Total Instrumental Profile

1 Precision and Calculation Time. To calculate one point on the instrumental profile we need to calculate a multidimensional integral. For the case where absorption can be neglected this integral reduces to a four-dimensional integral. To estimate how the number of points on the calculation grid affects the precision and calculation time, the calculations of the total instrumental profile were performed for four cases. They are given in Table 6.3. 

The precision of the calculations with nxnxnx n-calculation points was referred to the grid with 50 x 50 x 50 x 50 points as  

The number of calculation points on the instrumental profile for the given cases is 100. 

Taking into account absorption leads, generally, to a six-dimensional integral. However, within certain limits it can be reduce to the five-dimensional integral because the length of scattered X-rays in the sample changes insignificantly. 

The four-dimensional integral (case without absorption) can be reduced to a three-dimensional integral. 

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There are two different approaches for calculation of the instrumental function. The first is the convolution approach. Proposed more than 50 years ago, initially to describe the observed profile as a convolution of the instrumental and physical profiles, it was extended for the description of the instrumental profile by itself According to this approach the total instrumental profile is assumed to be the convolution of the specific instrumental functions. Representation of the total instrumental function as a convolution is based on the supposition that specific instrumental functions are completely independent. The specific instrumental functions for equatorial aberrations (caused by finite width of the source, sample, deviation of the sample surface from the focusing circle, deviation of the sample surface from its ideal position), axial aberration (finite length of the source, sample, receiving slit, and restriction on the axial divergence due to the Soller slits), and absorption were introduced. For the main contributors to the asymmetry - axial aberration and effect of the sample transparency - the derived (half)-analytical functions for corresponding specific functions are based on approximations. These aberrations are being studied intensively (see reviews refs. 46 and 47). 

Figure 6.20 compares two total instrumental profiles calculated with 50 X 50 X 50 X 50 and 5 x 5 x 5 x 5 points. As is easy to see, it is enough to take only 5 calculation points in each direction to reach a precision of 1 %. The calculation time for this case is about 0.05 s. The calculation time can be decreased still further by taking an unequal number of calculation points in each direction from the line position. 

Absorption lines are defined relative to the continuum. In the case of a resolved line, one may describe the line in terms of its depth relative to the local continuum across the line, say R(AA) = F[(A )/FC where AA is the wavelength measured from line centre, Fc is the flux in the continuum, and F) is the flux at a wavelength within the line. The total absorption by the line obtained by integrating R(AA) over the line profile is known as the equivalent width W. When a line profile is not resolved yet unaffected by blending from neighbouring lines, the equivalent width is independent of the resolution even though the line profile is set by the instrumental profile and not by the intrinsic stellar profile. 

The main difference between the proposed method and the convolution approach (in which the line profile is synthesized by convolving the specific instrumental functions) lies in the fact that the former provides an exact solution for the total instrumental function (exact solutions for specific instrumental functions can be obtained as special cases), whereas the latter is based on the approximations for the specific instrumental functions, and their coupling effects after the convolution are unknown. Unlike the ray-tracing method, in the proposed method the diffracted rays contributing to the registered intensity are considered as combined (part of the diffracted cone) and, correspondingly, the contribution to the instrumental line profile is obtained analytically for this part of the diffracted cone and not for a diffracted unit ray as in ray-tracing simulations. 

In the first step one should estimate the total amount of bandwidth increments which have to be recorded. It has been pointed out in Section 2.1.5 that for HR-CS AAS the width of the instrumental profile AAjnstr should depend on the wavelength A in a form which is well met by echelle spectrometers with ... 

The total peak profile is the sum of these two components, with a relative weight that depends on 0 and I. The Bragg component is mathematically a 5-function, but is in reality broadened by instrumental and sample imperfections. The shape of the diffuse component depends on the form of the correlation function. Many forms are possible, but two common ones are an exponential correlation function, leading to a Lorentzian line shape, and a Gaussian correlation function, leading to a Gaussian Hne shape. One can also use correlation functions that describe a preferred distance (e.g., island-island correlations) or with an in-plane anisotropy [42]. 

Intermediate precision is to determine method precision in different experiments using different analysts and/or instrument setup. Similar to that of repeatability, one should evaluate the results of individual related substances, total related substances, and the consistency of related substance profiles in all experiments. The percent RSD and confidence level of these results are reported to illustrate the intermediate precision. 

True profile analysis requires scanning over the whole mass range for the acquisition of all data on excreted compounds. Quantitation has been more challenging on a quadrupole instrument because total ion current peaks are seldom a single component and extracted-ion chromatograms (EICs) when recovered from scanned data are of poor quality due to the lower sensitivity of scanning GC-MS. Thus, we developed profile analysis based on SIM of selected analytes but tried to ensure the components of every steroid class of interest were included. For ion traps the fundamental form of data collection (in non-MS/MS mode must be full -scans). Thus, the quantitative data produced are EICs obtained from scanned data. The EICs are of the same ions used for SIM in quadrupole instruments and the calibration external standards are the same. 

Figure 2.13—Detection by mass spectrometry. TIC chromatogram obtained with a mass spectrometer as a detection system. The instrument is capable of obtaining hundreds of spectra per minute. The above chromatogram corresponds to the total ion current at each instant of the elution profile. It is possible to identify each of the components using its mass spectrum. In many instances, compounds can be identified with the use of a library of mass spectra. (Chromatogram of a mixture of 71 volatile organic compounds (VOCs), reproduced by permission ofTekmarand Restek, USA.)...

Ozone data includes measurements from 380 quality controlled Vaisala ECC-ozone soundings. Ozone profiles from soundings have been inspected visually and by comparing the profile based total column ozone to the spectrometric column ozone measured preferably by Dobson spectroradiometer in Marambio or by satellite based TOMS-instrument. No normalisation factor was used to correct the profiles dubious spikes were nevertheless corrected. Soundings were made twice a month from January until July and twice a week from August until January. Occasional interruptions of soundings have existed. 

MOP1TT Measurement of Pollution in the Troposphere Ozone Monitoring Instrument TR, profiles Total column of CO, CH, + CO profiles NASA TERRA (2000)... 

The Backscatter Ultraviolet atmospheric ozone experiment (BUV) was the first of a series of instruments made by NASA and later NOAA, which has successfully made long-term measurements of the vertical profile and total amount of ozone (Heath et al., 1973) (Table 1). BUV was launched aboard the Nimbus 4 satellite into a circular polar orbit at an altitude of 1100 km. This orbit is sun-synchronous and the satellite crosses the equator in an ascending mode every 107 minutes close to local noon. 

A more detailed overview of the main components of the GEOS-DAS system the forecast model, the input data (total ozone observations from Total Ozone Mapping Spectrometer /TOMS/ and vertical ozone profiles from the Solar Backscatter Ultra Violet instrument /SBUV/, the analysis scheme and its implementation could be easy found in the paper of Riishojgard [19]. 

Four major computational steps are necessary to separate the individual peaks and the different profile-broadening components (i) correction and normalisation of the diffraction data, (ii) resolution of the total peak scattering from the so-called background scatter, and resolution of crystallographic, para-crystalline, and amorphous peaks from each other, (iii) correction of the resolved profiles for instrumental broadening, (iv) separation of the corrected profiles into size and distortion components. In this paper we will discuss these steps in turn, but most attention will be paid to the hitherto largely neglected step of profile resolution. 

Figure 8 Automated high-throughput RNA analysis by capillary electrophoresis. Typical batch processing profiles of a 96-well sample plate. Total RNA sample preparations from rice (traces 1-76 from top), arabidopsis (traces 77-95), and yeast (trace 96) 6 pL each in 96-well plate. Conditions 50-pm-i.d. capillary, =10 cm (L = 30 cm) sieving medium, 1% PVP (polyvinylpirrolidone, MW= 1.3 MDa), 4 M urea, 1 xTBE, 0.5 pM ethidium bromide =500 V/cm 25°C. RNA samples were diluted in deionized water and denatured at 65°C for 5 min prior to analysis. Sample tray was stored at 4°C in the CE instrument during processing. Injection vacuum (5 s at 3.44 kPa). Separation matrix was replaced after each run, 2 min at 551 kPa. (Reproduced with permission from Ref. 102.)...

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