Abstract
The exact surface field for dielectric or absorbing spheres of various sizes is first compared to the fields obtained according to three approximations: Fraunhofer diffraction, (modified) anomalous diffraction and Fresnel's laws. In particular, it is shown that for large dielectric spheres, the characteristic reinforcements observed in the surface fields according to Fresnel correspond exactly to rainbow angles. The approximate far scattered fields, calculated using the vectorial Kirchhoff integral, are then studied. For the Fresnel and anomalous diffraction approximations, they are generally satisfactory when limited to small scattering angles and to large dimensions. In that case, the method can be fruitfully extended to non-spherical particles whose radii of curvature are not too small and especially to biological particles with low refractive index. An oblate spheroid and a surface of Cassini simulating a red cell at rest are used as examples.