Chapter 5 - From Diffraction Data to Electron Density

Abstract

This chapter begins by exploring Fourier sums and the Fourier transforms. Fourier transform is the lens-simlating operation that a computer performs to produce an image of molecules in the crystal. The Fourier transform describes precisely the mathematical relationship between an object and its diffraction pattern. The chapter emphasizes forms of these equations and the information they contain. This helps the reader to interpret the equations and to translate them into words and visual images. Afterwards, it represents structure factors and electron density, and shows how the Fourier transform interconverts them. The chapter highlights one-dimensional waves, three-dimensional waves, general features of the Fourier transform, and a short review of the same. It also discusses Fourier mathematics and diffraction. The topics covered include structure factor as a Fourier sum, electron density as a Fourier sum, computing electron density from data, and the phase problem. The chapter describes meaning of the Fourier equations and concludes by presenting a brief summary of the process from data to density.