Reciprocal-space

Reciprocal-space is a conceptual three-dimensional space which contains the full 3D scattering pattern of a given sample. It is the 3D Fourier transform of the sample's realspace electron-density distribution.

The distribution of intensity in reciprocal-space can be arbitrarily complex. For a sample with a distinct and non-trivial internal structure, the Fourier transform will be highly complex and difficult to interpret. However, samples of scientific interest generally have certain regularities, which give rise to a reciprocal-space with recognizable features, making the data easier to understand and analyze. In particular, a well-defined repeating structure in realspace gives rise to a sharp peak in reciprocal-space. The position of the peak encodes the repeat-spacing (the peak width encodes the correlation length, etc.).

Detector Image

The concept of reciprocal-space is extremely useful, because it allows one to connect between experiment geometry and the scattering equations. In particular, the scattering observed on a 2D detector plane during an experiment arises is actually a particular 'slice' through the 3D reciprocal-space. Thus, one can probe different regions of reciprocal-space by reorienting the sample with respect to the beam.

The 'slice' through reciprocal-space is not strictly a plane: it is actually the surface of a sphere, known as the Ewald sphere.