlsson, C. A. Carlsson, K. F. Berggren, R. Ribberfors, “Calculation of scattering cross-sections for increased accuracy in diagnostic radiology. I. Energy broadening of Compton scattered photons,” Med. Phys. 9, 868–879 (1982).
[Crossref]

Bernstein, H.

E. P. Muntz, T. Fewell, R. Jennings, H. Bernstein, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
[Crossref] [PubMed]

Berroir, A.

L. R. M. Morin, A. Berroir, “Calculation of x-ray single scattering in diagnostic radiology,” Phys. Med. Biol. 28, 789–797 (1983).
[Crossref] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 370–386.

Briggs, E. A.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, R. J. Howerton, “Atomic form factors, incoherent scattering functions and photon scattering cross-sections,”J. Phys. Chem. Ref. Data 4, 471–538 (1975); Errata 6, 615–616 (1977).
[Crossref]

Brown, R. T.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, R. J. Howerton, “Atomic form factors, incoherent scattering functions and photon scattering cross-sections,”J. Phys. Chem. Ref. Data 4, 471–538 (1975); Errata 6, 615–616 (1977).
[Crossref]

Carlsson, C. A.

G. Alm Carlsson, C. A. Carlsson, K. F. Berggren, R. Ribberfors, “Calculation of scattering cross-sections for increased accuracy in diagnostic radiology. I. Energy broadening of Compton scattered photons,” Med. Phys. 9, 868–879 (1982).
[Crossref]

Cashwell, D. E.

D. E. Cashwell, C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon, London, 1959).

Champeney, D. C.

D. C. Champeney, Fourier Transforms and Their Physical Applications (Academic, London, 1973), Chap. 13, pp. 181–197.

Compton, A. H.

A. H. Compton, “X-rays as a branch of optics,” J. Opt. Soc. Am./Rev. Sci. Instrum. 16, 71–87 (1928).
[Crossref]

Cooper, M. J.

M. J. Cooper, “Compton scattering and electron momentum determination,” Rep. Prog. Phys. 48, 415–481 (1985).
[Crossref]

Cromer, D. T.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, R. J. Howerton, “Atomic form factors, incoherent scattering functions and photon scattering cross-sections,”J. Phys. Chem. Ref. Data 4, 471–538 (1975); Errata 6, 615–616 (1977).
[Crossref]

Doria, D.

M. Singh, D. Doria, “An electronically collimated gamma camera for single photon emission computed tomography. Part 2: Image reconstruction and preliminary experimental measurements,” Med. Phys. 10, 428–435 (1983).
[Crossref] [PubMed]

Everett, C. J.

D. E. Cashwell, C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon, London, 1959).

Fewell, T.

E. P. Muntz, T. Fewell, R. Jennings, H. Bernstein, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
[Crossref] [PubMed]

Harding, G.

G. Harding, R. Tischler, “Dual energy Compton scatter tomography,” Phys. Med. Biol. 31, 477–489, 1986.
[Crossref] [PubMed]

G. Harding, J. Kosanetzky, U. Neitzel, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
[Crossref] [PubMed]

U. Neitzel, J. Kosanetzky, G. Harding, “Coherent scatter in radiographic imaging: a Monte Carlo simulation study,” Phys. Med. Biol. 30, 1289–1296 (1985).
[Crossref] [PubMed]

J. M. Kosanetzky, B. Knoerr, G. Harding, U. Neitzel, “X-ray diffraction measurements of some plastic materials and body tissues,” Med. Phys. (to be published).
[PubMed]

G. Harding, J. Kosanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. (to be published).

J. Kosanetzky, G. Harding, U. Neitzel, “Energy-resolved x-ray diffraction CT,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.

Heitler, W.

W. Heitler, The Quantum Theory of Radiation, 3rd ed. (Clarendon, Oxford, 1954), pp. 34–38.

Howerton, R. J.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, R. J. Howerton, “Atomic form factors, incoherent scattering functions and photon scattering cross-sections,”J. Phys. Chem. Ref. Data 4, 471–538 (1975); Errata 6, 615–616 (1977).
[Crossref]

Hubbell, J. H.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, R. J. Howerton, “Atomic form factors, incoherent scattering functions and photon scattering cross-sections,”J. Phys. Chem. Ref. Data 4, 471–538 (1975); Errata 6, 615–616 (1977).
[Crossref]

W. H. McMaster, N. Kerr del Grande, J. H. Mallett, J. H. Hubbell, “Compilation of x-ray cross-sections,” (Lawrence Livermore Radiation Laboratory, Livermore, Calif., 1969), Sec. 2, Rev. 1.

J. H. Hubbell, “Photon cross-sections, attenuation coefficients and energy absorption coefficients from 10 keV to 100 GeV,” (National Bureau of Standards, Gaithersburg, Md., 1969).

Hukins, D. W. L.

D. W. L. Hukins, X-Ray Diffraction by Disordered and Ordered Systems (Pergamon, Oxford, 1981), pp. 19–24.

Jennings, R.

E. P. Muntz, T. Fewell, R. Jennings, H. Bernstein, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
[Crossref] [PubMed]

Johns, P. C.

P. C. Johns, M. J. Yaffe, “Coherent scatter in diagnostic radiology,” Med. Phys. 10, 40–50 (1983).
[Crossref] [PubMed]

Kerr del Grande, N.

W. H. McMaster, N. Kerr del Grande, J. H. Mallett, J. H. Hubbell, “Compilation of x-ray cross-sections,” (Lawrence Livermore Radiation Laboratory, Livermore, Calif., 1969), Sec. 2, Rev. 1.

Knoerr, B.

J. M. Kosanetzky, B. Knoerr, G. Harding, U. Neitzel, “X-ray diffraction measurements of some plastic materials and body tissues,” Med. Phys. (to be published).
[PubMed]

Kosanetzky, J.

U. Neitzel, J. Kosanetzky, G. Harding, “Coherent scatter in radiographic imaging: a Monte Carlo simulation study,” Phys. Med. Biol. 30, 1289–1296 (1985).
[Crossref] [PubMed]

G. Harding, J. Kosanetzky, U. Neitzel, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
[Crossref] [PubMed]

J. Kosanetzky, G. Harding, U. Neitzel, “Energy-resolved x-ray diffraction CT,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.

G. Harding, J. Kosanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. (to be published).

Kosanetzky, J. M.

J. M. Kosanetzky, B. Knoerr, G. Harding, U. Neitzel, “X-ray diffraction measurements of some plastic materials and body tissues,” Med. Phys. (to be published).
[PubMed]

Mallett, J. H.

W. H. McMaster, N. Kerr del Grande, J. H. Mallett, J. H. Hubbell, “Compilation of x-ray cross-sections,” (Lawrence Livermore Radiation Laboratory, Livermore, Calif., 1969), Sec. 2, Rev. 1.

Markham, J.

N. A. Mullani, J. Markham, M. Ter Pogossian, “Feasibility of time of flight positron emission tomography,”J. Nucl. Med. 21, 1095–1097 (1980).
[PubMed]

McMaster, W. H.

W. H. McMaster, N. Kerr del Grande, J. H. Mallett, J. H. Hubbell, “Compilation of x-ray cross-sections,” (Lawrence Livermore Radiation Laboratory, Livermore, Calif., 1969), Sec. 2, Rev. 1.

Morin, L. R. M.

L. R. M. Morin, A. Berroir, “Calculation of x-ray single scattering in diagnostic radiology,” Phys. Med. Biol. 28, 789–797 (1983).
[Crossref] [PubMed]

L. R. M. Morin, “Molecular form factors and photon coherent scattering cross-sections of water,”J. Phys. Chem. Ref. Data 11, 1091–1098 (1982).
[Crossref]

Mullani, N. A.

N. A. Mullani, J. Markham, M. Ter Pogossian, “Feasibility of time of flight positron emission tomography,”J. Nucl. Med. 21, 1095–1097 (1980).
[PubMed]

Muntz, E. P.

E. P. Muntz, T. Fewell, R. Jennings, H. Bernstein, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
[Crossref] [PubMed]

Neitzel, U.

U. Neitzel, J. Kosanetzky, G. Harding, “Coherent scatter in radiographic imaging: a Monte Carlo simulation study,” Phys. Med. Biol. 30, 1289–1296 (1985).
[Crossref] [PubMed]

G. Harding, J. Kosanetzky, U. Neitzel, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
[Crossref] [PubMed]

J. Kosanetzky, G. Harding, U. Neitzel, “Energy-resolved x-ray diffraction CT,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.

G. Harding, J. Kosanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. (to be published).

J. M. Kosanetzky, B. Knoerr, G. Harding, U. Neitzel, “X-ray diffraction measurements of some plastic materials and body tissues,” Med. Phys. (to be published).
[PubMed]

Ribberfors, R.

G. Alm Carlsson, C. A. Carlsson, K. F. Berggren, R. Ribberfors, “Calculation of scattering cross-sections for increased accuracy in diagnostic radiology. I. Energy broadening of Compton scattered photons,” Med. Phys. 9, 868–879 (1982).
[Crossref]

Singh, M.

M. Singh, “An electronically collimated gamma camera. Part 1: Theoretical considerations and design criteria for single photon emission computed tomography,” Med. Phys. 10, 421–435 (1983).
[Crossref] [PubMed]

M. Singh, D. Doria, “An electronically collimated gamma camera for single photon emission computed tomography. Part 2: Image reconstruction and preliminary experimental measurements,” Med. Phys. 10, 428–435 (1983).
[Crossref] [PubMed]

Snyder, D. L.

D. L. Snyder, L. J. Thomas, M. Ter Pogossian, “A mathematical model for positron emission tomography systems having time of flight measurements,” IEEE Trans. Nucl. Sci. NS-28, 3575–3583 (1981).
[Crossref]

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, p. 470.

Ter Pogossian, M.

D. L. Snyder, L. J. Thomas, M. Ter Pogossian, “A mathematical model for positron emission tomography systems having time of flight measurements,” IEEE Trans. Nucl. Sci. NS-28, 3575–3583 (1981).
[Crossref]

N. A. Mullani, J. Markham, M. Ter Pogossian, “Feasibility of time of flight positron emission tomography,”J. Nucl. Med. 21, 1095–1097 (1980).
[PubMed]

Thomas, L. J.

D. L. Snyder, L. J. Thomas, M. Ter Pogossian, “A mathematical model for positron emission tomography systems having time of flight measurements,” IEEE Trans. Nucl. Sci. NS-28, 3575–3583 (1981).
[Crossref]

Tischler, R.

G. Harding, R. Tischler, “Dual energy Compton scatter tomography,” Phys. Med. Biol. 31, 477–489, 1986.
[Crossref] [PubMed]

Veigele, W. J.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, R. J. Howerton, “Atomic form factors, incoherent scattering functions and photon scattering cross-sections,”J. Phys. Chem. Ref. Data 4, 471–538 (1975); Errata 6, 615–616 (1977).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 370–386.

Yaffe, M. J.

P. C. Johns, M. J. Yaffe, “Coherent scatter in diagnostic radiology,” Med. Phys. 10, 40–50 (1983).
[Crossref] [PubMed]

IEEE Trans. Nucl. Sci. (1)

D. L. Snyder, L. J. Thomas, M. Ter Pogossian, “A mathematical model for positron emission tomography systems having time of flight measurements,” IEEE Trans. Nucl. Sci. NS-28, 3575–3583 (1981).
[Crossref]

Int. J. Radiat. Biol. (1)

J. Bednar, “Electronic excitations in condensed biological matter,” Int. J. Radiat. Biol. 48, 147–166 (1985).
[Crossref]

J. Nucl. Med. (1)

N. A. Mullani, J. Markham, M. Ter Pogossian, “Feasibility of time of flight positron emission tomography,”J. Nucl. Med. 21, 1095–1097 (1980).
[PubMed]

J. Opt. Soc. Am./Rev. Sci. Instrum. (1)

A. H. Compton, “X-rays as a branch of optics,” J. Opt. Soc. Am./Rev. Sci. Instrum. 16, 71–87 (1928).
[Crossref]

J. Phys. Chem. Ref. Data (2)

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, R. J. Howerton, “Atomic form factors, incoherent scattering functions and photon scattering cross-sections,”J. Phys. Chem. Ref. Data 4, 471–538 (1975); Errata 6, 615–616 (1977).
[Crossref]

L. R. M. Morin, “Molecular form factors and photon coherent scattering cross-sections of water,”J. Phys. Chem. Ref. Data 11, 1091–1098 (1982).
[Crossref]

Med. Phys. (5)

G. Alm Carlsson, C. A. Carlsson, K. F. Berggren, R. Ribberfors, “Calculation of scattering cross-sections for increased accuracy in diagnostic radiology. I. Energy broadening of Compton scattered photons,” Med. Phys. 9, 868–879 (1982).
[Crossref]

P. C. Johns, M. J. Yaffe, “Coherent scatter in diagnostic radiology,” Med. Phys. 10, 40–50 (1983).
[Crossref] [PubMed]

E. P. Muntz, T. Fewell, R. Jennings, H. Bernstein, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
[Crossref] [PubMed]

M. Singh, “An electronically collimated gamma camera. Part 1: Theoretical considerations and design criteria for single photon emission computed tomography,” Med. Phys. 10, 421–435 (1983).
[Crossref] [PubMed]

M. Singh, D. Doria, “An electronically collimated gamma camera for single photon emission computed tomography. Part 2: Image reconstruction and preliminary experimental measurements,” Med. Phys. 10, 428–435 (1983).
[Crossref] [PubMed]

Phys. Med. Biol. (4)

G. Harding, R. Tischler, “Dual energy Compton scatter tomography,” Phys. Med. Biol. 31, 477–489, 1986.
[Crossref] [PubMed]

L. R. M. Morin, A. Berroir, “Calculation of x-ray single scattering in diagnostic radiology,” Phys. Med. Biol. 28, 789–797 (1983).
[Crossref] [PubMed]

G. Harding, J. Kosanetzky, U. Neitzel, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
[Crossref] [PubMed]

U. Neitzel, J. Kosanetzky, G. Harding, “Coherent scatter in radiographic imaging: a Monte Carlo simulation study,” Phys. Med. Biol. 30, 1289–1296 (1985).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

M. J. Cooper, “Compton scattering and electron momentum determination,” Rep. Prog. Phys. 48, 415–481 (1985).
[Crossref]

Other (11)

G. Harding, J. Kosanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. (to be published).

D. W. L. Hukins, X-Ray Diffraction by Disordered and Ordered Systems (Pergamon, Oxford, 1981), pp. 19–24.

J. M. Kosanetzky, B. Knoerr, G. Harding, U. Neitzel, “X-ray diffraction measurements of some plastic materials and body tissues,” Med. Phys. (to be published).
[PubMed]

D. E. Cashwell, C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon, London, 1959).

W. Heitler, The Quantum Theory of Radiation, 3rd ed. (Clarendon, Oxford, 1954), pp. 34–38.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 370–386.

D. C. Champeney, Fourier Transforms and Their Physical Applications (Academic, London, 1973), Chap. 13, pp. 181–197.

J. Kosanetzky, G. Harding, U. Neitzel, “Energy-resolved x-ray diffraction CT,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.

W. H. McMaster, N. Kerr del Grande, J. H. Mallett, J. H. Hubbell, “Compilation of x-ray cross-sections,” (Lawrence Livermore Radiation Laboratory, Livermore, Calif., 1969), Sec. 2, Rev. 1.

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Figures (15)

Fig. 1
Fig. 1

Geometrical relationships in coherent scattering.

Fig. 2
Fig. 2

Differential cross section per unit volume of various materials constituting the American Association of Physicists in Medicine (AAPM) computed tomography (CT) performance phantom. Materials: (a) water, Lucite, polycarbonate, polystyrene; (b) nylon, polyethylene.

Fig. 3
Fig. 3

Differential cross section per unit volume of various animal tissues: (a) muscle, fat; (b) tendon; (c) dense bone; (d) white and gray brain matter.

Fig. 4
Fig. 4

Contributions to the scattering of 60-keV photons incident upon a water slab 20 cm thick at a detector plane 50 cm away as a function of the radial distance from the primary beam. Curves show the energy per unit detector area normalized against the integrated energy in the transmitted beam.

Fig. 5
Fig. 5

Illustration of projection relationship in x-ray diffraction tomography.

Fig. 6
Fig. 6

Schematic illustration of the measurement system for x-ray diffraction tomography.

Fig. 7
Fig. 7

Quasi-hexagonal detector array, viewed along the primary beam direction, used in the present work.

Fig. 8
Fig. 8

(a) Form and composition of the AAPM CT performance phantom. (b) Transmission CT (top) and nine scatter images of the AAPM CT performance phantom. The mean angles are (top left to bottom right) 1.5, 1.7, 2.7, 3.3, 4.1, 4.5, 5.0, 5.5, and 6.1 deg.

Fig. 9
Fig. 9

Same as in Fig. 8(b). The mean scatter angles are 0.9, 1.0, 1.6, 2.0, 2.4, 2.7, 3.0, 3.3, 3.6, and 4.0 deg.

Fig. 10
Fig. 10

Photon energy spectrum for W anode tube at 120 kVp and 5 mm of Al filtration.

Fig. 11
Fig. 11

Images of the plastic materials present in the AAPM phanton reconstructed from simulated data with 1% noise at the scatter angles 3.3, 3.8, and 4.3 deg. (a) Form and composition of the object from which simulated data were derived. (b) Monochromatic radiation at 60 keV. (c) Polychromatic radiation with spectrum given in Fig. 10. (d) Polychromatic radiation analyzed with detector having 15% FWHM energy resolution.

Fig. 12
Fig. 12

Images of a test object containing eight wedge-shaped channels in a Lucite block 40 mm thick. The channels are filled with salt concentrations (by weight) of (left to right): 10% (channels 1 and 2), 8% (channels 3 and 4), 6% (channels 5 and 6), and 3% (channels 7 and 8). (a) Transmission radiograph; (b) diffraction radiograph at 3.0 deg; (c) diffraction radiograph at 6.8 deg.

Fig. 13
Fig. 13

Comparison of collimated (a) and open (b) arrangements for scatter detection.

Fig. 14
Fig. 14

Images of the AAPM phantom reconstructed from simulated scatter data at 2.4 deg (60 keV), assuming that a collimated (a) or an open (b) detector is used.

Fig. 15
Fig. 15

Schematic illustration of a double detector arrangement operated in coincidence for determination of the incidence angle of a photon arriving at detector D1 (see the text).

Equations (8)

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d σ d Ω ( Thomson ) = r e 2 2 ( 1 + cos 2 θ ) .
d σ d Ω ( atom ) = d σ d Ω ( Thomson ) F 2 ( x , Z ) .
x = sin ( θ / 2 ) / λ ,
d σ d Ω ( volume ) = d σ d Ω ( atom ) M 0 s ( x ) ,
s ( x ) = 1 + exp ( - i x r ) P ( r ) d r .
d N i = N 0 T p ( l ) d σ total d Ω [ l , x i ( l ) ] Δ Ω i ( l ) T s ( l ) d l + M .
θ i = tan - 1 [ R i / ( L - l ) ] .
N i = N t l d σ total d Ω ( l , x i ) Δ Ω i d l .

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