The Huygens Principle as modified by Fresnel states that every unobstructed point on a wavefront acts, at a given instant, as a source of outgoing secondary spherical waves. The resulting net light amplitude at any position in the scattered light field is the vector sum of the amplitudes of all the individual waves.   

The original formulation was in terms of an artificial concept of a large number of point sources somehow re-radiating from a wavefront.   In fact, it is fundamentally sound as was shown by Kirchoff who derived a slightly modified form from a wave equation for the radiation. It is valid for describing diffraction in the far field well away from the diffraction source and when the source is larger than the light wavelength.

The Principle is very useful for visualizing what happens during diffraction. The rigorous Mie scattering theory used in the IRIS program to produce the simulations uses no approximations at all but unfortunately gives little mechanistic insight into what is taking place.