The diffraction pattern produced by the interaction of X-rays with a crystal can be understood as the Fourier transform of the complete electron density of the crystal structure. In principle the electron density can be simply reconstructed by Fourier synthesis. In reality, only the intensities of the waves of the diffraction pattern can be recorded.
The information about the phase of the wave, the relative timing when each wave hits, is lost in the experiment. The problem of elucidating the phases when only the magnitudes are known is referred to as the “phase problem”. Crystallographers consider a crystal structure to be solved when the phases of enough reflections are sufficiently determined so that most, if not all, of the atoms in the unique part of the unit cell are revealed. There are several ways to solve the crystal structure of a small molecule compound.