We investigate the identification problem of the fog Droplet Size Distribution (DSD) by an inverse method of the 1D radiative transfer equation thanks to spectral radiation measurements in the range 350 nm-2500 nm. This distribution together with Lorenz-Mie scattering theory allow to compute the optical properties (scattering coefficient, absorption coefficient, and phase function). We prove the well-posedness of the underlying inverse problem then we perform some numerical experiments using synthetic data. The numerical results suggest that the method allows to identify the DSD with different modellings of the radiative transfer (Beer-Lambert, isotropic and anisotropic collision operator).