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Applied Optics

Applied Optics


  • Vol. 25, Iss. 19 — Oct. 1, 1986
  • pp: 3508–3515

Two- and three-dimensional radiative transfer in the diffusion approximation

Andrew Zardecki, Siegfried A. W. Gersti, and Robert E. DeKinder, Jr.  »View Author Affiliations

Applied Optics, Vol. 25, Issue 19, pp. 3508-3515 (1986)

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A 3-D transport code DIF3D, based on the diffusion approximation, is used to model the spatial distribution of radiant energy arising from volumetric isotropic sources. The limits of validity of the diffusion approximation are formulated quantitatively by comparing the results, in the case of a slab geometry, of the diffusion and transport theories. For 3-D geometry, the results are presented in the form of isosurface plots, which give the surfaces of constant energy density. It is shown that as the detector sensitivity decreases, individual sources cannot be spatially distinguished, thus leading to a discrimination problem. Applications of the diffusion approximation to imaging through a medium with isotropic scattering are described. For a periodic distribution of line sources, the image is considerably degraded if the optical depth of the scattering medium is 0.4 or larger.

© 1986 Optical Society of America

Original Manuscript: May 29, 1986
Published: October 1, 1986

Andrew Zardecki, Siegfried A. W. Gersti, and Robert E. DeKinder, "Two- and three-dimensional radiative transfer in the diffusion approximation," Appl. Opt. 25, 3508-3515 (1986)

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  1. J. J. Duderstadt, W. R. Martin, Transport Theory (Wiley, New York, 1979).
  2. A. Zardecki, S. A. W. Gerstl, J. F. Embury, “Application of the 2-D Discrete-Ordinates Method to Multiple Scattering of Laser Radiation,” Appl. Opt. 22, 1346 (1983). [CrossRef] [PubMed]
  3. R. L. Fante, “Propagation of Electromagnetic Waves Through Turbulent Plasma Using Transport Theory,” IEEE Trans. Antennas Propag. AP-21, 750 (1973). [CrossRef]
  4. W. G. Tam, A. Zardecki, “Laser Beam Propagation in Particulate Media,” J. Opt. Soc. Am. 69, 68 (1979). [CrossRef]
  5. W. G. Tam, A. Zardecki, “Multiple Scattering Corrections to the Beer-Lambert Law. 1: Open Detector,” Appl. Opt. 21, 2405 (1982). [CrossRef] [PubMed]
  6. A. Zardecki, W. G. Tam, “Multiple Scattering Corrections to the Beer-Lambert Law. 2: Detector with a Variable Field of View,” Appl. Opt. 21, 2413 (1982). [CrossRef] [PubMed]
  7. A. Zardecki, A. Deepak, “Forward Multiple Scattering Corrections as a Function of the Detector Field of View,” Appl. Opt. 22, 2970 (1983). [CrossRef] [PubMed]
  8. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  9. A. Ishimaru, “Diffusion of a Pulse in Densely Distributed Scatterers,” J. Opt. Soc. Am. 68, 1045 (1978). [CrossRef]
  10. K. Furutsu, “Diffusion Equation Derived from Space-Time Transport Equation,” J. Opt. Soc. Am. 70, 360 (1980). [CrossRef]
  11. W. G. Tam, A. Zardecki, “Off-Axis Propagation of a Laser Beam in Low Visibility Weather Conditions,” Appl. Opt. 19, 2822 (1980). [CrossRef] [PubMed]
  12. A. Ishimaru, Y. Kuga, R. L.-T.- Cheung, K. Shimizu, “Scattering and Diffusion of a Beam Wave in Randomly Distributed Scatterers,” J. Opt. Soc. Am. 73, 131 (1983). [CrossRef]
  13. B. Friedman, Principles and Techniques of Applied Mathematics (Wiley, New York, 1956).
  14. S. A. W. Gerstl, A. Zardecki, “Discrete-Ordinates Finite-Element Method for Atmospheric Radiative Transfer and Remote Sensing,” Appl. Opt. 24, 81 (1985). [CrossRef] [PubMed]
  15. K. L. Derstine, “DIF3D: A Code to Solve One-, Two-, and Three-Dimensional Finite-Difference Diffusion Theory Problems,” Argonne National Laboratory Report ANL-82–64 (Apr.1984).
  16. K. D. Lathrop, “Remedies for Ray Effects,” Nucl. Sci. Eng. 45, 255 (1971).
  17. R. E. Hufnagel, N. R. Stanley, “Modulation Transfer Function Associated with Image Transmission through Turbulent Media,” J. Opt. Soc. Am. 54, 52 (1964). [CrossRef]
  18. A. Ishimaru, “Limitation on Image Resolution Imposed by a Random Medium,” Appl. Opt. 17, 348 (1978). [CrossRef] [PubMed]
  19. Y. Kuga, A. Ishimaru, “Modulation Transfer Function and Image Transmission through Randomly Distributed Spherical Particles,” J. Opt. Soc. Am. A 2, 2330 (1985). [CrossRef]
  20. N. S. Kopeika, “Spatial-Frequency Dependence of Scattered Background Light: The Atmospheric Modulation Transfer Function Resulting from Aerosols,” J. Opt. Soc. Am. 72, 548 (1982). [CrossRef]
  21. N. S. Kopeika, “Spatial Frequency and Wavelength-Dependent Effects of Aerosols on the Atmospheric Modulation Transfer Function,” J. Opt. Soc. Am. 72, 1092 (1982). [CrossRef]
  22. A. Zardecki, S. A. W. Gerstl, J. F. Embury, “Multiple Scattering Effects in Spatial Frequency Filtering,” Appl. Opt. 23, 4124 (1984). [CrossRef] [PubMed]
  23. W. G. Tam, A. Zardecki, “Spatial Frequency Dependent Image Degradation in a Particulate Medium,” Int. J. Infrared Millimeter Waves 6, 249 (1985). [CrossRef]
  24. K. R. Barnes, The Optical Transfer Function (American-Elsevier, New York, 1972).

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