Quantification of scattering corrections to the Beer-Lambert law for transmittance measurements in turbid media
We present a modelled approach of scattering contribution to the radiation transmission through a scattering medium, such as an aerosol, yielding a correction term to the Lambert-Beer law. The correction is essential because a certain amount of the forward scattered light flux is always overlaid on the transmitted radiation. Hence it enters together with the attenuated beam into the finite aperture of any detector system and therefore constitutes a potential problem in the inversion of measured data. This correction depends not only on the geometry of the measuring system but also substantially on the optical depth of the medium. We discuss the numerical analysis of the magnitude and functional behaviour of the scattering correction for a number of important measuring parameters and we give a simple approximation for the determination of the range of applicability of the scattering correction for single scattering conditions. Finally, we show that the derived expressions yield useful values of optical depths at which non-negligible multiple scattering effects occur.