The image of the scattering matter in three dimensions (the electron distribution) is obtained by performing a three-dimensional Fourier synthesis:
A wave of amplitude c and phase α represented as a vector with components c cos α and c sin α in an orthogonal system.
This is a summation over the volume of the unit cell, and includes amplitudes of structure factors and relative phase. This summation is the mathematical analog of what a microscope does. While we can easily derive the amplitudes (the diffraction experiment gives the magnitude of each structure factor or structure factor amplitude; this is obtained as a measure of intensity of the reflection, which is proportional to the square of the structure factor), we cannot measure the relative phase.