The results of investigations on numerical solution of the problems of the approximation theory for the aerosol scattering phase functions based on the inverse problem method are discussed. We concentrated on evaluation of the extrapolation problems efficiency for scattering phase functions at small and large scattering angles. The results obtained illustrate the possibilities of the program complex "Spectrum" developed by the authors for interpreting optical measurements obtained with the help of an airborne nephelometer for operative monitoring of the atmosphere optical state.