The brightness temperature of a nonscattering layered half-space is obtained through the transmittance function of the medium. The formalism that has been worked out takes advantage of the stratification of the natural structure to simplify the calculations and allows temperature variations within each layer. In addition, the introduction of a weighting function explicitly singles out the relative contribution to the brightness from a given depth of the emitting half-space. Formulas are given that can be advantageously used when the scale of temperature variations is smaller than that of the dielectric constant of the medium.
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Bardati et al. (1984) studied this question.
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