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Diffuse Reflection of a Searchlight Beam by Slab, Cylindrical, and Spherical Media
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1969
Year
Optical MaterialsEngineeringWave OpticAbstract Functional RelationsRayleigh ScatteringBeam OpticIncident Searchlight BeamSurface ReflectanceRadiative TransferOptical PropertiesDiffuse ReflectionReflectionSearchlight BeamComputational ElectromagneticsReflectancePhotonicsInverse Scattering TransformsRadiative Transfer ModellingReflection FunctionGeometrical OpticWave ScatteringLight ScatteringSpherical MediaWater Surface Reflectance
Abstract Functional relations for the reflection function of an incident searchlight beam are derived systematically in various geometries (slab, cylindrical, and spherical). The equation of transfer is considered in a general orthogonal curvilinear coordinate system. The coordinate axes for each case are appropriately established and the corresponding differential operators are constructed. The equation of transfer is then written down in explicit form for each case. With the aid of CHANDRASEKHAR's (1950) principle of invariance in connection with the equation of transfer, the functional equations for the scattering function are obtained in slab, cylindrical, and spherical geometries, when a narrow pencil of radiation is incident on the outer surface. In the case of a constant conical flux of radiation uniformly incident on the outer boundary, the result reduces to that given by several authors (BAILEY 1964; BAILEY and WING 1964; UENO, KAGIWADA, and KALABA 1969).