Overlapping correction

Combined Soot W2O, and CO2 Radiation The spectral overlap of H9O and CO9 radiation has been taken into account by the constants for obtaining Ec- Additional overlap occurs when soot emissivity , is added. If the emission bands of water vapor and CO9 were randomly placed in the spectrum and soot radiation were gray, the combined emissivity would be Eg phis , minus an overlap correction g s- But monochromatic soot emissivity is higher the shorter the wavelength, and in a highly sooted flame at 1500 K half the soot emission hes below 2.5 [Lm where H9O and CO9 emission is negligible. Then the correction g s must be reduced, and the following is recommended ... 

Emission ratio imaging is extremely popular due to its simplicity and speed. In essence, cells expressing donors and acceptors are illuminated at the donor wavelength and fluorescence intensity data are collected both at donor (D) and at acceptor (S) channels. Collected data may be either images, or, in case high acquisition speed is crucial and spatial information is not required, dualchannel photometer readings (see Textbox 1). S and D are not overlap-corrected and FRET is simply expressed as the ratio of intensities1 as ratio = S/D. 

What is the donor/acceptor ratio in a given cell Again, this ratio cannot be directly derived because it concerns two quantities that stem from fluorophores with different properties (absorption coefficient, quantum yield, spectra) and that emit into two channels differing in gain, filters, and excitation intensity. Thus, the (overlap corrected) intensity of acceptors in channel A will be a factor k times that of donors in D, at equimolar concentrations,3 or ... 

The value of P is important only with respect to technical considerations. The presence of finite orbital overlap between the initial and final states shghtly alters the p dependence of the relationship between Ft and A, The overlap corrections for the instanton analysis arise from the slightly different normalization of the symmetric and antisymmetric eigenstates, which can be obtained from the simple model in Fig. 2. The coefficients of the symmetric and antisymmetric eigenstates in terms of the zeroth order states, nominally + become instead... 

The classical multipolar induction terms, sometimes supplemented by simple overlap corrections, often work surprisingly well, especially for... 

The principal effect of the j, / corrections amounts more or less to a rescaling of the B°°10(R) transition elements. Specifically, the long-range correction (XL — 23) looks much like.a scaled-down version of B 10(R), and the overlap correction (XL = 01) is more or less a scaled-down version of B l0(R), so that to a first approximation, scaling factors could be used to model these corrections. 

A comparison between equations (7.8)-(7.9) and (7.12)-(7.13) shows that the exponential terms in Eqs. (7.12) and (7.13) represent the overlap effect (overlap correction). This new model of simultaneous nucleation and growth of nuclei, Eqs. 

Considering the peak overlap, because of which several reflections may contribute to the same profile area, the addition 5 should be reduced by an appropriate overlap correction. Finally, the estimated observed reflection intensity is given by ... 

The calculation of peak-overlap corrections assumes that relative peak intensities remain the same regardless of matrix (Roeder 1985). In addition, samples containing other elements with peaks in the La to Ly region for any particular REE may affect the relative intensities due to secondary fluorescence and absorption. Roeder (1985) measured the relative intensities of Dy LPi and Dy Lai in pure Dy and an alloy of 50 wt % Fe and 50 wt % Dy to investigate the effect of Fe absorption of Dy X-rays. The intensity ratio decreased from 0.44 (pure Dy) to 0.425 (50-50 Dy-Fe), showing that the absorption effect is detectable, but minor. In addition, detector gas absorption may cause changes in intensity ratios. 

If there is no suitable analytical hne free of spectral overlap, corrections can be made for the interfering element, but only if the overlapping element s intensity is less than 10% of the analyte intensity. Less than 1 % is even better, if possible. Corrections cannot be made if the overlapping line is one of the major elements in the sample (e.g., overlap from an iron line on Cr in a steel sample cannot be corrected mathematically). 

When quantitative analysis is needed on complex samples with peak overlaps, a method of extracting the individual intensities of each element is needed. These mathematical corrections are now performed in instrument data processing software, and may include overlap corrections, interelement corrections, matrix corrections, corrections for non-Gaussian peak shapes, and different statistical fitting routines. A combination of these corrections was used to determine the concentration of the elements in the alloy shown in Fig. 8.49. 

If the two classes are not linearly separable yet do not overlap, correct classification may be achieved by what is called a committee machine . Here a group of mutually independent decision vectors decides on the classification, the final result being given by a majority vote (Fig. lb). If the two classes overlap, no reliable decision is possible (Fig. Ic). 

In atomic emission spectroscopy flames, sparks, and MIPs will have their niche for dedicated apphcations, however the ICP stays the most versatile plasma for multi-element determination. The advances in instrumentation and the analytical methodology make quantitative analysis with ICP-AES rather straightforward once the matrix is understood and background correction and spectral overlap correction protocols are implemented. Modern spectrometer software automatically provides aids to overcome spectral and chemical interference as well as multivariate calibration methods. In this way, ICP-AES has matured in robustness and automation to the point where high throughput analysis can be performed on a routine basis. 

The following example may serve to illustrate the type of problem that can occur. The analytical problem involved the measurement of arsenic in a tin bronze which contained significant quantities of lead. The Pb La line (X = 1.176 A) interferes with the As Ka line (1.77 A), so a line overlap correction has to be made. A correction can, in principle, be made by use of a line overlap correction for lead, with possible additional corrections for matrix absorption. IVo sets of intensity measurements were made on each standard, the first of these, Ias> was made at 1.176 A and corresponds to the summation of the Pb La and As Ka intensities. The second, Ipb, was made at the Pb L/Si line (A, = 0.982 A), which is free from interference. Table 10.10 lists the measured intensities and arsenic concentrations in the nine standards available. All intensities are given in the form of intensity ratios. 

Patent foramen ovale (PFO) is a small opening that occurs between the two atria in fetuses septums to assist blood circulation. It typically closes shortly after birth and is often incorrectly classified as a form of ASD. The difference between PFOs and secundum ASDs is that PFO occurs as a result of failure of the septum primum and the secundum septum to fuse. Secundum defects on the other hand occur due to the failure of either the septum primum or secundum to overlap correctly. If the foramen ovale does not close, the result is a persistent hole which places an increased workload on the lungs and on the right side of the heart. ... 

The high- and low-energy methods, methods A and B described by Nicholson (6), can both be expressed as approximations derived from a more general expression. It is the expansion of the more general expression that leads to Hwang s overlap corrections (29). It has been observed (32) that Nicholson omitted part of the effect in his low-energy method. The proper treatment increases the temperature coefficient by as much as 30 % in some cases. 

APPENDIX B DERIVATION OF THE OVERLAP CORRECTION IN THE ONE-ISOTOPE APPROXIMATION... 

Since the resolution of a WDXRF spectrometer is relatively high, spectral overlap corrections are not required. However, with the EDXRF analyzer, some type of deconvolution method must be used to correct for spectral overlaps as it has poor resolution. The spectral deconvolution routines however, introduce error due to counting statistics for every overlap correction onto every other element being corrected for. This can double or triple the... 

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