Phase problem

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The phase problem in physics describes the loss of phase information of a wavefront during an intensity measurement , which is caused by the nature of the quantum mechanical measurement . It is relevant where wave-based measuring methods (e.g. with light , X-rays , neutrons , electrons ) with imaging systems such as CCD or CMOS cameras, flat panel detectors or photo plates are used, which can only measure the intensity. For some methods such as B. the crystal structure analysis or the phase contrast microscopy , the phase information is of great interest. In imaging processes, suitable combinations of absorbing , diffracting and refracting optics are used to convert phase effects into intensity modulations through interference and make them measurable. Such approaches come e.g. B. in differential interference microscopy or with wavefront sensors (z. B. Hartmann-Shack sensor ) used. In the crystal structure analysis, the measured diffraction pattern corresponds to the amplitude of the 3D Fourier transform of the electron density distribution of the crystal structure . The reconstruction of the electron density from the measurement thus represents an inverse problem , which can be enormously facilitated by additional information about the phase. In the case of small molecules with a very ordered structure, sharp diffraction reflections can be measured, from which the phase can be obtained mathematically through the relationship between the structure factors ( Patterson method ). When studying large molecules, on the other hand, an experimental solution to the phase problem is often required for the reconstruction. So z. B. individual atoms or parts of the molecule can be replaced isomorphically by heavy atoms without the crystal structure being significantly changed and thus the phase can be deduced from the known modifications.

Individual evidence

  1. ↑ a b Kevin Cowtan: Phase Problem in X-ray Crystallography, and Its Solution . In: eLS . American Cancer Society, doi : 10.1038 / npg.els.0002722 ( wiley.com [accessed March 30, 2018]).