Abstract

Mass fraction profiling is a specialized tomographic technique designed to allow one to measure the concentration profiles of the component species of a synthetic composite material. While developed for the express purpose of determining the dopant, density, and porosity profiles of unsintered soot boules, the method should also be useful in analyzing other types of ceramic such as dried gels. Mass fraction profiling amounts to a three-step process consisting of scanning the object of interest with well-collimated beams of x rays, reconstructing the attenuation coefficient profiles for several x-ray energies, and generating the density and concentration or mass fraction profiles. The method for determining these profiles is outlined, and some measurement results obtained for soot boules are presented.

© 1987 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Special Issue on Computed Tomography, Appl. Opt. 24 (1Dec.1985).
    [PubMed]
  2. W. J. Glantschnig, “Method And Apparatus For Analyzing A Porous Nonhomogeneous Cylindrical Object,” patent pending.
  3. T. Izawa, S. Sudo, F. Hanawa, “Continuous Fabrication Process for High-Silica Fiber Preforms,” Trans. IECE Jpn. E 62, 779 (1979).
  4. P. C. Schultz, “Fabrication of Optical Waveguides by the Outside Vapor Deposition Process,” Proc. IEEE 68, 1187 (1980).
    [CrossRef]
  5. A. J. Morrow, A. Sarkar, P. C. Schultz, “Outside Vapor Deposition,” in Optical Fiber Communications, Vol. 1, Fiber Fabrication, T. Li, Ed. (Academic, Orlando, 1985); N. Niizeki, N. Inagaki, T. Edahiro, “Vapor-Phase Axial Deposition Method,” in Optical Fiber Communications, Vol. 1, Fiber Fabrication, T. Li, Ed. (Academic, Orlando, FL.1985).
  6. E. Potkay, “Representation of the Vapor-Phase Axial Deposition Helical Layer Structure Through a ‘Spiral Transformation’,” J. Appl. Phys. 57, 1509 (1985).
    [CrossRef]
  7. H. Takahashi, S. Shibuya, T. Kuroha, “Applicative Investigation of X-Ray Nondestructive Inspection Technique for Measurement of Core Diameter and Germanium Doping Concentration Profiles of Optical Fiber Preforms,” in Technical Digest, Fifth European Conference on Optical Communication, Amsterdam (1979).
  8. R. M. Levitt, “Reconstruction Algorithms: Transform Methods,” Proc. IEEE 71, 390 (1983).
    [CrossRef]
  9. Y. Censor, “Finite Series-Expansion Reconstruction Methods,” Proc. IEEE 71, 409 (1983).
    [CrossRef]
  10. J. P. Stonestrom, R. E. Alvarez, A. Marcovski, “A Framework for Spectral Artifact Corrections in X-Ray CT,” IEEE Trans. Biomed. Eng. BME-28, 128 (1981).
    [CrossRef]
  11. G. Vernazza, F. Caratozzolo, S. B. Serpico, S. Geraci, “Some Results in Multi-Energy Digital Radiology,” Proc. (Soc. Photo-Opt. Instrum. Eng.) 535, 202 (1985).
  12. R. D. Evans, The Atomic Nucleus (McGraw-Hill, New York, 1955), Chap. 25.
  13. J. A. Victoreen, “The Absorption of Incident Quanta by Atoms as Defined by the Mass Photoelectric Absorption Coefficient and the Mass Scattering Coefficient,” J. Appl. Phys. 19, 855 (1948).
    [CrossRef]
  14. J. A. Victoreen, “The Calculation of X-Ray Mass Absorption coefficients,” J. Appl. Phys. 20, 1141 (1949).
    [CrossRef]
  15. C. M. Davisson, R. D. Evans, “Gamma-Ray Absorption Coefficients,” Rev. Mod Phys. 24, 79 (1952).
    [CrossRef]
  16. The International Union of Crystallography, International Tables for X-Ray Crystallography (D. Reidel, Boston, 1983), Vol. 3.
  17. M. Bocher, An Introduction to the Study of Integral Equations (Cambridge U.P., 1926).
  18. L. S. Watkins, “Laser Beam Refraction Traversely Through a Graded-Index Preform to Determine Refractive Index Ratio and Gradient Profile,” Appl. Opt. 18, 2214 (1979).
    [CrossRef] [PubMed]
  19. W. J. Glantschnig, “How Accurately Can One Reconstruct an Index Profile From Transverse Measurement Data?,” IEEE/OSA J. Lightwave Technol. LT-3, 678 (1985).
    [CrossRef]

1985 (4)

E. Potkay, “Representation of the Vapor-Phase Axial Deposition Helical Layer Structure Through a ‘Spiral Transformation’,” J. Appl. Phys. 57, 1509 (1985).
[CrossRef]

Special Issue on Computed Tomography, Appl. Opt. 24 (1Dec.1985).
[PubMed]

G. Vernazza, F. Caratozzolo, S. B. Serpico, S. Geraci, “Some Results in Multi-Energy Digital Radiology,” Proc. (Soc. Photo-Opt. Instrum. Eng.) 535, 202 (1985).

W. J. Glantschnig, “How Accurately Can One Reconstruct an Index Profile From Transverse Measurement Data?,” IEEE/OSA J. Lightwave Technol. LT-3, 678 (1985).
[CrossRef]

1983 (2)

R. M. Levitt, “Reconstruction Algorithms: Transform Methods,” Proc. IEEE 71, 390 (1983).
[CrossRef]

Y. Censor, “Finite Series-Expansion Reconstruction Methods,” Proc. IEEE 71, 409 (1983).
[CrossRef]

1981 (1)

J. P. Stonestrom, R. E. Alvarez, A. Marcovski, “A Framework for Spectral Artifact Corrections in X-Ray CT,” IEEE Trans. Biomed. Eng. BME-28, 128 (1981).
[CrossRef]

1980 (1)

P. C. Schultz, “Fabrication of Optical Waveguides by the Outside Vapor Deposition Process,” Proc. IEEE 68, 1187 (1980).
[CrossRef]

1979 (2)

L. S. Watkins, “Laser Beam Refraction Traversely Through a Graded-Index Preform to Determine Refractive Index Ratio and Gradient Profile,” Appl. Opt. 18, 2214 (1979).
[CrossRef] [PubMed]

T. Izawa, S. Sudo, F. Hanawa, “Continuous Fabrication Process for High-Silica Fiber Preforms,” Trans. IECE Jpn. E 62, 779 (1979).

1952 (1)

C. M. Davisson, R. D. Evans, “Gamma-Ray Absorption Coefficients,” Rev. Mod Phys. 24, 79 (1952).
[CrossRef]

1949 (1)

J. A. Victoreen, “The Calculation of X-Ray Mass Absorption coefficients,” J. Appl. Phys. 20, 1141 (1949).
[CrossRef]

1948 (1)

J. A. Victoreen, “The Absorption of Incident Quanta by Atoms as Defined by the Mass Photoelectric Absorption Coefficient and the Mass Scattering Coefficient,” J. Appl. Phys. 19, 855 (1948).
[CrossRef]

Alvarez, R. E.

J. P. Stonestrom, R. E. Alvarez, A. Marcovski, “A Framework for Spectral Artifact Corrections in X-Ray CT,” IEEE Trans. Biomed. Eng. BME-28, 128 (1981).
[CrossRef]

Bocher, M.

M. Bocher, An Introduction to the Study of Integral Equations (Cambridge U.P., 1926).

Caratozzolo, F.

G. Vernazza, F. Caratozzolo, S. B. Serpico, S. Geraci, “Some Results in Multi-Energy Digital Radiology,” Proc. (Soc. Photo-Opt. Instrum. Eng.) 535, 202 (1985).

Censor, Y.

Y. Censor, “Finite Series-Expansion Reconstruction Methods,” Proc. IEEE 71, 409 (1983).
[CrossRef]

Davisson, C. M.

C. M. Davisson, R. D. Evans, “Gamma-Ray Absorption Coefficients,” Rev. Mod Phys. 24, 79 (1952).
[CrossRef]

Evans, R. D.

C. M. Davisson, R. D. Evans, “Gamma-Ray Absorption Coefficients,” Rev. Mod Phys. 24, 79 (1952).
[CrossRef]

R. D. Evans, The Atomic Nucleus (McGraw-Hill, New York, 1955), Chap. 25.

Geraci, S.

G. Vernazza, F. Caratozzolo, S. B. Serpico, S. Geraci, “Some Results in Multi-Energy Digital Radiology,” Proc. (Soc. Photo-Opt. Instrum. Eng.) 535, 202 (1985).

Glantschnig, W. J.

W. J. Glantschnig, “How Accurately Can One Reconstruct an Index Profile From Transverse Measurement Data?,” IEEE/OSA J. Lightwave Technol. LT-3, 678 (1985).
[CrossRef]

W. J. Glantschnig, “Method And Apparatus For Analyzing A Porous Nonhomogeneous Cylindrical Object,” patent pending.

Hanawa, F.

T. Izawa, S. Sudo, F. Hanawa, “Continuous Fabrication Process for High-Silica Fiber Preforms,” Trans. IECE Jpn. E 62, 779 (1979).

Izawa, T.

T. Izawa, S. Sudo, F. Hanawa, “Continuous Fabrication Process for High-Silica Fiber Preforms,” Trans. IECE Jpn. E 62, 779 (1979).

Kuroha, T.

H. Takahashi, S. Shibuya, T. Kuroha, “Applicative Investigation of X-Ray Nondestructive Inspection Technique for Measurement of Core Diameter and Germanium Doping Concentration Profiles of Optical Fiber Preforms,” in Technical Digest, Fifth European Conference on Optical Communication, Amsterdam (1979).

Levitt, R. M.

R. M. Levitt, “Reconstruction Algorithms: Transform Methods,” Proc. IEEE 71, 390 (1983).
[CrossRef]

Marcovski, A.

J. P. Stonestrom, R. E. Alvarez, A. Marcovski, “A Framework for Spectral Artifact Corrections in X-Ray CT,” IEEE Trans. Biomed. Eng. BME-28, 128 (1981).
[CrossRef]

Morrow, A. J.

A. J. Morrow, A. Sarkar, P. C. Schultz, “Outside Vapor Deposition,” in Optical Fiber Communications, Vol. 1, Fiber Fabrication, T. Li, Ed. (Academic, Orlando, 1985); N. Niizeki, N. Inagaki, T. Edahiro, “Vapor-Phase Axial Deposition Method,” in Optical Fiber Communications, Vol. 1, Fiber Fabrication, T. Li, Ed. (Academic, Orlando, FL.1985).

Potkay, E.

E. Potkay, “Representation of the Vapor-Phase Axial Deposition Helical Layer Structure Through a ‘Spiral Transformation’,” J. Appl. Phys. 57, 1509 (1985).
[CrossRef]

Sarkar, A.

A. J. Morrow, A. Sarkar, P. C. Schultz, “Outside Vapor Deposition,” in Optical Fiber Communications, Vol. 1, Fiber Fabrication, T. Li, Ed. (Academic, Orlando, 1985); N. Niizeki, N. Inagaki, T. Edahiro, “Vapor-Phase Axial Deposition Method,” in Optical Fiber Communications, Vol. 1, Fiber Fabrication, T. Li, Ed. (Academic, Orlando, FL.1985).

Schultz, P. C.

P. C. Schultz, “Fabrication of Optical Waveguides by the Outside Vapor Deposition Process,” Proc. IEEE 68, 1187 (1980).
[CrossRef]

A. J. Morrow, A. Sarkar, P. C. Schultz, “Outside Vapor Deposition,” in Optical Fiber Communications, Vol. 1, Fiber Fabrication, T. Li, Ed. (Academic, Orlando, 1985); N. Niizeki, N. Inagaki, T. Edahiro, “Vapor-Phase Axial Deposition Method,” in Optical Fiber Communications, Vol. 1, Fiber Fabrication, T. Li, Ed. (Academic, Orlando, FL.1985).

Serpico, S. B.

G. Vernazza, F. Caratozzolo, S. B. Serpico, S. Geraci, “Some Results in Multi-Energy Digital Radiology,” Proc. (Soc. Photo-Opt. Instrum. Eng.) 535, 202 (1985).

Shibuya, S.

H. Takahashi, S. Shibuya, T. Kuroha, “Applicative Investigation of X-Ray Nondestructive Inspection Technique for Measurement of Core Diameter and Germanium Doping Concentration Profiles of Optical Fiber Preforms,” in Technical Digest, Fifth European Conference on Optical Communication, Amsterdam (1979).

Stonestrom, J. P.

J. P. Stonestrom, R. E. Alvarez, A. Marcovski, “A Framework for Spectral Artifact Corrections in X-Ray CT,” IEEE Trans. Biomed. Eng. BME-28, 128 (1981).
[CrossRef]

Sudo, S.

T. Izawa, S. Sudo, F. Hanawa, “Continuous Fabrication Process for High-Silica Fiber Preforms,” Trans. IECE Jpn. E 62, 779 (1979).

Takahashi, H.

H. Takahashi, S. Shibuya, T. Kuroha, “Applicative Investigation of X-Ray Nondestructive Inspection Technique for Measurement of Core Diameter and Germanium Doping Concentration Profiles of Optical Fiber Preforms,” in Technical Digest, Fifth European Conference on Optical Communication, Amsterdam (1979).

Vernazza, G.

G. Vernazza, F. Caratozzolo, S. B. Serpico, S. Geraci, “Some Results in Multi-Energy Digital Radiology,” Proc. (Soc. Photo-Opt. Instrum. Eng.) 535, 202 (1985).

Victoreen, J. A.

J. A. Victoreen, “The Calculation of X-Ray Mass Absorption coefficients,” J. Appl. Phys. 20, 1141 (1949).
[CrossRef]

J. A. Victoreen, “The Absorption of Incident Quanta by Atoms as Defined by the Mass Photoelectric Absorption Coefficient and the Mass Scattering Coefficient,” J. Appl. Phys. 19, 855 (1948).
[CrossRef]

Watkins, L. S.

Appl. Opt. (2)

IEEE Trans. Biomed. Eng. (1)

J. P. Stonestrom, R. E. Alvarez, A. Marcovski, “A Framework for Spectral Artifact Corrections in X-Ray CT,” IEEE Trans. Biomed. Eng. BME-28, 128 (1981).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (1)

W. J. Glantschnig, “How Accurately Can One Reconstruct an Index Profile From Transverse Measurement Data?,” IEEE/OSA J. Lightwave Technol. LT-3, 678 (1985).
[CrossRef]

J. Appl. Phys. (3)

J. A. Victoreen, “The Absorption of Incident Quanta by Atoms as Defined by the Mass Photoelectric Absorption Coefficient and the Mass Scattering Coefficient,” J. Appl. Phys. 19, 855 (1948).
[CrossRef]

J. A. Victoreen, “The Calculation of X-Ray Mass Absorption coefficients,” J. Appl. Phys. 20, 1141 (1949).
[CrossRef]

E. Potkay, “Representation of the Vapor-Phase Axial Deposition Helical Layer Structure Through a ‘Spiral Transformation’,” J. Appl. Phys. 57, 1509 (1985).
[CrossRef]

Proc. (Soc. Photo-Opt. Instrum. Eng.) (1)

G. Vernazza, F. Caratozzolo, S. B. Serpico, S. Geraci, “Some Results in Multi-Energy Digital Radiology,” Proc. (Soc. Photo-Opt. Instrum. Eng.) 535, 202 (1985).

Proc. IEEE (3)

R. M. Levitt, “Reconstruction Algorithms: Transform Methods,” Proc. IEEE 71, 390 (1983).
[CrossRef]

Y. Censor, “Finite Series-Expansion Reconstruction Methods,” Proc. IEEE 71, 409 (1983).
[CrossRef]

P. C. Schultz, “Fabrication of Optical Waveguides by the Outside Vapor Deposition Process,” Proc. IEEE 68, 1187 (1980).
[CrossRef]

Rev. Mod Phys. (1)

C. M. Davisson, R. D. Evans, “Gamma-Ray Absorption Coefficients,” Rev. Mod Phys. 24, 79 (1952).
[CrossRef]

Trans. IECE Jpn. (1)

T. Izawa, S. Sudo, F. Hanawa, “Continuous Fabrication Process for High-Silica Fiber Preforms,” Trans. IECE Jpn. E 62, 779 (1979).

Other (6)

R. D. Evans, The Atomic Nucleus (McGraw-Hill, New York, 1955), Chap. 25.

The International Union of Crystallography, International Tables for X-Ray Crystallography (D. Reidel, Boston, 1983), Vol. 3.

M. Bocher, An Introduction to the Study of Integral Equations (Cambridge U.P., 1926).

A. J. Morrow, A. Sarkar, P. C. Schultz, “Outside Vapor Deposition,” in Optical Fiber Communications, Vol. 1, Fiber Fabrication, T. Li, Ed. (Academic, Orlando, 1985); N. Niizeki, N. Inagaki, T. Edahiro, “Vapor-Phase Axial Deposition Method,” in Optical Fiber Communications, Vol. 1, Fiber Fabrication, T. Li, Ed. (Academic, Orlando, FL.1985).

W. J. Glantschnig, “Method And Apparatus For Analyzing A Porous Nonhomogeneous Cylindrical Object,” patent pending.

H. Takahashi, S. Shibuya, T. Kuroha, “Applicative Investigation of X-Ray Nondestructive Inspection Technique for Measurement of Core Diameter and Germanium Doping Concentration Profiles of Optical Fiber Preforms,” in Technical Digest, Fifth European Conference on Optical Communication, Amsterdam (1979).

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 (7)

Fig. 1
Fig. 1

Schematic representation of a well-collimated x-ray beam penetrating a cylindrically symmetric object in parallel beam geometry.

Fig. 2
Fig. 2

Measured beam intensities as a function of the impact distance t for two x-ray energies E1 and E2 as the beams are scanned through the boule perpendicular to the boule axis. The measured intensities are normalized with respect to the unattenuated beams.

Fig. 3
Fig. 3

Linear attenuation coefficient profiles of a soot boule for two distinct x-ray energies E1 and E2.

Fig. 4
Fig. 4

Germania mole fraction and mass density profiles of a nominally step-index boule with a germania doped core and pure silica cladding. The hole in the center resulted from the removal of the alumina mandrel on which this boule was grown.

Fig. 5
Fig. 5

Germania mole fraction and mass density profiles of a pure silica boule consisting of a solid silica mandrel in the center and pure silica soot on the outside.

Fig. 6
Fig. 6

Superposition of a photograph of a boule being grown with a multiple-torch vapor-phase axial deposition system and the density profile subsequently obtained for this boule.

Fig. 7
Fig. 7

Germania mole fraction and mass density profiles of a VAD boule consisting of a germania doped core and pure silica soot cladding layers deposited with multiple cladding torches.

Equations (12)

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

μ i ( E ) = N i ( atoms cm 3 ) j = 1 K σ j ( i ) ( E ) ( cm 2 atom ) ,
a i ( E ) = μ i ( E ) ρ i
μ ( E , r ) ρ ( r ) = i = 1 M a i ( E ) x i ( r ) .
μ ( E , r ) = ρ ( r ) i = 1 M a i ( E ) x i ( r ) .
[ a 1 ( E 1 ) a M ( E 1 ) a 1 ( E M ) a M ( E M ) ] ρ ( r ) [ x 1 ( r ) x M ( r ) ] = [ μ ( E 1 , r ) μ ( E M , r ) ] .
i = 1 M ρ ( r ) x i ( r ) = ρ ( r ) i = 1 M x i ( r ) = ρ ( r ) .
μ ¯ j ( r ) = 1 E j 2 - E j 1 E j 1 E j 2 μ ( E , r ) d E ,
a ¯ i j = 1 E j 2 - E j 1 E j 1 E j 2 a i ( E ) d E .
[ a ¯ 11 a ¯ M 1 a ¯ 1 M a ¯ M M ] ρ ( r ) [ x 1 ( r ) x M ( r ) ] = [ μ ¯ 1 ( r ) μ ¯ M ( r ) ] ,
1 ρ ( r ) = i = 1 M x i ( r ) ρ i .
μ ( E , r ) = 1 π r R d d t [ log i ( E , t ) i 0 ( E ) ] d t t 2 - r 2 ,
i ( E , t ) = i 0 exp [ - 2 t R μ ( E , r ) r d r r 2 - t 2 ] .

Metrics