It is pointed out that the methods of the approximate treatment of the Fraunhofer diffraction under spherical wave illumination in literatures [1-7] are not very proper. The Fraunhofer diffraction formulae, which describe the diffraction pattern received by an observing screen that is located at the convergence or divergence center of an illuminating spherical wave and is parallel with the diffracting screen, are deduced from the Rayleigh-Sommerfeld formula of the scalar diffraction theory. The scope of application of the formulae is discussed in detail. On the condition that the diffracting distance satisfies the far-field condition, it is pointed out that the formulae are tenable even if either the center of the lighting spherical wave or the observing point, or both, are located in the non-paraxial region. When the diffracting distance is nearer, the formulae are only tenable in the nearby region of the center of the illuminating spherical wave, but the center may be in the non-paraxial region. However, the further the diffracting distance is ,the bigger the tenable region is.The formulae may be reduced to the results presented in literatures[1],[6]and [7] in the particular case that the illuminating source and the observing point are all close to the axes.