1/8/2023 0 Comments Coherence x![]() The key feature of all these methods is the interference between the field scattered by different parts of the sample under study. Using the intense, coherent, and ultrashort X-ray pulses produced by so-called X-ray free-electron lasers and energy recovery linacs these techniques promise new insights in structural biology, condensed matter physics, magnetism and other correlated systems. ![]() In the former, the dynamics of a system are explored whereas in the latter two predominantly static real space images of the sample are obtained by phase retrieval techniques. New areas of research utilizing highly coherent X-ray beams have emerged, including X-ray photon correlation spectroscopy (XPCS), X-ray holography, and coherent X-ray diffractive imaging (CXDI). With the construction of third generation synchrotron sources, partially coherent X-ray sources have become feasible. Important contributions to this development were also provided by astronomists, as due to enormous intergalactic distances the radiation from stars has a high transverse coherence length at earth. Coherence is the defining feature of a laser, whose invention initiated a revolutionary development of experimental techniques based on interference, such as holography. A significant effort had to be made to extend the degree of coherence, which made the electromagnetic field determination using of the interference principle very challenging. Until the middle of the 20th century, the coherence of light available to experimentalists was poor. The ability of waves to interfere depends strongly on the degree of correlation between these waves, i.e. As such, the interference provides a superb measure of the phase differences of optical light, which may carry detailed information about a source or a scattering object. These modulations can be detected, provided the oscillating frequencies of the superposed fields are similar. While the oscillation frequency of individual fields is typically too large to be observed by a human eye or other detection systems, the phase differences between these fields manifest themselves as relatively slowly varying field strength modulations. If two waves interfere, the total radiation field is a sum of these two fields and depends strongly on the relative phases between these fields. They appear as a result of the superposition principle, valid in electrodynamics due to the linearity of the wave equation. For instance, the butterflies and soap bubbles owe their beautiful colors to interference effects. A few examples illustrate the possibilities of coherent X-rays for imaging and intensity correlation spectroscopy.Interference effects are among the most fascinating optical phenomena. A comparison between X-ray scattering, neutron scattering and mesoscopic electron transport is given. The loss of interference due to the finite detection time, to the finite detector pixel size and to uncontrolled degrees of freedom in the sample is discussed at length. Otherwise, a configurational average washes out the speckle and only diffuse scattering and possibly Bragg reflections will survive. When the illuminated sample volume is smaller than the coherence volume, the individuality of the defect arrangement in a sample shows up as speckle in the scattered intensity. The concept of coherence volume, defined in quantum optics terms, is generalized for scattering experiments. Their characterization in terms of coherence functions of the first and second order is introduced. All the currently available X-ray sources are chaotic sources. It has become possible to image opaque objects in phase contrast with a sensitivity far superior to imaging in absorption contrast. Speckle spectroscopy is extended to hard X-rays, improving the resolution to the nm range. Coherent X-rays are characterized by a large lateral coherence length. Highly brilliant synchrotron radiation sources have opened up the possibility of using coherent X-rays in spectroscopy and imaging.
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