Abstract

Results of computations of the intensity, degree of polarization, and the direction of polarization of the radiation transmitted after one, two, and three scatterings according to Rayleigh’s law, are presented for the case of a plane-parallel, homogeneous atmosphere of finite optical thickness. They clearly show that the inclusion of the first three orders of scattering is essential even when the normal scattering optical thickness of the atmosphere is of the order of 0.2. For still higher optical thicknesses, the present step-by-step treatment is not satisfactory, as it is necessary to include several higher orders of scattering. The anisotropic nature of the scattering air molecules should also be taken into account for obtaining reliable theoretical results, especially when the optical thickness is small.

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  1. S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, England, 1950), 1st ed.
  2. S. Chandrasekhar and D. Elbert, Nature 167, 51 (1951).
  3. S. Chandrasekhar and D. Elbert, Trans. Am. Phil. Soc. New Ser. 44, Part 6 (1954).
  4. Z. Sekera, "Investigation of Polarization of Skylight," Reports for Contract No. AF 19(122)-239. Nine technical reports and one final report (1952–1955).
  5. Z. Sekera and E. V. Ashburn, NAVORD Report 2061, U. S. Naval Ordnance Test Station, Inyokern, California (1953).
  6. K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley and Los Angeles, 1960).
  7. A. Hammad and S. Chapman, Phil. Mag. Ser. 7, 28, 99 (1939).
  8. A. Hammad, Astrophys. J. 108, 338 (1948).
  9. A. Hammad, J. Opt. Soc. Am. 43, 184 (1953).
  10. J. Lenoble, Ann. Géophys. 10, 117 (1954).
  11. K. Sekihara, Papers Meteorol. Geophys. (Tokyo) 6, 150 (1955).
  12. G. F. Walton, Phil. Mag. Ser. 7, 46, 281 (1955).
  13. A minus sign before µ0 represents the down coming radiation.
  14. T. W. Mullikin, Memorandum RM–3027–PR, The Rand Corporation, Santa Monica, California.
  15. J. L. Soret, Arch. Sci. Phys. Nat. 20, 429 (1888).
  16. P. Furukawa and Z. Sekera (unpublished results, private communication).
  17. Professor Hammad informs the author that his values for the degree of polarization around the neutral points were obtained from a smoothed-out curve.
  18. J. V. Dave, "On the Physical Meaning of the Successive Iteration of Auxiliary Equations in Radiative Transfer," Astrophys. J. (to be published).
  19. Z. Sekera, Report No. R-413–PR, The Rand Corporation, Santa Monica, California.
  20. Hammad and Chapman (Ref. 7) have expressed these functions in terms of exponential integrals.
  21. K. Sekihara, Papers Meteorol. Geoplhys. (Tokyo) 2, 158 (1951).
  22. H. C. Van de Hulst, Astrophys. J. 107, 220 (1948).
  23. S. Chandrasekhar and F. H. Breen, Astrophys. J. 108, 92 (1948).

Ashburn, E. V.

Z. Sekera and E. V. Ashburn, NAVORD Report 2061, U. S. Naval Ordnance Test Station, Inyokern, California (1953).

Breen, F. H.

S. Chandrasekhar and F. H. Breen, Astrophys. J. 108, 92 (1948).

Chandrasekhar, S.

S. Chandrasekhar and F. H. Breen, Astrophys. J. 108, 92 (1948).

S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, England, 1950), 1st ed.

S. Chandrasekhar and D. Elbert, Trans. Am. Phil. Soc. New Ser. 44, Part 6 (1954).

S. Chandrasekhar and D. Elbert, Nature 167, 51 (1951).

Chapman, S.

A. Hammad and S. Chapman, Phil. Mag. Ser. 7, 28, 99 (1939).

Coulson, K. L.

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley and Los Angeles, 1960).

Dave, J. V.

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley and Los Angeles, 1960).

J. V. Dave, "On the Physical Meaning of the Successive Iteration of Auxiliary Equations in Radiative Transfer," Astrophys. J. (to be published).

Elbert, D.

S. Chandrasekhar and D. Elbert, Nature 167, 51 (1951).

S. Chandrasekhar and D. Elbert, Trans. Am. Phil. Soc. New Ser. 44, Part 6 (1954).

Furukawa, P.

P. Furukawa and Z. Sekera (unpublished results, private communication).

Hammad, A.

A. Hammad, J. Opt. Soc. Am. 43, 184 (1953).

A. Hammad and S. Chapman, Phil. Mag. Ser. 7, 28, 99 (1939).

A. Hammad, Astrophys. J. 108, 338 (1948).

Lenoble, J.

J. Lenoble, Ann. Géophys. 10, 117 (1954).

Mullikin, T. W.

T. W. Mullikin, Memorandum RM–3027–PR, The Rand Corporation, Santa Monica, California.

Sekera, Z.

Z. Sekera, Report No. R-413–PR, The Rand Corporation, Santa Monica, California.

Z. Sekera, "Investigation of Polarization of Skylight," Reports for Contract No. AF 19(122)-239. Nine technical reports and one final report (1952–1955).

Z. Sekera and E. V. Ashburn, NAVORD Report 2061, U. S. Naval Ordnance Test Station, Inyokern, California (1953).

P. Furukawa and Z. Sekera (unpublished results, private communication).

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley and Los Angeles, 1960).

Sekihara, K.

K. Sekihara, Papers Meteorol. Geophys. (Tokyo) 6, 150 (1955).

K. Sekihara, Papers Meteorol. Geoplhys. (Tokyo) 2, 158 (1951).

Soret, J. L.

J. L. Soret, Arch. Sci. Phys. Nat. 20, 429 (1888).

Van de Hulst, H. C.

H. C. Van de Hulst, Astrophys. J. 107, 220 (1948).

Walton, G. F.

G. F. Walton, Phil. Mag. Ser. 7, 46, 281 (1955).

Other (23)

S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, England, 1950), 1st ed.

S. Chandrasekhar and D. Elbert, Nature 167, 51 (1951).

S. Chandrasekhar and D. Elbert, Trans. Am. Phil. Soc. New Ser. 44, Part 6 (1954).

Z. Sekera, "Investigation of Polarization of Skylight," Reports for Contract No. AF 19(122)-239. Nine technical reports and one final report (1952–1955).

Z. Sekera and E. V. Ashburn, NAVORD Report 2061, U. S. Naval Ordnance Test Station, Inyokern, California (1953).

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley and Los Angeles, 1960).

A. Hammad and S. Chapman, Phil. Mag. Ser. 7, 28, 99 (1939).

A. Hammad, Astrophys. J. 108, 338 (1948).

A. Hammad, J. Opt. Soc. Am. 43, 184 (1953).

J. Lenoble, Ann. Géophys. 10, 117 (1954).

K. Sekihara, Papers Meteorol. Geophys. (Tokyo) 6, 150 (1955).

G. F. Walton, Phil. Mag. Ser. 7, 46, 281 (1955).

A minus sign before µ0 represents the down coming radiation.

T. W. Mullikin, Memorandum RM–3027–PR, The Rand Corporation, Santa Monica, California.

J. L. Soret, Arch. Sci. Phys. Nat. 20, 429 (1888).

P. Furukawa and Z. Sekera (unpublished results, private communication).

Professor Hammad informs the author that his values for the degree of polarization around the neutral points were obtained from a smoothed-out curve.

J. V. Dave, "On the Physical Meaning of the Successive Iteration of Auxiliary Equations in Radiative Transfer," Astrophys. J. (to be published).

Z. Sekera, Report No. R-413–PR, The Rand Corporation, Santa Monica, California.

Hammad and Chapman (Ref. 7) have expressed these functions in terms of exponential integrals.

K. Sekihara, Papers Meteorol. Geoplhys. (Tokyo) 2, 158 (1951).

H. C. Van de Hulst, Astrophys. J. 107, 220 (1948).

S. Chandrasekhar and F. H. Breen, Astrophys. J. 108, 92 (1948).

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