If the summation over discrete atoms in the structure factor expression:

is replaced by an integration of a continuous, cyclic electron density function, ρ, an expression is obtained that is of the form of a Fourier Transform:

This implies that the electron density is the Fourier Transform of the Structure Factor. Likewise, the Structure Factor is the Fourier Transform of the electron density:

While this equation is a useful depiction of the relationship between electron density and the structure factor, it is usually used in the form of a summation:

This equation says that the electron density, ρ, can be calculated at any point (x, y, z) by constructing a Fourier Series which has coefficients that are equal to the Structure Factors.