![]() The bright spot at the centre of the Fourier transform (FT) of the photograph directly corresponds to the F(0, 0, 0) spot in the diffraction pattern. Īnalogy between single-crystal X-ray diffraction and image manipulation. We draw an analogy between a single-crystal X-ray experiment and manipulation of digital images, as shown in Fig. This paper aims to present examples that can be used to illustrate graphically Fourier transform properties in crystallography courses, introducing notions such as resolution, convolution and signal-to-noise ratio using the free (time-limited licence) demo version of a very simple but nevertheless powerful software ( DigitalMicrograph from Gatan ), originally intended for electron microscopy data collection and analysis. ![]() Moreover, it is not possible to measure all Fourier coefficients of the electron density, firstly because of spatial limitations around the diffractometer (the diffraction angle has maximum practical value 2 θ max < 180°, depending on the experimental setup), and secondly because one uses nonzero wavelength λ (from the Bragg law the reciprocal resolution is, and since λ is finite the resolution cannot be infinite). Specialized experimental techniques such as multi-beam X-ray diffraction or convergent-beam electron diffraction offer possibilities to measure relative phases between some structure factors (see for example Spence & Zuo, 1992 ). ![]() However, according to (3), the diffraction process leads to the determination of only the moduli, the information about the phase being lost. ![]()
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