Abstract

The complete radiation field including polarization is calculated by the matrix operator method for scattering layers of various optical thicknesses. Results obtained for Rayleigh scattering are compared with those for scattering from a continental haze. Radiances calculated using Stokes vectors show differences as large as 23% compared to the approximate scalar theory of radiative transfer, while the same differences are only of the order of 0.1% for a continental haze phase function. The polarization of the reflected and transmitted radiation is given for a wide range of optical thicknesses of the scattering layer, for various solar zenith angles, and various surface albedos. Two entirely different types of neutral points occur for aerosol phase functions. Rayleigh-like neutral points (RNP) arise from the zero polarization in single scattering that occurs for all phase functions at scattering angles of 0° and 180°. For Rayleigh phase functions, the position of the RNP varies appreciably with the optical thickness of the scattering layer. At low solar elevations there may be four RNP. For a continental haze phase function the position of the RNP in the reflected radiation shows only a small variation with the optical thickness, and the RNP exists in the transmitted radiation only for extremely small optical thicknesses. Another type of neutral point (NRNP) exists for aerosol phase functions. It is associated with the zeros of the single scattered polarization, which occur between the end points of the curve; these are called non-Rayleigh neutral points (NRNP). There may be from zero to four of these neutral points associated with each zero of the single scattering curve. They occur over a range of azimuthal angles, unlike the RNP that are in the principal plane only. The position of these neutral points is given as a function of solar angle and optical thickness.

© 1976 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Radiation in the earth’s atmosphere: its radiance, polarization, and ellipticity

Stephen J. Hitzfelder, Gilbert N. Plass, and George W. Kattawar
Appl. Opt. 15(10) 2489-2500 (1976)

Matrix Operator Theory of Radiative Transfer. 2: Scattering from Maritime Haze

George W. Kattawar, Gilbert N. Plass, and Frances E. Catchings
Appl. Opt. 12(5) 1071-1084 (1973)

Multiple scattered radiation emerging from Rayleigh and continental haze layers. 2: Ellipticity and direction of polarization

Gilbert N. Plass, George W. Kattawar, and Stephen J. Hitzfelder
Appl. Opt. 15(4) 1003-1011 (1976)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (27)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (3)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription