Background data reduction

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Figure 9. Data reduction and data analysis in EXAFS spectroscopy. (A) EXAFS spectrum x(k) versus k after background removal. (B) The solid curve is the weighted EXAFS spectrum k3x(k) versus k (after multiplying (k) by k3). The dashed curve represents an attempt to fit the data with a two-distance model by the curve-fitting (CF) technique. (C) Fourier transformation (FT) of the weighted EXAFS spectrum in momentum (k) space into the radial distribution function p3(r ) versus r in distance space. The dashed curve is the window function used to filter the major peak in Fourier filtering (FF). (D) Fourier-filtered EXAFS spectrum k3x (k) versus k (solid curve) of the major peak in (C) after back-transforming into k space. The dashed curve attempts to fit the filtered data with a single-distance model. (From Ref. 25, with permission.)...

Standard data reduction, i.e. bias and flat field correction, has been performed with Iraf. The Iraf task APEXTRACT/APALL was used to extract the spectra, with interactively selected background sampling, in order to avoid contamination for the star spectrum. The wavelength calibration has been done using daily He, Ne, HgCd arcs, and, in order to improve the calibration, wavelengths values for the transitions used were taken from http //physics.nist.gov/. 

Data reduction of EXAFS spectra was performed using WinXAS [14], The normalized spectra were analyzed over the Arrange of 2.5 to 10 A1. A square-weighted degree 7 spline was used to remove the background of the x(k) function. Finally, the data in -space were converted to R-space using a Bessel window to obtain the radial distribution function. 

This data reduction algorithm has a big advantage Many inelastic scattered electrons contribute to the background which is not peaked at the locations of the Bragg-peaks. Their contribution is automatically subtracted. On the other hand form the plasmon-loss electrons a diffraction pattern that gives no significant different result in the refinement process that follows. A... 

In addition, a few crystalline phases, such as ice III, IV and VII, are not accessible through the recovery technique and measurements have to be made at the necessary pressures. So far only ice III (having an almost identical structure as ice IX) and VII has been measured under direct pressure [52]. Although this requires the presence of bulky metal pressure cells in the neutron beam, a correct choice of elements (e.g. A1 and a special ZrTi alloy) with high quality background measurements would minimise the problems associated with data reduction processes. 

For each Bragg reflection, the raw data normally consist of the Miller indices (h,k,l), the integrated intensity I(hkl), and its standard deviation [ a[I) ]. In Equation 7.2 (earlier), the relationship between the measured intensity / [hkl] and the required structure factor amplitude F[hkl) is shown. This conversion of I hkl) to F hkl) involves the application of corrections for X-ray background intensity, Lorentz and polarization factors, absorption effects, and radiation damage. This process is known as data reduction.The corrections for photographic and diffractometer data are slightly different, but the principles behind the application of these corrections are the same for both. 

Ex situ IR data are collected on dried, diluted powder films in a low vacuum enviromnent or one purged with a dry gas such as N2. Attenuated total reflectance (ATR)-IR spectroscopy provides surface-sensitive IR measurements and can be used for in situ studies of sorption phenomena. Raman spectroscopy is a related vibrational spectroscopy that provides complimentary information to IR. It can also be used to collect vibrational spectra of aqueous samples. Typical data reduction for vibrational spectra involves subtraction of a background spectmm collected under identical conditions from the raw, averaged sample spectrum. Data analysis usually consists of an examination of changes in peak position and shape and peak fitting (Smith, 1996). These and other spectral parameters are tracked as a function of maaoscopic variables such as pH, adsorption density, and ionic strength. 

Dr. javid Jones provided valuable background information and stimulating discussions on the use of viscoelastic data reduction schemes for various types of materials. 

The transmission extended x-ray absorption fine structure (EXAFS) spectra were collected on the A-2, C-1, and C-2 stations of the Cornell High Energy Synchrotron Source (CHESS). Data reduction followed a standard procedure of pre-edge and post-edge background removal, extraction of the EXAFS oscillations taking the Fourler-transform of and finally applying an inverse transform... 

Observations are made through spectral filters, narrow enough to avoid contamination by cometary spectral lines, and spectral data obtained at the same time are used to verity this assumption. Reference stars are used for calibration the sky background polarization and the alignment of the four images need to be taken into account in the data reduction. 

To introduce signal manipulation based on Fourier and Hadamard transformations and their appropriate usage for filtering, convolution, deconvolution, integration, data reduction, and background correction... 

Data Reduction and Background Correction Reduction of data points is important if, for example, further processing of a spectrum is only feasible if the number of data points is decreased. For reduction of measurements in the original data vector, the data are transformed by means of FT or HT. After that, back transformation is performed on the basis of a limited number of Fourier or Hadamard coefficients. For back transformation, the coefficients are sorted according to importance, and the effect of less important coefficients is thus eUminated (cf. Zupan, Section 3.3). Practically, the number of coefficients is not changed, but unimportant coefficients are set to zero. 

In an attempt to determine whether peracid oxidation of cyclopropenes to enones proceeds by ct- or ic-bond oxidation, Friedrich and Fiato compared the second-order rate constant for allylically substituted cyclopropenes and cyclopentenes. The results (Table 1) indicate rather small allylic substitution effects in the cyclopentenes, but larger rate reductions in the cyclopropenes. The magnitude of the effect is not in line with an epoxidation-type transition state and may be more consistent with o attack, but insufficient background data are available to allow firm conclusions from these results. A comparison of oxidation rates of 1,2-diphenyl-cyclopropene, -cyclobutene, and -cyclopentene yielded data which were much more consistent with oxabicyclobutane formation, as did an examination of substituent effects at the vinylic positions in cyclopropene. ... 

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