Physics – Optics
Scientific paper
Oct 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978ap%26ss..58..419d&link_type=abstract
Astrophysics and Space Science, vol. 58, no. 2, Oct. 1978, p. 419-425.
Physics
Optics
11
Atmospheric Radiation, Laplace Transformation, Linear Equations, Radiative Transfer, Singular Integral Equations, Atmospheric Optics, Differential Equations, Wave Propagation, Wave Reflection
Scientific paper
An exact method is developed for constructing solutions for emergent intensity from the bounding faces of an atmosphere of finite thickness. The integrodifferential equation for radiation intensity at any optical depth in the case of diffuse reflection and transmission is subjected to a one-sided Laplace transform in finite atmospheres to obtain linear integral equations, which are then converted into linear singular equations with the aid of Plemelj's formulas. These linear singular equations are solved exactly by means of the theory of linear singular operators. Solutions to some of the linear singular equations are derived in order to provide an exact expression for emergent radiation from the bounding faces of a finite atmosphere in terms of Chandrasekhar's (1950) XY equations.
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