Difference-density signal

Beyond the first-order impulsive description of the difference signal, given above, a time-averaged difference density Ap = pon (R tp) — poff(R tp) is obtained from the transformation. The effect of the finite duration of the X-ray pulse is a convolution with the instantaneous signal according to (34). A deconvolution of the X-ray pulse is in principle possible, provided the intensity profile is known and that the pump-probe delay time tp is well defined. 

Fig. 4 Inversion of the diffraction signal at a pump-probe delay time of 1,650 fs. Left panel difference diffraction curves for the isotropic and anisotropic signal Right panel comparison between the original difference density and the inversion via (59). The upper curve is the original difference density, the other curves are reconstructions with different values of c/max and the damping constant k (see [21] for details). Adapted from [21]...

When a second conformation is built into IFo — Fc difference electron density, the IFo — Fc difference density after some cycles of refinement does not reach the expected level. However, upon removal of the second conformation, the IFo — l c density frequently reappears. To avoid endless cycling, a pragmatic criterion for accepting a second conformation is to not require the presence of 2Fo — IFc density but to require the absence of any signal at less than the —3a-level in the IFo — l c difference density map. 

For samples of polycrystalline or disordered solids the concentration of spins per unit weight is usually the quantity of interest. Errors due to different densities of the sample and the reference and of different samples can then occur. A procedure to normalize the signal intensity by the mass to length ratio of the sample has therefore been recommended for quantitative measurements on powder samples [14]. The procedure may be motivated for a sample contained in a normal ESR sample tube as follows ... 

E plots the Raman band and CARS signal at 1000 cm" that are assigned predominantly to proteins. A wider gap is similarly resolved here. Cluster analysis of the Raman image identifies three main groups of spectra that are displayed in Figure 3.5. The spectrum of the tissue (blue cluster) contains spectral contributions of proteins and nucleic acids, whereas lipid bands are weak. The intensities of lipid bands increase and the intensities of proteins and nucleic acids decrease in the spectra of the gaps. It can be concluded that the gap is filled with lipids of different density. The result of the underlying chemical composition can only be obtained by multivariate analysis of hyperspectral Raman data such as k-means cluster analysis. Similar observations were also made for brain tissue as described in the later section. 

The base of this estimation is the signal to noise ratio. The lowest signal to noise ratio S/N which is necessary as a minimum to discern a signal from noise is S/N = 2 1 (4). Referring to the limiting values for the granularity Oj, of the film system classes the smallest density difference AD of an defect which would just be visible should be at least two times greater than On. 

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