Abstract

A scheme is derived for deducing the Legendre moments of the optical scattering function of a homogeneous, optically thick planar medium. The radiometer need only scan the backscattered light intensity over the azimuthal angle, for a fixed polar angle, at times long after irradiation of the scattering volume by a laser pulse.

© 1982 Optical Society of America

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  1. E. D. Hinkley, ed., Laser Monitoring of the Atmosphere (Springer-Verlag, Berlin, 1976).
  2. S. Svanberg, "Lasers as probes for air and sea," Contemp. Phys. 21, 541–576 (1980).
  3. C. E. Siewert, "On the inverse problem for a three-term phase function," J. Quant. Spectrosc. Radiat. Transfer 22, 441–446 (1979).
  4. W. L. Dunn and J. R. Maiorino, "On the numerical characteristics of an inverse solution for three-term radiative transfer," J. Quant. Spectrosc. Radiat. Transfer 24, 203–209 (1980).
  5. N. J. McCormick, "Transport scattering coefficients from reflection and transmission measurements," J. Math. Phys. 20, 1504–1507 (1979).
  6. N. J. McCormick and R. Sanchez, "Inverse problem transport calculations for anisotropic scattering coefficients," J. Math. Phys. 22, 199–208 (1981).
  7. R. Sanchez and N. J. McCormick, "General solutions to inverse transport problems," J. Math. Phys. 22, 847–855 (1981).
  8. S. Ito and K. Furutsu, "Theory of light pulse propagation through thick clouds," J. Opt. Soc. Am. 70, 366–374 (1981).
  9. R. T. H. Collis and P. B. Russell, "Lidar measurement of particles and gases by elastic backscattering and differential absorption," Ref. 1, pp. 71–151.
  10. S. Chandrasekhar, Radiative Transfer (Oxford U. Press, Oxford, England, 1950; reprinted by Dover Publications).
  11. K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Pa., 1967).
  12. I. Kuščer and P. F. Zweifel, "Time-dependent one-speed albedo problem for a semi-infinite medium," J. Math. Phys. 6,1125–1130 (1965).
  13. P. F. Zweifel, Reactor Physics (McGraw-Hill, New York, 1973).
  14. J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).
  15. I. Kuščer and N. J. McCormick, "Reciprocity in time-dependent neutron transport theory," Nucl. Sci. Eng. 26, 522–529 (1966).
  16. The equation follows directly from Eq. (26) of Ref. 15, except the optical thickness of the target for the validity of diffusion theory has been taken to be X; for the azimuthally symmetric (m = 0) analysis, however, a better approximation is to replace X with X + 4.2D°/ ν to account for two optical extrapolation distances.
  17. E. Jahnke, F. Emde, and F. Lösch, Tables of Higher Functions (Teubher; Stuttgart, 1960).
  18. For small values of X/D°, especially when the scattering is strongly anisotropic, the results of Ito and Furutsu become suspect because their distributed source arising from first collisions [Ref. 8, Eq. (13)] is assumed to be isotropic.

1981 (3)

N. J. McCormick and R. Sanchez, "Inverse problem transport calculations for anisotropic scattering coefficients," J. Math. Phys. 22, 199–208 (1981).

R. Sanchez and N. J. McCormick, "General solutions to inverse transport problems," J. Math. Phys. 22, 847–855 (1981).

S. Ito and K. Furutsu, "Theory of light pulse propagation through thick clouds," J. Opt. Soc. Am. 70, 366–374 (1981).

1980 (2)

S. Svanberg, "Lasers as probes for air and sea," Contemp. Phys. 21, 541–576 (1980).

W. L. Dunn and J. R. Maiorino, "On the numerical characteristics of an inverse solution for three-term radiative transfer," J. Quant. Spectrosc. Radiat. Transfer 24, 203–209 (1980).

1979 (2)

N. J. McCormick, "Transport scattering coefficients from reflection and transmission measurements," J. Math. Phys. 20, 1504–1507 (1979).

C. E. Siewert, "On the inverse problem for a three-term phase function," J. Quant. Spectrosc. Radiat. Transfer 22, 441–446 (1979).

1966 (1)

I. Kuščer and N. J. McCormick, "Reciprocity in time-dependent neutron transport theory," Nucl. Sci. Eng. 26, 522–529 (1966).

1965 (1)

I. Kuščer and P. F. Zweifel, "Time-dependent one-speed albedo problem for a semi-infinite medium," J. Math. Phys. 6,1125–1130 (1965).

Case, K. M.

K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Pa., 1967).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford U. Press, Oxford, England, 1950; reprinted by Dover Publications).

Collis, R. T. H.

R. T. H. Collis and P. B. Russell, "Lidar measurement of particles and gases by elastic backscattering and differential absorption," Ref. 1, pp. 71–151.

Duderstadt, J. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Dunn, W. L.

W. L. Dunn and J. R. Maiorino, "On the numerical characteristics of an inverse solution for three-term radiative transfer," J. Quant. Spectrosc. Radiat. Transfer 24, 203–209 (1980).

Emde, F.

E. Jahnke, F. Emde, and F. Lösch, Tables of Higher Functions (Teubher; Stuttgart, 1960).

Furutsu, K.

Hamilton, L. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Ito, S.

Jahnke, E.

E. Jahnke, F. Emde, and F. Lösch, Tables of Higher Functions (Teubher; Stuttgart, 1960).

Kušcer, I.

I. Kuščer and N. J. McCormick, "Reciprocity in time-dependent neutron transport theory," Nucl. Sci. Eng. 26, 522–529 (1966).

I. Kuščer and P. F. Zweifel, "Time-dependent one-speed albedo problem for a semi-infinite medium," J. Math. Phys. 6,1125–1130 (1965).

Lösch, F.

E. Jahnke, F. Emde, and F. Lösch, Tables of Higher Functions (Teubher; Stuttgart, 1960).

Maiorino, J. R.

W. L. Dunn and J. R. Maiorino, "On the numerical characteristics of an inverse solution for three-term radiative transfer," J. Quant. Spectrosc. Radiat. Transfer 24, 203–209 (1980).

McCormick, N. J.

R. Sanchez and N. J. McCormick, "General solutions to inverse transport problems," J. Math. Phys. 22, 847–855 (1981).

N. J. McCormick and R. Sanchez, "Inverse problem transport calculations for anisotropic scattering coefficients," J. Math. Phys. 22, 199–208 (1981).

N. J. McCormick, "Transport scattering coefficients from reflection and transmission measurements," J. Math. Phys. 20, 1504–1507 (1979).

I. Kuščer and N. J. McCormick, "Reciprocity in time-dependent neutron transport theory," Nucl. Sci. Eng. 26, 522–529 (1966).

Russell, P. B.

R. T. H. Collis and P. B. Russell, "Lidar measurement of particles and gases by elastic backscattering and differential absorption," Ref. 1, pp. 71–151.

Sanchez, R.

N. J. McCormick and R. Sanchez, "Inverse problem transport calculations for anisotropic scattering coefficients," J. Math. Phys. 22, 199–208 (1981).

R. Sanchez and N. J. McCormick, "General solutions to inverse transport problems," J. Math. Phys. 22, 847–855 (1981).

Siewert, C. E.

C. E. Siewert, "On the inverse problem for a three-term phase function," J. Quant. Spectrosc. Radiat. Transfer 22, 441–446 (1979).

Svanberg, S.

S. Svanberg, "Lasers as probes for air and sea," Contemp. Phys. 21, 541–576 (1980).

Zweifel, P. F.

I. Kuščer and P. F. Zweifel, "Time-dependent one-speed albedo problem for a semi-infinite medium," J. Math. Phys. 6,1125–1130 (1965).

K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Pa., 1967).

P. F. Zweifel, Reactor Physics (McGraw-Hill, New York, 1973).

Contemp. Phys. (1)

S. Svanberg, "Lasers as probes for air and sea," Contemp. Phys. 21, 541–576 (1980).

J. Math. Phys. (4)

I. Kuščer and P. F. Zweifel, "Time-dependent one-speed albedo problem for a semi-infinite medium," J. Math. Phys. 6,1125–1130 (1965).

N. J. McCormick, "Transport scattering coefficients from reflection and transmission measurements," J. Math. Phys. 20, 1504–1507 (1979).

N. J. McCormick and R. Sanchez, "Inverse problem transport calculations for anisotropic scattering coefficients," J. Math. Phys. 22, 199–208 (1981).

R. Sanchez and N. J. McCormick, "General solutions to inverse transport problems," J. Math. Phys. 22, 847–855 (1981).

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transfer (2)

C. E. Siewert, "On the inverse problem for a three-term phase function," J. Quant. Spectrosc. Radiat. Transfer 22, 441–446 (1979).

W. L. Dunn and J. R. Maiorino, "On the numerical characteristics of an inverse solution for three-term radiative transfer," J. Quant. Spectrosc. Radiat. Transfer 24, 203–209 (1980).

Nucl. Sci. Eng. (1)

I. Kuščer and N. J. McCormick, "Reciprocity in time-dependent neutron transport theory," Nucl. Sci. Eng. 26, 522–529 (1966).

Other (9)

The equation follows directly from Eq. (26) of Ref. 15, except the optical thickness of the target for the validity of diffusion theory has been taken to be X; for the azimuthally symmetric (m = 0) analysis, however, a better approximation is to replace X with X + 4.2D°/ ν to account for two optical extrapolation distances.

E. Jahnke, F. Emde, and F. Lösch, Tables of Higher Functions (Teubher; Stuttgart, 1960).

For small values of X/D°, especially when the scattering is strongly anisotropic, the results of Ito and Furutsu become suspect because their distributed source arising from first collisions [Ref. 8, Eq. (13)] is assumed to be isotropic.

E. D. Hinkley, ed., Laser Monitoring of the Atmosphere (Springer-Verlag, Berlin, 1976).

P. F. Zweifel, Reactor Physics (McGraw-Hill, New York, 1973).

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

R. T. H. Collis and P. B. Russell, "Lidar measurement of particles and gases by elastic backscattering and differential absorption," Ref. 1, pp. 71–151.

S. Chandrasekhar, Radiative Transfer (Oxford U. Press, Oxford, England, 1950; reprinted by Dover Publications).

K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Pa., 1967).

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