Extension of the doubling method to inhomogeneous sources

Abstract This paper gives a general theory for applying the doubling method to spatially inhomogeneous radiation sources whose angular and spatial variations separate. In particular, inhomogeneous sources of thermal radiation may be efficiently treated by the methods herein, as well as direct and specularly-reflected beams of radiation which do not lie along a quadrature direction for the intensity. Doubling rules for a linear-in-optical-depth source (which may approximate a source of thermal radiation) and for an exponential-in-optical-depth source are derived as special cases.

[1]  George W. Kattawar,et al.  Matrix operator theory of radiative transfer. 2: scattering from maritime haze. , 1973, Applied optics.

[2]  H. B. Howell,et al.  On the Matrix Method Applied to the Multiple Scattering of Polarized Light , 1970 .

[3]  Numerical Approximations in Radiative Transfer , 1962 .

[4]  G. E. Hunt,et al.  Discrete space theory of radiative transfer I. Fundamentals , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  J. Hansen,et al.  Multiple Scattering of Polarized Light in Planetary Atmospheres. Part I. The Doubling Method , 1971 .

[6]  James B. Pollack,et al.  Near-Infrared Light Scattering by Terrestrial Clouds , 1970 .

[7]  G. Hunt,et al.  Discrete space theory of radiative transfer II. Stability and non-negativity , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  H. B. Howell,et al.  Matrix Methods for Multiple-Scattering Problems , 1966 .

[9]  J. Hansen.  Multiple Scattering of Polarized Light in Planetary Atmospheres Part II. Sunlight Reflected by Terrestrial Water Clouds , 1971 .

[10]  J. Hansen.  Exact and Approximate Solutions for Multiple Scattering by Cloudy and Hazy Planetary Atmospheres , 1969 .

[11]  G. Plass,et al.  Matrix operator theory of radiative transfer. 1: rayleigh scattering. , 1973, Applied optics.

[12]  W. Irvine.  Multiple scattering by large particles. II - Optically thick layers. , 1968 .

[13]  J. Hansen.  Radiative transfer by doubling very thin layers , 1969 .