So far only linear propagation with =0 and has been treated. According to the Huygens-Fresnel principle ``every unobstructed point of a wavefront, at a given instant in time, serves as a source of a spherical wavelet (with the same frequency as that of the primary wave). The amplitude of the optical field at any point beyond is the superposition of all these wavelets (considering their amplitudes and relative phase)". For monochromatic waves this gives some interesting results. This is what happens when water waves pass an opening in a breakwater. If the incoming waves are plane waves they spread out into spherical shaped waves when passing through the opening.
In optics is distinguished between the far and near field diffraction or, respectively, Frauenhofer and Fresnel diffraction. Consider an aperture of random shape. Looking through it at very close distance towards a monochromatic light source infinitely long away a diffuse image is seen. Moving the hole away the image becomes more and more structured. You can also simply make a small slit with two fingers and look through it with one eye at a very close distance. This is the near field and the phenomenon is known as Fresnel diffraction. When the hole is moved even farther away the image bears little resemblance with the actual aperture, and it is the size and not the shape of the pattern which changes. This is the far field or Frauenhofer diffraction. It is important here because it limits the thickness of the laser light sheet.