text: The radiometric description of the electromagnetic radiative field at a point in space and time is completely represented by the spectral radiance (or specific intensity) at that point. In a region in which the material is uniform and the radiative field is isotropic and homogeneous, let the spectral radiance (or specific intensity) be denoted by , a scalar-valued function of its arguments , , , and , where  denotes a unit vector with the direction and sense of the geometrical vector  from the source point  to the detection point , where  denotes the coordinates of , at time  and wave frequency . Then, in the region,  takes a constant scalar value, which we here denote by . In this case, the value of the vector flux density at  is the zero vector, while the scalar or hemispheric flux density at  in every direction in both senses takes the constant scalar value . The reason for the value  is that the hemispheric integral is half the full spherical integral, and the integrated effect of the angles of incidence of the radiation on the detector requires a halving of the energy flux according to Lambert's cosine law; the solid angle of a sphere is .
  The vector definition is suitable for the study of general radiative fields. The scalar or hemispheric spectral flux density is convenient for discussions in terms of the two-stream model of the radiative field, which is reasonable for a field that is uniformly stratified in flat layers, when the base of the hemisphere is chosen to be parallel to the layers, and one or other sense (up or down) is specified. In an inhomogeneous non-isotropic radiative field, the spectral flux density defined as a scalar-valued function of direction and sense contains much more directional information than does the spectral flux density defined as a vector, but the full radiometric information is customarily stated as the spectral radiance (or specific intensity).