Abstract

Measurements of the reflecting and polarizing properties of various soils, sands, and vegetation in the visible- and near-ir spectral regions show that dark surfaces polarize the reflected radiation strongly while highly reflecting surfaces have relatively weak polarizing properties. In general, the reflectance of mineral surfaces increases, and the degree of polarization of the reflected radiation decreases, with increasing wavelength and increasing angle of incidence. There is little or no indication of specular reflection from the surfaces for which measurements were made. Introduction of the reflection data into the equation of radiative transfer for clear and slightly turbid models of the earth’s atmosphere shows that the upward radiation that would be incident on a high-altitude aircraft or satellite would be dominated by surface-reflected radiation for the red and near-ir regions over highly reflecting surfaces such as deserts, whereas atmospheric scattering is most important for short wavelengths and dark surfaces. Because of polarization effects, atmospheric transmission of optical contrasts is better in one orthogonal intensity component than the other, the difference being sufficient to merit polarizing optics in reconnaissance instrumentation under certain conditions.

© 1966 Optical Society of America

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References

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  1. S. Fritz, Compendium of Meteorology (American Meteorological Society, Boston, 1951), p. 13.
  2. S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, 1950).
  3. K. L. Coulson, J. Plan. Space Sci. 1, 265 (1959).
    [CrossRef]
  4. R. S. Fraser, Z. Sekera, Appendix E, Final Report of Contr. AF 19(122)–239, Univ. of California, Los Angeles (1955).
  5. R. S. Fraser, Final Report, Contr. NAS5-3891, TRW Space Technology Laboratories, Redondo Beach, Calif. (1964).
  6. K. L. Coulson, E. L. Gray, G. M. Bouricius, Icarus 5, 139 (1966).
    [CrossRef]
  7. A. Dollfus, Ann. Astrophys. Suppl. Article 4 (1957).
  8. E. M. Feigelson, M. S. Malkevich, S. Ya. Kogan, T. D. Karonatova, K. S. Glazova, M. A. Kuznetsova, Calculation of the Brightness of Light (Consultants Bureau, New York, 1960).
  9. K. S. Shifrin, N. P. Pyatovskaya, Tr. Leningr. Glav. Geophys. Obs. 166, 3 (1964).
  10. Z. Sekera, J. V. Dave, Sci. Rept. 4, Contr. AF 19(604)–2429, Univ. of California, Los Angeles (1960).
  11. J. V. Dave, J. Atm. Sci. 22, 273 (1965).
    [CrossRef]
  12. R. S. Fraser, J. Opt. Soc. Am. 54,157, 289 (1964).
    [CrossRef]
  13. Cornell Aeronautical Laboratory, Report No. VF-1260-P-8, Contr. AF 33(616)–5870 (1961) (ASTIA No. AD 260694).
  14. E. L. Krinov, Spektralnaia otrazhatelnaia sposobnost prirodnykh obrazovanii (Academy of Sciences USSR, Moscow, 1947).
  15. K. Ya. Kondratiev, Z. F. Mironova, A. N. Otto, Pure Appl. Geophys. 59, 207 (1965).
    [CrossRef]
  16. D. M. Gates, W. Tantraporn, Science 115, 613 (1952).
    [CrossRef] [PubMed]
  17. D. M. Gates, H. G. Keegan, J. C. Schleter, V. R. Weidner, Appl. Opt. 4, 11 (1965).
    [CrossRef]
  18. L. F. Richardson, Quart. J. Roy. Met. Soc. 56, 31 (1930).
    [CrossRef]
  19. K. G. Bauer, J. A. Dutton, J. Geophys. Res. 67, 2367 (1962).
    [CrossRef]
  20. S. Fritz, Bull. Am. Met. Soc. 29, 303 (1948).
  21. K. J. Hanson, H. J. Viebrock, Mo. Wea. Rev. 92, 223 (1964).
    [CrossRef]
  22. J. N. Jaroslawzew, Izv. Akad. Nauk USSR, Ser. Geofiz. No. 1 (1952).
  23. K. Ya. Kondratiev, M. P. Manolova, Meteorol. Gidrol. No. 6, 31 (1955).
  24. M. A. Romanova, Air Survey of Sand Deposits by Spectral Luminance (Consultants Bureau, New York, 1964).
    [CrossRef]
  25. E. V. Ashburn, R. G. Weldon, J. Opt. Soc. Am. 46, 583 (1956).
    [CrossRef]
  26. K. L. Coulson, Sci. Rept. No. 2, Contr. AF 19(604)–1303, Univ. of California (1956).
  27. N. S. Orlova, Tr. Astron. Obs.16, Leningrad State Univ.166 (1952).
  28. B. Hapke, H. Van Horn, J. Geophys. Res. 68, 4545 (1963).
    [CrossRef]
  29. J. van Diggelen, Rech. Obs. (Utrecht) 14, 1 (1959).
  30. K. L. Coulson, G. M. Bouricius, E. L. Gray, J. Geophys. Res. 70, 4601 (1965).
    [CrossRef]
  31. D. Deirmendjian, Memo. RM-3228-PR, Rand Corp., Santa Monica, Calif. (1962).
  32. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).
  33. F. Exner, Met. Zeit. 37, No. 5 (1920).
  34. B. Lyot, Ann. Obs. (Paris), Sect. Meudon 8(1929).
  35. B. Lyot, A. Dollfus, Compt. Rend. 228, 1773 (1949).
  36. A. Cailleux, A. Dollfus, Compt. Rend. 230, 1411 (1950).
  37. B. Hapke, Rept. No. 169, Cornell Univ. Center for Radio-phys. and Space Res. (1964).
  38. D. L. Coffeen, Astron. J. 70, 403 (1965).
    [CrossRef]
  39. T. Gehrels, T. M. Teska, Appl. Opt. 2, 67 (1963).
    [CrossRef]
  40. H. A. Borthwick, U. S. Dept. Agriculture (private communication).
  41. K. L. Coulson, E. L. Gray, G. M. Bouricius, T. I. S. Rept. R65SD4, General Electric Co., Space Sciences Laboratory, Philadelphia, Pa.
  42. K. L. Coulson, G. M. Bouricius, E. L. Gray, Final Rept., Contr. NAS5-3925, General Electric Co., Space Sciences Laboratory, Philadelphia, Pa.
  43. K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley, 1960).
  44. R. S. Fraser, Sci. Rept. No. 2, Contr. AF 19(604)–2429, Univ. of California, Los Angeles (1959).

1966 (1)

K. L. Coulson, E. L. Gray, G. M. Bouricius, Icarus 5, 139 (1966).
[CrossRef]

1965 (5)

J. V. Dave, J. Atm. Sci. 22, 273 (1965).
[CrossRef]

K. Ya. Kondratiev, Z. F. Mironova, A. N. Otto, Pure Appl. Geophys. 59, 207 (1965).
[CrossRef]

K. L. Coulson, G. M. Bouricius, E. L. Gray, J. Geophys. Res. 70, 4601 (1965).
[CrossRef]

D. L. Coffeen, Astron. J. 70, 403 (1965).
[CrossRef]

D. M. Gates, H. G. Keegan, J. C. Schleter, V. R. Weidner, Appl. Opt. 4, 11 (1965).
[CrossRef]

1964 (3)

K. J. Hanson, H. J. Viebrock, Mo. Wea. Rev. 92, 223 (1964).
[CrossRef]

R. S. Fraser, J. Opt. Soc. Am. 54,157, 289 (1964).
[CrossRef]

K. S. Shifrin, N. P. Pyatovskaya, Tr. Leningr. Glav. Geophys. Obs. 166, 3 (1964).

1963 (2)

B. Hapke, H. Van Horn, J. Geophys. Res. 68, 4545 (1963).
[CrossRef]

T. Gehrels, T. M. Teska, Appl. Opt. 2, 67 (1963).
[CrossRef]

1962 (1)

K. G. Bauer, J. A. Dutton, J. Geophys. Res. 67, 2367 (1962).
[CrossRef]

1959 (2)

J. van Diggelen, Rech. Obs. (Utrecht) 14, 1 (1959).

K. L. Coulson, J. Plan. Space Sci. 1, 265 (1959).
[CrossRef]

1957 (1)

A. Dollfus, Ann. Astrophys. Suppl. Article 4 (1957).

1956 (1)

1955 (1)

K. Ya. Kondratiev, M. P. Manolova, Meteorol. Gidrol. No. 6, 31 (1955).

1952 (2)

J. N. Jaroslawzew, Izv. Akad. Nauk USSR, Ser. Geofiz. No. 1 (1952).

D. M. Gates, W. Tantraporn, Science 115, 613 (1952).
[CrossRef] [PubMed]

1950 (1)

A. Cailleux, A. Dollfus, Compt. Rend. 230, 1411 (1950).

1949 (1)

B. Lyot, A. Dollfus, Compt. Rend. 228, 1773 (1949).

1948 (1)

S. Fritz, Bull. Am. Met. Soc. 29, 303 (1948).

1930 (1)

L. F. Richardson, Quart. J. Roy. Met. Soc. 56, 31 (1930).
[CrossRef]

1929 (1)

B. Lyot, Ann. Obs. (Paris), Sect. Meudon 8(1929).

1920 (1)

F. Exner, Met. Zeit. 37, No. 5 (1920).

Ashburn, E. V.

Bauer, K. G.

K. G. Bauer, J. A. Dutton, J. Geophys. Res. 67, 2367 (1962).
[CrossRef]

Borthwick, H. A.

H. A. Borthwick, U. S. Dept. Agriculture (private communication).

Bouricius, G. M.

K. L. Coulson, E. L. Gray, G. M. Bouricius, Icarus 5, 139 (1966).
[CrossRef]

K. L. Coulson, G. M. Bouricius, E. L. Gray, J. Geophys. Res. 70, 4601 (1965).
[CrossRef]

K. L. Coulson, E. L. Gray, G. M. Bouricius, T. I. S. Rept. R65SD4, General Electric Co., Space Sciences Laboratory, Philadelphia, Pa.

K. L. Coulson, G. M. Bouricius, E. L. Gray, Final Rept., Contr. NAS5-3925, General Electric Co., Space Sciences Laboratory, Philadelphia, Pa.

Cailleux, A.

A. Cailleux, A. Dollfus, Compt. Rend. 230, 1411 (1950).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, 1950).

Coffeen, D. L.

D. L. Coffeen, Astron. J. 70, 403 (1965).
[CrossRef]

Coulson, K. L.

K. L. Coulson, E. L. Gray, G. M. Bouricius, Icarus 5, 139 (1966).
[CrossRef]

K. L. Coulson, G. M. Bouricius, E. L. Gray, J. Geophys. Res. 70, 4601 (1965).
[CrossRef]

K. L. Coulson, J. Plan. Space Sci. 1, 265 (1959).
[CrossRef]

K. L. Coulson, Sci. Rept. No. 2, Contr. AF 19(604)–1303, Univ. of California (1956).

K. L. Coulson, E. L. Gray, G. M. Bouricius, T. I. S. Rept. R65SD4, General Electric Co., Space Sciences Laboratory, Philadelphia, Pa.

K. L. Coulson, G. M. Bouricius, E. L. Gray, Final Rept., Contr. NAS5-3925, General Electric Co., Space Sciences Laboratory, Philadelphia, Pa.

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

Dave, J. V.

J. V. Dave, J. Atm. Sci. 22, 273 (1965).
[CrossRef]

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

Z. Sekera, J. V. Dave, Sci. Rept. 4, Contr. AF 19(604)–2429, Univ. of California, Los Angeles (1960).

Deirmendjian, D.

D. Deirmendjian, Memo. RM-3228-PR, Rand Corp., Santa Monica, Calif. (1962).

Dollfus, A.

A. Dollfus, Ann. Astrophys. Suppl. Article 4 (1957).

A. Cailleux, A. Dollfus, Compt. Rend. 230, 1411 (1950).

B. Lyot, A. Dollfus, Compt. Rend. 228, 1773 (1949).

Dutton, J. A.

K. G. Bauer, J. A. Dutton, J. Geophys. Res. 67, 2367 (1962).
[CrossRef]

Exner, F.

F. Exner, Met. Zeit. 37, No. 5 (1920).

Feigelson, E. M.

E. M. Feigelson, M. S. Malkevich, S. Ya. Kogan, T. D. Karonatova, K. S. Glazova, M. A. Kuznetsova, Calculation of the Brightness of Light (Consultants Bureau, New York, 1960).

Fraser, R. S.

R. S. Fraser, J. Opt. Soc. Am. 54,157, 289 (1964).
[CrossRef]

R. S. Fraser, Sci. Rept. No. 2, Contr. AF 19(604)–2429, Univ. of California, Los Angeles (1959).

R. S. Fraser, Final Report, Contr. NAS5-3891, TRW Space Technology Laboratories, Redondo Beach, Calif. (1964).

R. S. Fraser, Z. Sekera, Appendix E, Final Report of Contr. AF 19(122)–239, Univ. of California, Los Angeles (1955).

Fritz, S.

S. Fritz, Bull. Am. Met. Soc. 29, 303 (1948).

S. Fritz, Compendium of Meteorology (American Meteorological Society, Boston, 1951), p. 13.

Gates, D. M.

Gehrels, T.

Glazova, K. S.

E. M. Feigelson, M. S. Malkevich, S. Ya. Kogan, T. D. Karonatova, K. S. Glazova, M. A. Kuznetsova, Calculation of the Brightness of Light (Consultants Bureau, New York, 1960).

Gray, E. L.

K. L. Coulson, E. L. Gray, G. M. Bouricius, Icarus 5, 139 (1966).
[CrossRef]

K. L. Coulson, G. M. Bouricius, E. L. Gray, J. Geophys. Res. 70, 4601 (1965).
[CrossRef]

K. L. Coulson, E. L. Gray, G. M. Bouricius, T. I. S. Rept. R65SD4, General Electric Co., Space Sciences Laboratory, Philadelphia, Pa.

K. L. Coulson, G. M. Bouricius, E. L. Gray, Final Rept., Contr. NAS5-3925, General Electric Co., Space Sciences Laboratory, Philadelphia, Pa.

Hanson, K. J.

K. J. Hanson, H. J. Viebrock, Mo. Wea. Rev. 92, 223 (1964).
[CrossRef]

Hapke, B.

B. Hapke, H. Van Horn, J. Geophys. Res. 68, 4545 (1963).
[CrossRef]

B. Hapke, Rept. No. 169, Cornell Univ. Center for Radio-phys. and Space Res. (1964).

Jaroslawzew, J. N.

J. N. Jaroslawzew, Izv. Akad. Nauk USSR, Ser. Geofiz. No. 1 (1952).

Karonatova, T. D.

E. M. Feigelson, M. S. Malkevich, S. Ya. Kogan, T. D. Karonatova, K. S. Glazova, M. A. Kuznetsova, Calculation of the Brightness of Light (Consultants Bureau, New York, 1960).

Keegan, H. G.

Kogan, S. Ya.

E. M. Feigelson, M. S. Malkevich, S. Ya. Kogan, T. D. Karonatova, K. S. Glazova, M. A. Kuznetsova, Calculation of the Brightness of Light (Consultants Bureau, New York, 1960).

Kondratiev, K. Ya.

K. Ya. Kondratiev, Z. F. Mironova, A. N. Otto, Pure Appl. Geophys. 59, 207 (1965).
[CrossRef]

K. Ya. Kondratiev, M. P. Manolova, Meteorol. Gidrol. No. 6, 31 (1955).

Krinov, E. L.

E. L. Krinov, Spektralnaia otrazhatelnaia sposobnost prirodnykh obrazovanii (Academy of Sciences USSR, Moscow, 1947).

Kuznetsova, M. A.

E. M. Feigelson, M. S. Malkevich, S. Ya. Kogan, T. D. Karonatova, K. S. Glazova, M. A. Kuznetsova, Calculation of the Brightness of Light (Consultants Bureau, New York, 1960).

Lyot, B.

B. Lyot, A. Dollfus, Compt. Rend. 228, 1773 (1949).

B. Lyot, Ann. Obs. (Paris), Sect. Meudon 8(1929).

Malkevich, M. S.

E. M. Feigelson, M. S. Malkevich, S. Ya. Kogan, T. D. Karonatova, K. S. Glazova, M. A. Kuznetsova, Calculation of the Brightness of Light (Consultants Bureau, New York, 1960).

Manolova, M. P.

K. Ya. Kondratiev, M. P. Manolova, Meteorol. Gidrol. No. 6, 31 (1955).

Mironova, Z. F.

K. Ya. Kondratiev, Z. F. Mironova, A. N. Otto, Pure Appl. Geophys. 59, 207 (1965).
[CrossRef]

Orlova, N. S.

N. S. Orlova, Tr. Astron. Obs.16, Leningrad State Univ.166 (1952).

Otto, A. N.

K. Ya. Kondratiev, Z. F. Mironova, A. N. Otto, Pure Appl. Geophys. 59, 207 (1965).
[CrossRef]

Pyatovskaya, N. P.

K. S. Shifrin, N. P. Pyatovskaya, Tr. Leningr. Glav. Geophys. Obs. 166, 3 (1964).

Richardson, L. F.

L. F. Richardson, Quart. J. Roy. Met. Soc. 56, 31 (1930).
[CrossRef]

Romanova, M. A.

M. A. Romanova, Air Survey of Sand Deposits by Spectral Luminance (Consultants Bureau, New York, 1964).
[CrossRef]

Schleter, J. C.

Sekera, Z.

Z. Sekera, J. V. Dave, Sci. Rept. 4, Contr. AF 19(604)–2429, Univ. of California, Los Angeles (1960).

R. S. Fraser, Z. Sekera, Appendix E, Final Report of Contr. AF 19(122)–239, Univ. of California, Los Angeles (1955).

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

Shifrin, K. S.

K. S. Shifrin, N. P. Pyatovskaya, Tr. Leningr. Glav. Geophys. Obs. 166, 3 (1964).

Tantraporn, W.

D. M. Gates, W. Tantraporn, Science 115, 613 (1952).
[CrossRef] [PubMed]

Teska, T. M.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

van Diggelen, J.

J. van Diggelen, Rech. Obs. (Utrecht) 14, 1 (1959).

Van Horn, H.

B. Hapke, H. Van Horn, J. Geophys. Res. 68, 4545 (1963).
[CrossRef]

Viebrock, H. J.

K. J. Hanson, H. J. Viebrock, Mo. Wea. Rev. 92, 223 (1964).
[CrossRef]

Weidner, V. R.

Weldon, R. G.

Ann. Astrophys. Suppl. Article (1)

A. Dollfus, Ann. Astrophys. Suppl. Article 4 (1957).

Ann. Obs. (Paris), Sect. Meudon (1)

B. Lyot, Ann. Obs. (Paris), Sect. Meudon 8(1929).

Appl. Opt. (2)

Astron. J. (1)

D. L. Coffeen, Astron. J. 70, 403 (1965).
[CrossRef]

Bull. Am. Met. Soc. (1)

S. Fritz, Bull. Am. Met. Soc. 29, 303 (1948).

Compt. Rend. (2)

B. Lyot, A. Dollfus, Compt. Rend. 228, 1773 (1949).

A. Cailleux, A. Dollfus, Compt. Rend. 230, 1411 (1950).

Icarus (1)

K. L. Coulson, E. L. Gray, G. M. Bouricius, Icarus 5, 139 (1966).
[CrossRef]

Izv. Akad. Nauk USSR (1)

J. N. Jaroslawzew, Izv. Akad. Nauk USSR, Ser. Geofiz. No. 1 (1952).

J. Atm. Sci. (1)

J. V. Dave, J. Atm. Sci. 22, 273 (1965).
[CrossRef]

J. Geophys. Res. (3)

B. Hapke, H. Van Horn, J. Geophys. Res. 68, 4545 (1963).
[CrossRef]

K. L. Coulson, G. M. Bouricius, E. L. Gray, J. Geophys. Res. 70, 4601 (1965).
[CrossRef]

K. G. Bauer, J. A. Dutton, J. Geophys. Res. 67, 2367 (1962).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Plan. Space Sci. (1)

K. L. Coulson, J. Plan. Space Sci. 1, 265 (1959).
[CrossRef]

Met. Zeit. (1)

F. Exner, Met. Zeit. 37, No. 5 (1920).

Meteorol. Gidrol. (1)

K. Ya. Kondratiev, M. P. Manolova, Meteorol. Gidrol. No. 6, 31 (1955).

Mo. Wea. Rev. (1)

K. J. Hanson, H. J. Viebrock, Mo. Wea. Rev. 92, 223 (1964).
[CrossRef]

Pure Appl. Geophys. (1)

K. Ya. Kondratiev, Z. F. Mironova, A. N. Otto, Pure Appl. Geophys. 59, 207 (1965).
[CrossRef]

Quart. J. Roy. Met. Soc. (1)

L. F. Richardson, Quart. J. Roy. Met. Soc. 56, 31 (1930).
[CrossRef]

Rech. Obs. (Utrecht) (1)

J. van Diggelen, Rech. Obs. (Utrecht) 14, 1 (1959).

Science (1)

D. M. Gates, W. Tantraporn, Science 115, 613 (1952).
[CrossRef] [PubMed]

Tr. Leningr. Glav. Geophys. Obs. (1)

K. S. Shifrin, N. P. Pyatovskaya, Tr. Leningr. Glav. Geophys. Obs. 166, 3 (1964).

Other (19)

Z. Sekera, J. V. Dave, Sci. Rept. 4, Contr. AF 19(604)–2429, Univ. of California, Los Angeles (1960).

E. M. Feigelson, M. S. Malkevich, S. Ya. Kogan, T. D. Karonatova, K. S. Glazova, M. A. Kuznetsova, Calculation of the Brightness of Light (Consultants Bureau, New York, 1960).

R. S. Fraser, Z. Sekera, Appendix E, Final Report of Contr. AF 19(122)–239, Univ. of California, Los Angeles (1955).

R. S. Fraser, Final Report, Contr. NAS5-3891, TRW Space Technology Laboratories, Redondo Beach, Calif. (1964).

S. Fritz, Compendium of Meteorology (American Meteorological Society, Boston, 1951), p. 13.

S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, 1950).

Cornell Aeronautical Laboratory, Report No. VF-1260-P-8, Contr. AF 33(616)–5870 (1961) (ASTIA No. AD 260694).

E. L. Krinov, Spektralnaia otrazhatelnaia sposobnost prirodnykh obrazovanii (Academy of Sciences USSR, Moscow, 1947).

M. A. Romanova, Air Survey of Sand Deposits by Spectral Luminance (Consultants Bureau, New York, 1964).
[CrossRef]

K. L. Coulson, Sci. Rept. No. 2, Contr. AF 19(604)–1303, Univ. of California (1956).

N. S. Orlova, Tr. Astron. Obs.16, Leningrad State Univ.166 (1952).

D. Deirmendjian, Memo. RM-3228-PR, Rand Corp., Santa Monica, Calif. (1962).

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

B. Hapke, Rept. No. 169, Cornell Univ. Center for Radio-phys. and Space Res. (1964).

H. A. Borthwick, U. S. Dept. Agriculture (private communication).

K. L. Coulson, E. L. Gray, G. M. Bouricius, T. I. S. Rept. R65SD4, General Electric Co., Space Sciences Laboratory, Philadelphia, Pa.

K. L. Coulson, G. M. Bouricius, E. L. Gray, Final Rept., Contr. NAS5-3925, General Electric Co., Space Sciences Laboratory, Philadelphia, Pa.

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

R. S. Fraser, Sci. Rept. No. 2, Contr. AF 19(604)–2429, Univ. of California, Los Angeles (1959).

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Figures (24)

Fig. 1
Fig. 1

Directional reflectance of dessert sand at five different wavelengths (principal plane, θ0 = 53°).

Fig. 2
Fig. 2

Directional reflectance of desert sand at three different angles of incidence (principal plane, λ = 6430 Å).

Fig. 3
Fig. 3

Directional reflectance of black loam soil at four different wavelengths (principal plane, θ0 = 78.5°).

Fig. 4
Fig. 4

Directional reflectance of black loam soil at three different angles of incidence (principal plane, λ = 6430 Å).

Fig. 5
Fig. 5

Hemispheric reflectance patterns of desert sand (dashed isopleths) and black loam soil (solid isopleths). The antisource direction is indicated by the cross at θ = 53°, ϕ = 180° (λ = 6430 Å).

Fig. 6
Fig. 6

Directional reflectance of green grass turf at four different wavelengths (principal plane, θ0 = 53°).

Fig. 7
Fig. 7

Directional reflectance of green grass turf at three different angles of incidence (principal plane, λ = 6430 Å).

Fig. 8
Fig. 8

Directional reflectance of various types of mineral surfaces (principal plane, λ = 6430 Å, θ0 = 53°).

Fig. 9
Fig. 9

Degree of polarization of radiation of five different wavelengths reflected from desert sand (principal plane, θ0 = 53°).

Fig. 10
Fig. 10

Degree of polarization of radiation reflected from desert sand for three different angles of incidence (principal plane, λ = 4920 Å).

Fig. 11
Fig. 11

Degree of polarization of radiation of four different wavelengths reflected from black loam soil (principal plane, θ0 = 78.5°).

Fig. 12
Fig. 12

Degree of polarization of radiation reflected from black loam soil for three different angles of incidence (principal plane, λ = 4920 Å).

Fig. 13
Fig. 13

Hemispheric patterns of the degree of polarization of radiation reflected from desert sand (dashed isopleths) and black loam soil (solid isopleths). The antisource direction is indicated by the cross at θ = 53°, ϕ = 180°. (λ = 4920 Å).

Fig. 14
Fig. 14

Degree of polarization of radiation of four different wavelengths reflected from green grass turf (principal plane, θ0 = 53°.

Fig. 15
Fig. 15

Degree of polarization of radiation reflected from green grass turf for three different angles of incidence (principal plane, λ = 4920 Å).

Fig. 16
Fig. 16

Degree of polarization of radiation reflected from various types of mineral surfaces (principal plane, λ = 4920 Å, θ0 = 53°).

Fig. 17
Fig. 17

Total relative intensity and relative intensity of individual components of radiation emerging from the top of a slightly turbid atmosphere overlying a surface of desert sand (principal plane, λ = 6430 Å, θ0 = 53°).

Fig. 18
Fig. 18

Total relative intensity and relative intensity of indivudual components of radiation emerging from the top of a slightly turbid atmosphere overlying a surface of desert sand (principal plane, λ = 4920 Å, θ0 = 78.5°).

Fig. 19
Fig. 19

Total relative intensity and relative intensity of individual components of radiation emerging from the top of a slightly turbid atmosphere overlying a surface of green grass turf. The components IdD and Idd are everywhere less than 0.002 and are not plotted (principal plane, λ = 4050 Å, θ0 = 53°).

Fig. 20
Fig. 20

Total relative intensity and relative intensity of individual components of radiation emerging from the top of a Rayleigh atmosphere overlying a surface of white quartz beach sand (principal plane, λ = 6430 Å, θ0 = 53°).

Fig. 21
Fig. 21

Degree of polarization of radiation emerging from the top of a slightly turbid atmosphere for different atmosphere and desert sand surface combinations (principal plane, λ = 6430 Å, θ0 = 53°; λ = 4920 Å, θ0 = 78.5°).

Fig. 22
Fig. 22

Contrast transmission coefficients for the total radiant intensity (Y) and the orthogonal intensity components (Yi, Yj) for a slightly turbid atmosphere overlying a desert sand surface (principal, plane, λ = 4920 Å, θ0 = 78.5°).

Fig. 23
Fig. 23

Contrast transmission coefficients for the total radiant intensity (Y) and the orthogonal intensity components (Yi, Yj) for a slightly turbid atmosphere overlying a desert sand surface (principal plane, λ = 6430 Å, θ0 = 53°).

Fig. 24
Fig. 24

Contrast transmission coefficients for the total radiant intensity (Y) and the orthogonal intensity components (Yi, Yj) for a slightly turbid atmosphere overlying a surface of green grass turf (principal plane, λ = 4050 Å, θ0 = 53°).

Tables (1)

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Table I Description of the Materials for which Reflection Data Are Given in Fig. 8

Equations (8)

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ρ ( θ , ϕ ) = ρ s [ I ( θ , ϕ ) / I s ] = I ( θ , ϕ ) / π I s ,
P = ( I max - I min ) / ( I max + I min ) ,
I ( 0 ; μ , ϕ ) = I s ( 0 ; μ , ϕ ) + I g ( τ 1 ; μ , ϕ ) exp ( - τ 1 / μ ) + 1 / ( 4 π μ ) 0 1 0 2 π T ( τ 1 ; μ , ϕ ; μ , ϕ ) I g ( μ , ϕ ) d μ d ϕ .
I r g ( μ , ϕ ) = ½ ρ F ( inc ) [ 1 - P ( μ , ϕ ) cos 2 χ ( μ , ϕ ) ] I e g ( μ , ϕ ) = ½ ρ F ( inc ) [ 1 + P ( μ , ϕ ) cos 2 χ ( μ , ϕ ) ] U g ( μ , ϕ ) = [ I e g ( μ , ϕ ) - I r g ( μ , ϕ ) ] tan 2 χ ( μ , ϕ ) ,
C ( τ 1 ; μ , ϕ ) = [ I t ( μ , ϕ ; μ 0 , ϕ 0 ) - I b ( μ , ϕ ; μ 0 , ϕ 0 ) ] / I b ( μ , ϕ ; μ 0 , ϕ 0 ) .
C ( 0 ; μ , ϕ ) = [ I t ( 0 ; μ , ϕ ) - I b ( 0 ; μ , ϕ ) ] / I b ( 0 ; μ , ϕ ) .
C ( 0 ; μ , ϕ ) = Y ( μ , ϕ ) C ( τ 1 ; μ , ϕ ) .
Y ( μ , ϕ ) = ( I D D + I d D ) / ( I D D + I D d + I d D + I d d + I s ) .

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