Abstract

Optical tomography is used to map the iodine vapor density in a plane. Two-dimensional images are obtained with 1-cm spatial resolution using a fan beam geometry with a 28-cm radius fan source circle. The images are reconstructed using the convolution backprojection algorithm with data collected in 0.1 sec from 90 detectors on a full circle using 90–360 fan source positions. Experimental results quantitatively confirm a theoretical analysis of the noise in the reconstructed image, including the effects of correlated noise, position within the image, and spatial resolution. The noise amplitude–absorption length product for a 2-cm pixel size is 6 × 10−4 which is equivalent to an iodine concentration of 6 ppm.

© 1984 Optical Society of America

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  1. Special issue on Computerized Tomography, Proc. IEEE 71 (Mar.1983).
  2. A. M. Cormack, “Early 2-D Reconstruction (CT Scanning) and Recent Topics Stemming from It, Nobel Lecture 1979,” J. Comput. Assist. Tomogr. 4, 658 (1980).
    [CrossRef] [PubMed]
  3. G. N. Hounsfield, “Computed Medical Imaging, Nobel Lecture 1979,” J. Comput. Assist. Tomogr. 4, 665 (1980).
    [CrossRef] [PubMed]
  4. G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computed Tomography (Academic, New York, 1980).
  5. H. H. Barrett, W. Swindell, Radiological Imaging, Vols. 1 and 2 (Academic, New York, 1980).
  6. R. N. Bracewell, A. C. Riddle, “Inversion of Fan Beam Scans in Radio Astronomy,” Astrophys. J. 150, 427 (1967).
    [CrossRef]
  7. G. T. Herman, A. V. Lakshminarayanan, A. Naparstek, “Convolution Reconstruction Techniques for Divergent Beams,” Comput. Biol. Med. 6, 259 (1976).
    [CrossRef] [PubMed]
  8. R. L. Byer, L. A. Shepp, “Two-Dimensional Remote Air-Pollution Monitoring Via Tomography,” Opt. Lett. 4, 75, (1979).
    [CrossRef] [PubMed]
  9. M. J. Dyer, D. R. Crosley, “Two-Dimensional Imaging of OH Laser-Induced Fluorescence in a Flame,” Opt. Lett. 7, 382 (1982).
    [CrossRef] [PubMed]
  10. G. Kychakoff, R. D. Howe, R. K. Hanson, “Quantitative Flow Visualization Technique for Measurements in Combustion Gases,” Appl. Opt. 23, 704 (1984).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. M. B. Long, D. C. Fourguette, M. C. Escoda, C. B. Layne, “Instantaneous Ramanography of a Turbulent Diffusion Flame,” Opt. Lett. 8, 244 (1983).
    [CrossRef] [PubMed]
  14. E. Wolf, “Three Dimensional Structure Determination of Semi-Transparent Objects from Holographic Data,” Opt. Commun. 1, 153 (1969).
    [CrossRef]
  15. E. Wolf, “Determination of Scattered Fields by Holography,” J. Opt. Soc. Am. 60, 18 (1970).
    [CrossRef]
  16. M. V. Berry, D. F. Gibbs, “The Interpretation of Optical Projections,” Proc. R. Soc. London Ser. A314, 143 (1970).
    [CrossRef]
  17. B. W. Stuck, “Estimating the Spatial Concentration of Certain Types of Air Pollutants,” J. Opt. Soc. Am. 67, 668 (1977).
    [CrossRef]
  18. D. C. Wolfe, R. L. Byer, “Model Studies of Laser Absorption Computed Tomography for Remote Air Pollution Measurements,” Appl. Opt. 21, 1165 (1982).
    [CrossRef] [PubMed]
  19. K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181 (1981).
    [CrossRef]
  20. I. Willms, “A Measurement Procedure for Acquisition of Spatial Inhomogeneous Aerosol Concentrations,” Aerosols in Science, Medicine and Technology, 9 Conference 1981, Gesellschaft fur Aerosolforschung, Schmallenberg.
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    [CrossRef]
  22. G. T. Herman, A. Naparstek, “Fast Image Reconstruction Based on a Radon Inversion for Applications for Rapidly Collected Data,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 33, 511 (1978).
    [CrossRef]
  23. G. N. Ramachandran, A. V. Lakshminarayanan, “Three Dimensional Reconstructions from Radiographs and Electron Micrographs: Application of Convolution Instead of Fourier Transforms,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236 (1971).
    [CrossRef] [PubMed]
  24. L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21 (1974).
  25. D. A. Chesler, S. J. Riederer, “Ripple Suppression During Reconstruction in Transverse Tomography,” Phys. Med. Biol. 20, 632 (1975).
    [CrossRef] [PubMed]
  26. R. A. Brooks, G. H. Glover, A. J. Talbert, R. L. Eisner, F. A. DiBianca, “A Source of Streaks in Computed Tomograms,” J. Comput. Assist. Tomogr. 3, 511 (1979).
    [CrossRef] [PubMed]
  27. Ref. 4, p. 163ff.
  28. R. A. Brooks, G. H. Weiss, A. J. Talbert, “A New Approach to Interpolation in Computed Tomography,” J. Comput. Assist. Tomogr. 2, 577 (1978).
    [CrossRef] [PubMed]
  29. P. M. Joseph, R. A. Schulz, “View Sampling Requirements in Fan Beam Computed Tomography,” Med. Phys. 7, 692 (1980).
    [CrossRef] [PubMed]
  30. K. Bennett, R. L. Byer, “Fan Beam Tomography Noise Theory,” J. Opt. Soc. Am. A, submitted.
  31. M. Francon, Laser Speckle and Applications (Academic, New York, 1979), Chap. 2.
  32. H. Oertel, K. Buhler, “A Special Differential Interferometer Used for Heat Convection Applications,” Int. J. Heat Mass Transfer 21, 1111 (1978).
    [CrossRef]
  33. O. Kafri, “Noncoherent Method for Mapping Phase Objects,” Opt. Lett. 5, 555 (1980).
    [CrossRef] [PubMed]
  34. E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, “Temperature Mapping in Flames by Moire Deflectometry,” Appl. Opt. 22, 698 (1983).
    [CrossRef] [PubMed]

1984 (1)

1983 (3)

1982 (3)

1981 (3)

D. R. Crosley, “Collisional Effects on Laser Induced Fluorescence Flame Measurements,” Opt. Eng. 20, 511 (1981).
[CrossRef]

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181 (1981).
[CrossRef]

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Gouiard, “Optical Tomography for Flow Field Diagnostics,” Int. J. Heat Mass Transfer 24, 1139 (1981).
[CrossRef]

1980 (4)

A. M. Cormack, “Early 2-D Reconstruction (CT Scanning) and Recent Topics Stemming from It, Nobel Lecture 1979,” J. Comput. Assist. Tomogr. 4, 658 (1980).
[CrossRef] [PubMed]

G. N. Hounsfield, “Computed Medical Imaging, Nobel Lecture 1979,” J. Comput. Assist. Tomogr. 4, 665 (1980).
[CrossRef] [PubMed]

P. M. Joseph, R. A. Schulz, “View Sampling Requirements in Fan Beam Computed Tomography,” Med. Phys. 7, 692 (1980).
[CrossRef] [PubMed]

O. Kafri, “Noncoherent Method for Mapping Phase Objects,” Opt. Lett. 5, 555 (1980).
[CrossRef] [PubMed]

1979 (2)

R. A. Brooks, G. H. Glover, A. J. Talbert, R. L. Eisner, F. A. DiBianca, “A Source of Streaks in Computed Tomograms,” J. Comput. Assist. Tomogr. 3, 511 (1979).
[CrossRef] [PubMed]

R. L. Byer, L. A. Shepp, “Two-Dimensional Remote Air-Pollution Monitoring Via Tomography,” Opt. Lett. 4, 75, (1979).
[CrossRef] [PubMed]

1978 (3)

G. T. Herman, A. Naparstek, “Fast Image Reconstruction Based on a Radon Inversion for Applications for Rapidly Collected Data,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 33, 511 (1978).
[CrossRef]

R. A. Brooks, G. H. Weiss, A. J. Talbert, “A New Approach to Interpolation in Computed Tomography,” J. Comput. Assist. Tomogr. 2, 577 (1978).
[CrossRef] [PubMed]

H. Oertel, K. Buhler, “A Special Differential Interferometer Used for Heat Convection Applications,” Int. J. Heat Mass Transfer 21, 1111 (1978).
[CrossRef]

1977 (1)

1976 (1)

G. T. Herman, A. V. Lakshminarayanan, A. Naparstek, “Convolution Reconstruction Techniques for Divergent Beams,” Comput. Biol. Med. 6, 259 (1976).
[CrossRef] [PubMed]

1975 (1)

D. A. Chesler, S. J. Riederer, “Ripple Suppression During Reconstruction in Transverse Tomography,” Phys. Med. Biol. 20, 632 (1975).
[CrossRef] [PubMed]

1974 (1)

L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21 (1974).

1971 (1)

G. N. Ramachandran, A. V. Lakshminarayanan, “Three Dimensional Reconstructions from Radiographs and Electron Micrographs: Application of Convolution Instead of Fourier Transforms,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236 (1971).
[CrossRef] [PubMed]

1970 (2)

E. Wolf, “Determination of Scattered Fields by Holography,” J. Opt. Soc. Am. 60, 18 (1970).
[CrossRef]

M. V. Berry, D. F. Gibbs, “The Interpretation of Optical Projections,” Proc. R. Soc. London Ser. A314, 143 (1970).
[CrossRef]

1969 (1)

E. Wolf, “Three Dimensional Structure Determination of Semi-Transparent Objects from Holographic Data,” Opt. Commun. 1, 153 (1969).
[CrossRef]

1967 (1)

R. N. Bracewell, A. C. Riddle, “Inversion of Fan Beam Scans in Radio Astronomy,” Astrophys. J. 150, 427 (1967).
[CrossRef]

Baganoff, D.

J. C. McDaniel, D. Baganoff, R. L. Byer, “Density Measurements in Compressible Flows Using Off-Resonant Laser Induced Fluorescence,” Phys. Fluids 25, 1105 (1982).
[CrossRef]

Barrett, H. H.

H. H. Barrett, W. Swindell, Radiological Imaging, Vols. 1 and 2 (Academic, New York, 1980).

Bar-Ziv, E.

Bennett, K.

K. Bennett, R. L. Byer, “Fan Beam Tomography Noise Theory,” J. Opt. Soc. Am. A, submitted.

Berry, M. V.

M. V. Berry, D. F. Gibbs, “The Interpretation of Optical Projections,” Proc. R. Soc. London Ser. A314, 143 (1970).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, A. C. Riddle, “Inversion of Fan Beam Scans in Radio Astronomy,” Astrophys. J. 150, 427 (1967).
[CrossRef]

Brooks, R. A.

R. A. Brooks, G. H. Glover, A. J. Talbert, R. L. Eisner, F. A. DiBianca, “A Source of Streaks in Computed Tomograms,” J. Comput. Assist. Tomogr. 3, 511 (1979).
[CrossRef] [PubMed]

R. A. Brooks, G. H. Weiss, A. J. Talbert, “A New Approach to Interpolation in Computed Tomography,” J. Comput. Assist. Tomogr. 2, 577 (1978).
[CrossRef] [PubMed]

Buhler, K.

H. Oertel, K. Buhler, “A Special Differential Interferometer Used for Heat Convection Applications,” Int. J. Heat Mass Transfer 21, 1111 (1978).
[CrossRef]

Byer, R. L.

D. C. Wolfe, R. L. Byer, “Model Studies of Laser Absorption Computed Tomography for Remote Air Pollution Measurements,” Appl. Opt. 21, 1165 (1982).
[CrossRef] [PubMed]

J. C. McDaniel, D. Baganoff, R. L. Byer, “Density Measurements in Compressible Flows Using Off-Resonant Laser Induced Fluorescence,” Phys. Fluids 25, 1105 (1982).
[CrossRef]

R. L. Byer, L. A. Shepp, “Two-Dimensional Remote Air-Pollution Monitoring Via Tomography,” Opt. Lett. 4, 75, (1979).
[CrossRef] [PubMed]

K. Bennett, R. L. Byer, “Fan Beam Tomography Noise Theory,” J. Opt. Soc. Am. A, submitted.

Chesler, D. A.

D. A. Chesler, S. J. Riederer, “Ripple Suppression During Reconstruction in Transverse Tomography,” Phys. Med. Biol. 20, 632 (1975).
[CrossRef] [PubMed]

Cormack, A. M.

A. M. Cormack, “Early 2-D Reconstruction (CT Scanning) and Recent Topics Stemming from It, Nobel Lecture 1979,” J. Comput. Assist. Tomogr. 4, 658 (1980).
[CrossRef] [PubMed]

Crosley, D. R.

M. J. Dyer, D. R. Crosley, “Two-Dimensional Imaging of OH Laser-Induced Fluorescence in a Flame,” Opt. Lett. 7, 382 (1982).
[CrossRef] [PubMed]

D. R. Crosley, “Collisional Effects on Laser Induced Fluorescence Flame Measurements,” Opt. Eng. 20, 511 (1981).
[CrossRef]

DiBianca, F. A.

R. A. Brooks, G. H. Glover, A. J. Talbert, R. L. Eisner, F. A. DiBianca, “A Source of Streaks in Computed Tomograms,” J. Comput. Assist. Tomogr. 3, 511 (1979).
[CrossRef] [PubMed]

Dyer, M. J.

Eisner, R. L.

R. A. Brooks, G. H. Glover, A. J. Talbert, R. L. Eisner, F. A. DiBianca, “A Source of Streaks in Computed Tomograms,” J. Comput. Assist. Tomogr. 3, 511 (1979).
[CrossRef] [PubMed]

Emmerman, P. J.

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Gouiard, “Optical Tomography for Flow Field Diagnostics,” Int. J. Heat Mass Transfer 24, 1139 (1981).
[CrossRef]

Escoda, M. C.

Fourguette, D. C.

Francon, M.

M. Francon, Laser Speckle and Applications (Academic, New York, 1979), Chap. 2.

Gibbs, D. F.

M. V. Berry, D. F. Gibbs, “The Interpretation of Optical Projections,” Proc. R. Soc. London Ser. A314, 143 (1970).
[CrossRef]

Glover, G. H.

R. A. Brooks, G. H. Glover, A. J. Talbert, R. L. Eisner, F. A. DiBianca, “A Source of Streaks in Computed Tomograms,” J. Comput. Assist. Tomogr. 3, 511 (1979).
[CrossRef] [PubMed]

Gouiard, R.

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Gouiard, “Optical Tomography for Flow Field Diagnostics,” Int. J. Heat Mass Transfer 24, 1139 (1981).
[CrossRef]

Hanson, R. K.

Herman, G. T.

G. T. Herman, A. Naparstek, “Fast Image Reconstruction Based on a Radon Inversion for Applications for Rapidly Collected Data,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 33, 511 (1978).
[CrossRef]

G. T. Herman, A. V. Lakshminarayanan, A. Naparstek, “Convolution Reconstruction Techniques for Divergent Beams,” Comput. Biol. Med. 6, 259 (1976).
[CrossRef] [PubMed]

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

Hounsfield, G. N.

G. N. Hounsfield, “Computed Medical Imaging, Nobel Lecture 1979,” J. Comput. Assist. Tomogr. 4, 665 (1980).
[CrossRef] [PubMed]

Howe, R. D.

Joseph, P. M.

P. M. Joseph, R. A. Schulz, “View Sampling Requirements in Fan Beam Computed Tomography,” Med. Phys. 7, 692 (1980).
[CrossRef] [PubMed]

Kafri, O.

Keren, E.

Kirchartz, K. R.

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181 (1981).
[CrossRef]

Kychakoff, G.

Lakshminarayanan, A. V.

G. T. Herman, A. V. Lakshminarayanan, A. Naparstek, “Convolution Reconstruction Techniques for Divergent Beams,” Comput. Biol. Med. 6, 259 (1976).
[CrossRef] [PubMed]

G. N. Ramachandran, A. V. Lakshminarayanan, “Three Dimensional Reconstructions from Radiographs and Electron Micrographs: Application of Convolution Instead of Fourier Transforms,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236 (1971).
[CrossRef] [PubMed]

Layne, C. B.

Logan, B. F.

L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21 (1974).

Long, M. B.

McDaniel, J. C.

J. C. McDaniel, D. Baganoff, R. L. Byer, “Density Measurements in Compressible Flows Using Off-Resonant Laser Induced Fluorescence,” Phys. Fluids 25, 1105 (1982).
[CrossRef]

Muller, U.

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181 (1981).
[CrossRef]

Naparstek, A.

G. T. Herman, A. Naparstek, “Fast Image Reconstruction Based on a Radon Inversion for Applications for Rapidly Collected Data,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 33, 511 (1978).
[CrossRef]

G. T. Herman, A. V. Lakshminarayanan, A. Naparstek, “Convolution Reconstruction Techniques for Divergent Beams,” Comput. Biol. Med. 6, 259 (1976).
[CrossRef] [PubMed]

Oertel, H.

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181 (1981).
[CrossRef]

H. Oertel, K. Buhler, “A Special Differential Interferometer Used for Heat Convection Applications,” Int. J. Heat Mass Transfer 21, 1111 (1978).
[CrossRef]

Ramachandran, G. N.

G. N. Ramachandran, A. V. Lakshminarayanan, “Three Dimensional Reconstructions from Radiographs and Electron Micrographs: Application of Convolution Instead of Fourier Transforms,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236 (1971).
[CrossRef] [PubMed]

Riddle, A. C.

R. N. Bracewell, A. C. Riddle, “Inversion of Fan Beam Scans in Radio Astronomy,” Astrophys. J. 150, 427 (1967).
[CrossRef]

Riederer, S. J.

D. A. Chesler, S. J. Riederer, “Ripple Suppression During Reconstruction in Transverse Tomography,” Phys. Med. Biol. 20, 632 (1975).
[CrossRef] [PubMed]

Santoro, R. J.

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Gouiard, “Optical Tomography for Flow Field Diagnostics,” Int. J. Heat Mass Transfer 24, 1139 (1981).
[CrossRef]

Schulz, R. A.

P. M. Joseph, R. A. Schulz, “View Sampling Requirements in Fan Beam Computed Tomography,” Med. Phys. 7, 692 (1980).
[CrossRef] [PubMed]

Semerjian, H. G.

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Gouiard, “Optical Tomography for Flow Field Diagnostics,” Int. J. Heat Mass Transfer 24, 1139 (1981).
[CrossRef]

Sgulim, S.

Shepp, L. A.

R. L. Byer, L. A. Shepp, “Two-Dimensional Remote Air-Pollution Monitoring Via Tomography,” Opt. Lett. 4, 75, (1979).
[CrossRef] [PubMed]

L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21 (1974).

Stuck, B. W.

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging, Vols. 1 and 2 (Academic, New York, 1980).

Talbert, A. J.

R. A. Brooks, G. H. Glover, A. J. Talbert, R. L. Eisner, F. A. DiBianca, “A Source of Streaks in Computed Tomograms,” J. Comput. Assist. Tomogr. 3, 511 (1979).
[CrossRef] [PubMed]

R. A. Brooks, G. H. Weiss, A. J. Talbert, “A New Approach to Interpolation in Computed Tomography,” J. Comput. Assist. Tomogr. 2, 577 (1978).
[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 (1978).
[CrossRef] [PubMed]

Willms, I.

I. Willms, “A Measurement Procedure for Acquisition of Spatial Inhomogeneous Aerosol Concentrations,” Aerosols in Science, Medicine and Technology, 9 Conference 1981, Gesellschaft fur Aerosolforschung, Schmallenberg.

Wolf, E.

E. Wolf, “Determination of Scattered Fields by Holography,” J. Opt. Soc. Am. 60, 18 (1970).
[CrossRef]

E. Wolf, “Three Dimensional Structure Determination of Semi-Transparent Objects from Holographic Data,” Opt. Commun. 1, 153 (1969).
[CrossRef]

Wolfe, D. C.

Zierep, J.

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181 (1981).
[CrossRef]

Acta Mech. (1)

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181 (1981).
[CrossRef]

Appl. Opt. (3)

Astrophys. J. (1)

R. N. Bracewell, A. C. Riddle, “Inversion of Fan Beam Scans in Radio Astronomy,” Astrophys. J. 150, 427 (1967).
[CrossRef]

Comput. Biol. Med. (1)

G. T. Herman, A. V. Lakshminarayanan, A. Naparstek, “Convolution Reconstruction Techniques for Divergent Beams,” Comput. Biol. Med. 6, 259 (1976).
[CrossRef] [PubMed]

IEEE Trans. Nucl. Sci. (1)

L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21 (1974).

Int. J. Heat Mass Transfer (2)

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Gouiard, “Optical Tomography for Flow Field Diagnostics,” Int. J. Heat Mass Transfer 24, 1139 (1981).
[CrossRef]

H. Oertel, K. Buhler, “A Special Differential Interferometer Used for Heat Convection Applications,” Int. J. Heat Mass Transfer 21, 1111 (1978).
[CrossRef]

J. Comput. Assist. Tomogr. (4)

R. A. Brooks, G. H. Glover, A. J. Talbert, R. L. Eisner, F. A. DiBianca, “A Source of Streaks in Computed Tomograms,” J. Comput. Assist. Tomogr. 3, 511 (1979).
[CrossRef] [PubMed]

R. A. Brooks, G. H. Weiss, A. J. Talbert, “A New Approach to Interpolation in Computed Tomography,” J. Comput. Assist. Tomogr. 2, 577 (1978).
[CrossRef] [PubMed]

A. M. Cormack, “Early 2-D Reconstruction (CT Scanning) and Recent Topics Stemming from It, Nobel Lecture 1979,” J. Comput. Assist. Tomogr. 4, 658 (1980).
[CrossRef] [PubMed]

G. N. Hounsfield, “Computed Medical Imaging, Nobel Lecture 1979,” J. Comput. Assist. Tomogr. 4, 665 (1980).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

Med. Phys. (1)

P. M. Joseph, R. A. Schulz, “View Sampling Requirements in Fan Beam Computed Tomography,” Med. Phys. 7, 692 (1980).
[CrossRef] [PubMed]

Opt. Commun. (1)

E. Wolf, “Three Dimensional Structure Determination of Semi-Transparent Objects from Holographic Data,” Opt. Commun. 1, 153 (1969).
[CrossRef]

Opt. Eng. (1)

D. R. Crosley, “Collisional Effects on Laser Induced Fluorescence Flame Measurements,” Opt. Eng. 20, 511 (1981).
[CrossRef]

Opt. Lett. (4)

Phys. Fluids (1)

J. C. McDaniel, D. Baganoff, R. L. Byer, “Density Measurements in Compressible Flows Using Off-Resonant Laser Induced Fluorescence,” Phys. Fluids 25, 1105 (1982).
[CrossRef]

Phys. Med. Biol. (1)

D. A. Chesler, S. J. Riederer, “Ripple Suppression During Reconstruction in Transverse Tomography,” Phys. Med. Biol. 20, 632 (1975).
[CrossRef] [PubMed]

Proc. IEEE (1)

Special issue on Computerized Tomography, Proc. IEEE 71 (Mar.1983).

Proc. Natl. Acad. Sci. U.S.A. (1)

G. N. Ramachandran, A. V. Lakshminarayanan, “Three Dimensional Reconstructions from Radiographs and Electron Micrographs: Application of Convolution Instead of Fourier Transforms,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236 (1971).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. (1)

M. V. Berry, D. F. Gibbs, “The Interpretation of Optical Projections,” Proc. R. Soc. London Ser. A314, 143 (1970).
[CrossRef]

SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. (1)

G. T. Herman, A. Naparstek, “Fast Image Reconstruction Based on a Radon Inversion for Applications for Rapidly Collected Data,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 33, 511 (1978).
[CrossRef]

Other (6)

I. Willms, “A Measurement Procedure for Acquisition of Spatial Inhomogeneous Aerosol Concentrations,” Aerosols in Science, Medicine and Technology, 9 Conference 1981, Gesellschaft fur Aerosolforschung, Schmallenberg.

Ref. 4, p. 163ff.

K. Bennett, R. L. Byer, “Fan Beam Tomography Noise Theory,” J. Opt. Soc. Am. A, submitted.

M. Francon, Laser Speckle and Applications (Academic, New York, 1979), Chap. 2.

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

H. H. Barrett, W. Swindell, Radiological Imaging, Vols. 1 and 2 (Academic, New York, 1980).

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Figures (12)

Fig. 1
Fig. 1

Fan beam tomography geometry. For each fan source position, the line integral of the absorption along the rays from the source to the detectors is measured. The detectors and fan sources are uniformly spaced along the perimeter of the fan source circle.

Fig. 2
Fig. 2

Fan Beam Geometry. S j is the jth position of M equally spaced source positions along the perimeter of the fan source circle of radius ρ; β j is the angle of S j from the y axis. The 2N + 1 detectors rotate about the origin O to maintain their positions relative to the source; L ˜ is the distance from the source to the reconstructed point P(x,y) with polar coordinates ( r ˜ ,ϕ); and γ0 is the angle of the ray in a fan with source at S j which goes through P. γ is the angle of the ray to detector n′; γ and γ0 are measured relative to the ray from S j to O.

Fig. 3
Fig. 3

Fan beam tomography reconstruction showing aliasing from noiseless simulated projections of a disk object. The vertical scale is linear. The reconstructed image is 0.73 of the fan source circle radius using 180 fan source positions with 90 detectors around the full circle.

Fig. 4
Fig. 4

Schematic diagram of tomography apparatus. Argon-ion laser light is guided by an optical fiber to the tomography chamber containing the iodine source and detectors. A computer controls the data acquisition electronics and reconstructs the image.

Fig. 5
Fig. 5

Cutaway view of the fan beam geometry optical tomography chamber. The rotating mirror scans the laser spot around the Lambertian scattering screen. The screen and detectors are on the perimeter of a 28-cm radius circle. Iodine vapor absorbs light creating the test object.

Fig. 6
Fig. 6

Two-dimensional image of the 9.0-cm diam iodine vapor cloud at a vapor density of 0.6 Torr. The vertical scale is linear with a peak absorption of 0.036 cm−1 which is a factor of 125 greater than the statistical noise level of the reconstructed image. Ridges near the edge of the figure are reconstruction artifacts similar to those in Fig. 3.

Fig. 7
Fig. 7

(a) Image of 2.5-cm diam iodine vapor vortex reconstructed with unsmoothed RL kernel. The spatial resolution is limited by the detector spacing to ~1 cm. The reconstruction is centered 13.8 cm from the origin of the fan source circle. (b) Same as (a) but reconstructed with kernel convolved with a triangle filter of width d = 2 reducing the spatial resolution by a factor of 2. Note the loss of detail. (c) Same as (b) but with d = 4.

Fig. 8
Fig. 8

(a) Image of low absorption iodine vapor cloud reconstructed with unmodified RL kernel. The iodine partial pressure is 0.06 Torr and the peak absorption coefficient is 0.007 cm−1. (b) Same as (a) but reconstructed with RL kernel convolved with a triangle filter of width d = 2. (c) Same as (b) but with d = 4. Note the dramatic reduction in noise and reconstruction artifacts.

Fig. 9
Fig. 9

Measured and predicted rms noise amplitudes for twelve independent null tomographic images. A null tomogram does not have the iodine absorber present and thus ideally has unity transmission across the image.

Fig. 10
Fig. 10

Dependence of the rms noise amplitude in the reconstructed image on the normalized distance r of the point from the center of the fan source circle. The solid line is the parameterless prediction of Eq. (9), including the correlations of the projection data noise. The dots are measured noise amplitude values.

Fig. 11
Fig. 11

Dependence of the rms noise amplitude on the number of fan source positions. The solid lines are least-squares fits to the measured points. The mean slope of the lines is 0.507 with a standard deviation of 0.016. The lines AD correspond to different data sets with fans omitted to generate data sets with fewer fans.

Fig. 12
Fig. 12

Root-mean-square noise amplitude vs spatial resolution. The points are the rms noise in tomograms reconstructed using the RL kernel convolved with triangle filters of different widths d. The same projection data taken without iodine vapor present are used for all the reconstructions. The solid curve is the theoretical projection data. The dashed curve is the theoretical prediction of Eq. (9) assuming that the projection data are uncorrelated.

Equations (12)

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μ ( r ) = j = 1 M ρ L ˜ 2 n = - N N k [ ( n - n ) a ] h j ( n ) cos ( n a ) ,
n a = γ 0 = arctan [ r ˜ cos ( β j - ϕ ) ρ + r ˜ sin ( β j - ϕ ) ] .
k ( n a ) = { π 4 M a n = 0 , - a π M sin 2 ( n a ) n = ± 1 , ± 3 , 0 n = ± 2 , ± 4 , .
R = M ρ M + 4 π ν M ρ ,
ν M = M 4 π ( 1 R - 1 ρ ) .
e j ( n ) e j ( n ) = σ p 2 f ( n - n ) δ j , j ,
s ( n ) = { d - n d 2 n d , 0 n > d
k ¯ ( n a ) = n = - N , N k ( n a ) s ( n - n )
σ ˜ 2 ( r ) = M ρ 2 σ p 2 ( 1 + ½ r 2 ) ( 1 - r 2 ) 3 t = 0 N f ( t ) × n = - R { s } ( t - n ) R ¯ { k } ( n ) ,             [ r < 1 ]
R ¯ { k } ( t ) = R { k } ( t ) + R { k } ( t - 1 ) + R { k } ( t + 1 ) ,
R { k } ( 0 ) = π 2 12 M 2 a 2 , R { k } ( t ) = ( - 1 ) t 2 M 2 t 2 a 2 ,             t = ± 1 , ± 2 , .
δ min = σ ˜ ρ a d σ p 0.5 M d ,             d > 1.

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