a “decent” approximation to the targeted square wave is obtained.
In addition to showing an application of the use of Fourier series, this simple example
illustrates several experimental difficulties that arise in X-ray crystallography. Because
the Fourier series is “truncated” (rather than being infinite), the function obtained as an
approximation has “ripples” (termination errors). The approximation will get better as the
number of terms in the series increases, i.e., as the number of h terms in
increases.
In crystallography this entails collecting more hkl reflections at higher
θ angles. As θ increases, the d-spacing
between Bragg planes decreases and the resolution increases. Usually, the resolution of an X-ray
experiment is calculated as the minimum d-spacing measured. Thus, while small molecule
crystallographers might collect data to 0.8 Å resolution, protein data may be only to 2 or
3 Å resolution.
In addition those “ripples” in the electron density map can obscure real structural features; thus
it can be difficult to locate a hydrogen atom (because it only has one electron) especially when
it is in the vicimity of a heavier atom.
