Abstract

The effects of higher-order scattering on intensity, degree of polarization, and direction of the plane of polarization in a molecular atmosphere have been calculated.

Inclusion of higher-order scattering changes these parameters strongly. Particularly, consideration of higher-order scattering is essential in the blue wavelength range (large optical thickness). The influence increases with decreasing zenith distance of the sun. The earth albedo augments the effect, except for direction of the polarization, which is independent of higher-order scattering.

© 1964 Optical Society of America

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References

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  1. S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, England, 1950), 1st. ed.
  2. 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).
  3. J. V. Dave, J. Opt. Soc. Am. 54, 307, 1288E (1964).
    [CrossRef]
  4. K. Bullrich, “Optical Transmission of the Atmosphere in Greenland I,” .

1964 (1)

Bullrich, K.

K. Bullrich, “Optical Transmission of the Atmosphere in Greenland I,” .

Chandrasekhar, S.

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

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.

J. V. Dave, J. Opt. Soc. Am. 54, 307, 1288E (1964).
[CrossRef]

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).

Sekera, Z.

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. Opt. Soc. Am. (1)

Other (3)

K. Bullrich, “Optical Transmission of the Atmosphere in Greenland I,” .

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

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).

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Figures (6)

F. 1
F. 1

Ratio of IM/IP; IM denotes the intensity due to multiple scattering, i.e., primary and higher-order scattering, and IP denotes the intensity due to primary scattering only. Albedo of the earth 0.0. Distances from center 0 of semicircles represent zenith distances. Azimuths from sun are measured counterclockwise from right-hand half of horizontal axis. Zenith angle of sun: 36.9° in upper diagrams, μ0 = 0.8; 66.4° in lower diagrams, μ0 = 0.4. Optical thickness τ: 0.5 (λ = 371 nm) in left-hand diagrams; 0.1 (λ = 546 nm) in center diagrams; 0.05 (λ = 644 nm) in right-hand diagrams.

F. 2
F. 2

Same as Fig. 1. Albedo 0.8.

F. 3
F. 3

Ratio PM/PP; PM denotes the degree of Polarization due to multiple scattering (primary and higher-order scattering); PP degree of polarization primary scattering. Albedo of the earth 0.0. Same solar zenith angles and optical thicknesses as in Figs. 1 and 2.

F. 4
F. 4

Same as Fig. 3. Albedo 0.8.

F. 5
F. 5

Differences PMPP of the degree of polarization for multiple scattering PM and for primary scattering PP in the sun’s vertical. Top: solar zenith angle 36.9° (μ0 = 0.8). Middle: 53.1° (μ0 = 0.6). Bottom: 66.4° (μ0 = 0.4). Curves numbered (1): τ = 0.25 (λ = 436 nm); (2): τ = 0.1 (λ = 546 nm); (3): τ = 0.02 (λ = 809 nm). —Albedo = 0.8, – – – – A = 0.25, –·–·–·– A = 0.0.

F. 6
F. 6

Angular differences of the directions of the plane of polarization χMχP; χM denotes the direction due to multiple scattering, and χP due to primary scattering.