Background subtraction

Background Subtraction. If the characteristic peaks to be measured appear isolated in the spectrum, so that there are regions in the background which are clear of characteristic peaks, an empirical background can be fitted by computer on to the spectrum when it is displayed on the VDU. This method gives better results with greater intensity levels in the spectrum. 

In complex materials, where peaks are situated very close to each other, or when the peaks are below 1.5 keV, this method is not practicable, and a mathematical modelling approach is made. Modelling the Bremsstrahlung intensity produces a 

This part is roughly divided into three parts background subtraction, clustering and image registration. It exposes our method of mapping telemetry profiles to create a global perspective. 

Apply a threshold Th , the absolute difference for the mask foreground. 

The accuracy of this approach depends heavily on the threshold. In our case it is of the order of 10 cm because of the error in the sensor. 

The distribution of laser points in the image is discrete and it is difficult to locate points directly with a maximum density around. The mean shift presented by Comaniciu and Meer [COM 99] is a powerful non-parametric algorithm that allows us to find the local maximum of a function of the underlying density. It estimates the feature space as an empirical probability density function. For each data point, the mean shift defines a window and calculates the average of data within the window. Then it moves the center of the window to the average in the direction of the 

Kernel density estimator for a given set of d-dimensional points is  

The last step in processing the experimental PM IRRAS spectra involves the subtraction of the background. This background arises from the slowly varying broad-band absorbance of infrared radiation by the aqueous electrolyte. In order to remove the background, a procedure similar to that published by Earner et al. [66] was developed by Zamlynny [36]. The baseline is created from the experimental data points using spline interpolation. Successful interpolation requires knowledge of the exact positions of the absorption bands and a little experience. 

The following approach [79] can be used to ehminate the error introduced by this spline. In plots 31c and 31d, points o and c are at the centers of the symmetric (Vs(CH2)) stretching bands in the simulated spectrum and the PM IRRAS spectrum, respectively. Point b in panel 31 d is located at exactly the same wavenumber as the point d which was used to build the sphne in panel 31c. We assume that the following relationship should apply to the PM IRRAS spectrum  

The subscript exp is used to emphasize that this is the experimental spectrum of the film of adsorbed molecules. 

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Figure C2.18.4. Upper panel shows the 2p photoemission spectmm of the Si(l 11)-(2 x ]) cleaved surface after exposure to approximately 50 L of XeF2. The lower panel shows the 2p 2 component of the spectmm after background subtraction. In addition to the unshifted Si(2p2/2), there are tliree chemically shifted satellites...

Most EDS systems are controlled by minicomputers or microcomputers and are easy to use for the basic operations of spectrum collection and peak identification, even for the computer illiterate. However, the use of advanced analysis techniques, including deconvolution of overlapped peaks, background subtraction, and quantitative analysis will require some extra training, which usually is provided at installation or available at special schools. 

EXAFS data are multiplied by ( = 1, 2, or 3) to compensate for amplitude attenuation as a function of k, and are normalized to the magnitude of the edge jump. Normalized, background-subtracted EXAFS data, versus k (such as... 

Figures Background-subtracted, normalized, and ili -weighted Mo K-edge EXAFS, versus k (A ), for molybdenum metal foil obtained from the primary experimental data of Figure 2 with Eq = 20,025 eV.

As an example of the use of AES to obtain chemical, as well as elemental, information, the depth profiling of a nitrided silicon dioxide layer on a silicon substrate is shown in Figure 6. Using the linearized secondary electron cascade background subtraction technique and peak fitting of chemical line shape standards, the chemistry in the depth profile of the nitrided silicon dioxide layer was determined and is shown in Figure 6. This profile includes information on the percentage of the Si atoms that are bound in each of the chemistries present as a function of the depth in the film. 

Fig. 2.8. Example of a chemical shift in the Sn 3d peak for a very thin layer of Sn oxide in Sn metal. (A) spectrum after linear background subtraction, (B) spectrum resolved into its respective components. (a) Sn, (b) Sn .

A further critical point are the intensities correlated to spectra of the pure elements. Calculated and experimentally determined values can diverge considerably, and the best data sets for 7 measured on pure reference samples still show a scatter of up to 10%. The use of an internal standard or a simultaneously measured external standard seems to be the most successful way to reducing the inaccuracy below 10%. (Eor a more detailed discussion of background subtraction and quantification see, e.g., Seah [2.9].)... 

Fig. 8. Mass spectrum, with background subtracted, of pbo-toionized (Cfto) Rbv clusters containing both singly and doubly ionized species tbe solid line connects peaks belonging to groups of singly ionized clusters with a fixed value of n. Note tbe dominant peaks corresponding to (C (,Rb, ) Rb and (QoRb,.,) Rb2 (marked...

Fig. 12. Mass spectra of singly charged clusters composed of a single Qo molecule coated with a large amount of Na (background subtracted). The even-odd alternation extends up to approximately x = 66. Note that x = 12 does not appear as a magic number in these spectra.

Background current, 21, 65 Background subtraction, 40, 106 Bacteria electrode, 182 Band microelectrodes, 130, 135 Beryllium, 82 Bienzyme electrodes, 175 Biocatalytic devices, 172 Biological recognition, 171 Biosensors, 50, 171 Bipotentiostat, 106 Blood electrolyte, 165 Boltzmann equation, 19 Brain analysis, 40, 116 Butler-Volmer equation, 14... 

This spectrum shows ions at m/z 163, 195, 214, 217, 229, 236 and 251. The spectrum with the background subtracted, obtained as explained above, is shown in Figure 3.19. As before, the ions at m/z 214 and 236 have been removed. 

Figure 3.17 Background-subtracted mass spectrum obtained from the component eluting after 4.65 min in the LC-MS analysis of a pesticide mixture. From applications literature published by Micromass UK Ltd, Manchester, UK, and reproduced with permission.

While m/z 229 and 251 were observed in the spectrum of the previously eluting component (see Figure 3.16), it is necessary to confirm that their presence in this spectrum is solely from that source and not from another component whose mass spectrum also contains these ions. If this can be done, the spectrum of the second component can be obtained by background subtraction. 

Further experimental work involving cone voltage studies may provide further confirmatory evidence but the most likely explanation is that the mass spectrum of the component with retention time 4.65 min is that shown in Figure 3.17, while the mass spectrum of the second component is that obtained by background subtraction, and is shown in Figure 3.22. 

Background-subtracted spectrum A mass spectrum from which ions arising from species other than the analyte have been removed by computer manipulation. 

For XES, quantitification techniques have been developed by Cliff and Lorimer (14) for correcting the background-subtracted x-ray intensity ratio of two elements, )>y sensitivity... 

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