Polarization, intensity correction

Fig. 13. Measured scattering intensity of HDPE melt. Intensity corrections for air scattering, polarization, absorption, sample geometry and Compton scattering have beat performed...

Early powder diffraction experiments relied mostly on the Debye-Scherrer experiment to record a diffractogram. A broad film strip set into a cylindrical chamber produced the first known two-dimensional powder diffraction data. In contrast to modern methods the thin equatorial strip was the only part of interest and intensities merely optically and qualitatively analysed. This changed drastically with the use of electronic scintillation counters. Intensities were no longer a matter of quality but quantity. Inevitably the introduction of intensity correction functions long known to the single-crystal metier, i.e. Lorentz and polarization corrections (see Section 14.3), made their way into the field of powder diffraction. 

The second and third terms of the right hand side of Eq. (25) constitute the second- and third-order nonlinear contributions to the total polarization. These corrections to the polarization are responsible for numerous nonlinear optical processes such as the generation of light beams with new frequencies or an intensity dependent refractive index. 

Most of these diagrams contain two intermediate electron propagators and, therefore, double summations over the whole spectrum of the Dirac equation in the external nuclear field. This makes their computation numerically intensive. Both the selfenergy and vacuum-polarization screening corrections are ultraviolet divergent and require renormalization to yield a finite result. 

After the corrections of the individual measurements for absorption and polarization the corrected intensity of the empty container is subtracted from the corrected intensity of the container. Idled vviili... 

Intensity and Polarization. To correct for changes in the pump and probe intensities a fraction of the incident pump and probe beams is measured simultaneously with the transient absorption signal using additional photodiodes (PDl and PD2, Fig. 3). To avoid unwanted polarization effects, polarizers should be placed in both the pump and probe beams with an angle between the polarization directions of 54.7° (the magic angle). 

MOW used scanning densitometry over the entire flat film. Supplemental techniques were enlisted to obtain absolute Intensities and the Intensities of four meridional reflections. They observed 29 spots (1960). The formulae of Cox and Shaw (23) were used to make the Lorentz [geometric] and polarization (Lp) corrections. 

Sometimes it is necessaiy to correct the polarized intensity decays for background signals. The counts measured... 

Observed and calculated intensities of reflections on two oscillation photographs, one of which is reproduced in Fig. 5, are given in Table III. The first number below each set of indices (hkl) is the visually estimated observed intensity, and the second the intensity calculated by the usual Bade-methode formula with the use of the Pauling-Sherman /0-values1), the Lorentz and polarization factors being included and the temperature factor omitted. No correction for position on the film has been made. It is seen that the agreement is satisfactory for most of the... 

The distance of each reflection from the center of the pattern is a function of the fiber-to-film distance, as well as the unit-cell dimensions. Therefore, by measuring the positions of the reflections, it is possible to determine the unit-cell dimensions and, subsequently, index (or assign Miller indices to) all the reflections. Their intensities are measured with a microdensitometer or digitized with a scanner and then processed.8-10 After applying appropriate geometrical corrections for Lorentz and polarization effects, the observed structure amplitudes are computed. This experimental X-ray data set is crucial for the determination and refinement of molecular and packing models, and also for the adjudication of alternatives. 

Here and giobai are the number of atoms of the composition unit and wj and the atomic weights of the ith atom of the /th phase or of the overall sample. A and P are the absorption and polarization factors for which the measured intensities must be corrected. 

Integral intensities were obtained after dead-time corrections, background subtraction and normalization to averaged monitor counts. The Lp correction was applied in the usual way. Since the polarization ratio was not measured at BW5 so far, 90% linear horizontally polarized radiation was assumed for all scans. Calculations show that even a change in the beam polarization of 10% would effect the intensities of the highest order reflections of less than 1.5%. 

Fluorescence and phosphorescence spectra corrected for the instrumental sensitivity were measured with a spectrometer described previously (()). Corrected excitation spectra were obtained with constant excitation intensity controlled by a rhodamine B quantum counter. For phosphorescence polarization measurements the apparatus was set up in an "In Line" arrangement (j ) and equipped with a Glan-Thomson polarizer and a sheet polarizer (analyser) (10). 

Synchrotron light is, in general, polarized in horizontal direction ([10], p. 9-13). Nevertheless, the polarization of the beam is never perfect. In order to be able to carry out a quantitative polarization correction, the quality of polarization should be monitored by means of a polarization monitor [11] that is positioned in the primary beam. The polarization monitor is registering the horizontally polarized component, 4, and the vertically polarized component, 4- From these two intensities the quality... 

When the incident light is horizontally polarized, the horizontal Ox axis is an axis of symmetry for the fluorescence intensity Iy = Iz. The fluorescence observed in the direction of this axis (i.e. at 90° in a horizontal plane) should thus be unpolarized (Figure 5.3). This configuration is of practical interest in checking the possible residual polarization due to imperfect optical tuning. When a monochromator is used for observation, the polarization observed is due to the dependence of its transmission efficiency on the polarization of light. Then, measurement of the polarization with a horizontally polarized incident beam permits correction to get the true emission anisotropy (see Section 6.1.6). 

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