Absolute intensity calibration

In the majority of experimental studies what is of interest is the variation in the scattering intensity as a function of the scattering angle, and it is sufficient in such cases to have the observed intensity I(q) expressed in any arbitrary units, for example, counts per second. There are, however, cases in which the observed intensity must 

There are essentially three types of experimental procedures for determining the absolute intensity. These are (1) determining the intensity of the primary beam itself after attenuating it by some known factor, (2) measuring the scattering intensity from a material whose scattering power is known from theoretical considerations, and (3) using a secondary standard sample that has been calibrated by one of the above two methods. 

An unattenuated primary beam is so much stronger than the scattered beam that no detector is capable of measuring both the primary and the scattered beam under similar conditions. Attenuating the primary beam by inserting a filter of known absorption coefficient naturally comes to mind, but the method is difficult and can give erroneous results unless the beam has been rendered strictly monochromatic. Spectral components in the beam with even a small difference in wavelength and in absorption 

Other material specimens, once carefully calibrated by one of the primary methods explained above, can be used as a secondary standard. The material for such a secondary standard should be easy to handle, give a moderately strong scattering intensity, and remain unaltered over a long period of time under repeated usage. Polyethylene and glassy carbon have been used for this purpose. 

Winick, H., in Synchrotron Radiation Research, Chapter 2, H. Winick and S. Doniach, Eds., Plenum Press, New York, 1980. 

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Absolute system calibration with a set of narrow distributed nb glucans (pullulans) by means of dual detection of mass and scattering intensity applying a mixed peak position/ broad standard calibration... 

Calibration to absolute intensity means that the scattered intensity is normalized with respect to both the photon flux in the primary beam and the irradiated volume V. Thereafter the scattering intensity is either expressed in terms of electron density or in terms of a scattering length density. Both definitions are related to each other by Compton s classical electron radius. 

Fields of Application. In SAXS a calibration to absolute intensity is required if extrapolated or integrated numerical values must be compared on an absolute scale. Examples are the determination of density fluctuations or the density difference between matrix and domains as a function of materials composition. 

General Routes. If a SAXS beamline in normal transmission geometry is used, calibration to absolute intensity is, in general, carried out indirectly using secondary standards. Direct methods require direct measurement of the primary beam intensity under consideration of the geometrical setup of the beamline. On a routine basis such direct calibration was commercially available for the historic Kratky camera equipped with zero-dimensional detector and moving slit device 14. 

Electron Density. Continuing the preceding considerations, calibration to absolute intensity means normalization to the scattering of a single electron , Ie that can be expressed in electron units, [e.u.]. Inevitably a calibration to absolute units involves also a normalization with respect to the irradiated volume V. Thus, for the field of materials science a suitable dimension of the absolute intensity is [I/V] = e.u./nm3 - The intensity measured in the detector is originating from a material with an average electron density of 400 electrons per nanometers cubed . The electron density itself is easily computed from mass density and chemical composition of the material (cf. Sect. 2.2.1). 

For the calibration to absolute intensity several direct and indirect methods have been proposed (Feigin and Svergun [86], p. 73-76). 

Direct calibration to absolute intensity is not a usual procedure at synchrotron beamlines. Nevertheless, the technical possibilities for realization are improving. Therefore the basic result for the total scattering intensity measured in normal transmission geometry is presented. At a synchrotron beamline point-focus can be realized in good approximation and the intensity /(s) is measured. Then integration of Eq. (7.19) results in... 

The measured SAXS curve of the calibration sample must have been pre-processed in the usual way (cf. Sects. 7.3 - 7.6). Therefore it is important to have calibration samples with a well-defined thickness27. Because synchrotron beamlines can be adjusted to a fairly wide range of radiation power, it is important to have thin calibration samples for a high-power adjustment (e.g., common SAXS with wide slit openings) and thick calibration samples for low-power adjustments (e.g., USAXS with microbeam). For calibration samples from synthetic polymers, thicknesses ranging between 0.2 mm and 3 mm are reasonable. It appears worth to be noted that not only polymers, but as well glassy carbon [88] can be used as a solid secondary standard for the calibration to absolute intensity. 

Pure liquids can be used for the purpose of calibration to absolute intensity, because their diffuse scattering Ipi (0) = limv qIFi (s) caused from density fluctuations can be computed theoretically. Some examples are in the literature [91,93-95],... 

Application in Materials Science. For simple fluids the amount of the density fluctuation background can be computed. Thus its measurement can be used for the calibration of SAXS data to absolute intensity [91,94], This method is convenient if liquid samples are studied. 

Finally, calibration of an unknown scattering pattern is carried out by (1) reducing the intensity in the same way as was done with the scattering of the noble metal sol, (2) obtaining the absolute intensity by... 

We notice that anisotropic scattering patterns can be calibrated to absolute intensity, as well. 

The mean-centering operation effectively removes the absolute intensity information from each of the variables, thus enabling snbsequent modeling methods to focus on the response variations about the mean. In PAT instrument calibration applications, mean-centering is almost always nsefnl, because it is almost always the case that relevant analyzer signal is represented by variation in responses at different variables, and that the absolute values of the responses at those variables are not relevant to the problem at hand. 

The reaction now affords investigators another valuable tool because the absolute intensity of the chemiluminescence has been carefully measured. It can thus be used as a standard light source against which other chemiluminescent reactions can be measured without the need of detector calibrations and geometry corrections. This convenience is due largely to the fine work of Fontijn, Meyer, and Schiff,145,147 who used chemical actinometry to measure the emission from a discharge-flow system. In their first report on this reaction, they determined the value of k12 as 1.0 x 104 M x sec-1 for emission in the... 

The accurate determination of incident light intensity is of pivotal importance in any quantitative photochemical experiment. While various physical devices are available for making absolute intensity measurements,168 these devices can be difficult to calibrate and usually are rather expensive. A much simpler approach involves the use of a chemical actinometer. This type of system is based upon a photochemical reaction for which product quantum yields are reasonably insensitive to variations in reactant concentration, temperature, light intensity and excitation wavelength. Once the quantum yield is calibrated by an absolute method, a chemical actinometer becomes a rapid, inexpensive and highly accurate secondary standard for light intensity measurements. 

The measurement of quantum yield is a more complicated process. Before these measurements can be made, the instrument must be calibrated. A thermopile or chemical actinometer may be used to measure the absolute intensity of incident light on the sample. Alternatively, quantum yields may be measured relative to some accepted standard. Two commonly used fluorescence standards are quinine sulfate in 0.5 M H2S04 (jQ = 0.70) and fluorescein in 0.1 M NaOH (f9 = 0.93). The quantum yield of the unknown, Q, is then calculated by Equation 5.7. 

Quantitation. Combined GC-SICM has been used mainly for quantitation. For a particular GA the absolute intensity of a characteristic ion in its mass spectrum is related to the amount of GA present, using standards to calibrate the instrument. Frydman et al. (35) used this "external standard method" to measure the levels of a number of GAs throughout the development of pea seeds. An alternative and preferable approach employs... 

In addition to using the absolute intensities of the atomic emission lines, the peak intensity ratios of these lines have been used to analyze samples. Tran et al. [77] analyzed the atomic intensity ratios of several organic compounds with the hope to determine the empirical formula of a compound based on the ratios from several elements. Calibration curves were built based on C H, C 0, and C N atomic emission ratios from various compounds that covered a wide range of stoichiometries. Then, four compounds with known stoichiometries were tested against the calibration curves. The ratios determined from the calibration curves were compared with the actual stoichiometries and showed accuracy of 3% on average. In the study of nitroaromatic and polycyclic aromatic hydrocarbon samples, the ratios between C2 and CN and between O and N of different samples were shown to correlate with the molecular formula [75], Anzano et al. [71] also attribute success of their correlation of plastics to differences in the C/H atomic emission intensity ratio of each sample. 

In order to probe some of these questions - an essential endeavor in forming a clear interpretation of our results - we wish to compare our experimentally-determined data with predictions from a simple model. The experimental data available (See Fig. 3) are instantaneous values of flame temperature from the N2 Stokes/anti-Stokes intensity ratio (plotted as histograms in Fig. 4) and simultaneously-obtained values of Nj density (determined from the absolute value of the N. Stokes intensity calibrated against the value obtained for N2 in ambient air). Accordingly, we have produced "comparison" plots using the following scheme (24) If we calculate flame gas density and temperature as a function of flame stoichiometry (i.e., as a function of the fuel/air equivalence ratio see Fig.7), then we can... 

In PBM, Confidence Indices are automatically computed each time the set of selected ions is scanned — which is several times each second — and the single best fit, among all the scans of the experimental sample, is retained in the computer memory. Simultaneously the absolute intensity of each uncontaminated ion is compared with the absolute intensity of the corresponding ion (that was generated by a known quantity of the reference compound during the calibration procedure) to produce an independent "mass fragmentographic-type"... 

From the fact that the emission intensity depended linearly on the SO concentration, it was possible, by measuring the decay in emission intensity with reaction time when excess O3 was added, to compute the total rate of reaction ( 3 3+ 34 -1- 35) at various temperatures. The result was 334- 34+ 35 = (1.5+0.2)x 10 exp (—2100/Rr)l.mole .sec" for T = 223-300 °K. By using the absolute intensity of the NO-O glow determined by Fontijn et as a calibration standard, Halstead and Thrush were able to determine the absolute values of 7oi and 7o3, viz. 

For this evaluation, an intensity calibration in absolute units (here crn g srad) ) is necessary. 

Like chemical actinometers, photocells have to be calibrated against a thermopile-galvanometer system this has to be done frequently as there tends to be some variation with time. Under these conditions, they can be used to measure the absolute intensity of monochromatic light. The cell best suited for photochemical studies is the photoemissive type, which operates via the photoelectric emission of electrons from an irradiated surface. The metallic cathode is mounted either in a vacuum or in a small pressure of one of the inert gases. The cell may involve a single phototube or a multielement photomultiplier. An amplification of about 10 is achieved with the latter. 

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