There are two relevant parameters for diffracted waves: amplitude and phase.

The result is bent or diffracted waves.

The narrower the slit, the wider the diffracted wave and the greater the uncertainty in momentum afterwards.

When the diffracted wave is considered to be in the near field, and the Fresnel diffraction equation can be used to calculate its form.

The first goal of the crystallographer is to obtain an electron density map, density being related with diffracted wave as follows:

Now, substituting in , the intensity (squared amplitude) of the diffracted waves at an angle θ is given by:

Clearly a highly coherent beam of waves is required for CDI to work since the technique requires interference of diffracted waves.

The problem of calculating what a diffracted wave looks like, is the problem of determining the phase of each of the simple sources on the incoming wave front.

A light wave incident on a grating is split into several waves; the direction of these diffracted waves is determined by the grating spacing and the wavelength of the light.

Then a Fourier transform is applied back and forth to move between real space and reciprocal space with the modulus squared of the diffracted wave field set equal to the measured diffraction intensities in each cycle.

Coherent electron diffraction imaging works the same as CXDI in principle only electrons are the diffracted waves and an imaging plate is used to detect electrons rather than a CCD.

When it is illuminated by only one of the waves used to create it, it can be shown that one of the diffracted waves emerges at the same angle as that at which the second wave was originally incident so that the second wave has been 'reconstructed'.

The Fraunhofer diffraction equation is an approximation which can be applied when the diffracted wave is observed in the far field, and also when a lens is used to focus the diffracted light; in many instances, a simple analytical solution is available to the Fraunhofer equation - several of these are derived below.