Mie forward scattering: improved semiempirical approximation with application to particle size distribution inversion

The approximations of Penndorf and Shifrin-Punina to the Mie solution at forward scattering angles are extended to smaller size parameter values. The present approximation, Eq. (7), is found to represent accurately the Mie result down to x ~ 0.5-1.0 for refractive index m = 1.33, and to x ~ 2.0 for much larger index values. The implications of this result are discussed relative to the reconstruction of particle size distributions utilizing the Shifrin-Fymat analytical inversion formula of forward scattered intensities.