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Whenever a solar radiometer is used to measure direct solar radiation, some diffuse sky radiation invariably enters the detector's field of view along with the direct beam. Therefore, the atmospheric optical depth obtained by the use of Bouguer's transmission law (also called Beer-Lambert's law), that is valid only for direct radiation, needs to be corrected by taking account of the scattered radiation. In this paper we shall discuss the correction factors needed to account for the diffuse (i.e., singly and multiply scattered) radiation and the algorithms developed for retrieving aerosol size distribution from such measurements. For a radiometer with a small field of view (half-cone angle < 5 degrees ) and relatively clear skies (optical depths < 0.4), it is shown that the total diffuse contribution represents approximately 1% of the total intensity. It is assumed here that the main contributions to the diffuse radiation within the detector's view cone are due to single scattering by molecules and aerosols and multiple scattering by molecules alone, aerosol multiple scattering contributions being treated as negligibly small. The theory and the numerical results discussed in this paper will be helpful not only in making corrections to the measured optical depth data but also in designing improved solar radiometers.
Box et al. (Fri,) studied this question.