Accuracy of intensity measurements

As I see it, structural biochemists and polymer scientists using fiber diffraction data should strive to mimic classical crystallographic studies so as to arrive at similarly credible solutions of structures by similarly noncontroversial methods of procedure that are similarly reproducible in other laboratories. We are obviously on the threshold of greatly improving the accuracy of intensity measurement but I will leave discussion of... 

Conclusions. "R-factors" calculated between pairs of structure-factor sets determined by three different laboratories varied between 16 and 22%, and these large inaccuracies were the dominant contributor to errors in the parameters of the crystalline structure. Thus if the accuracy with which the structure of polymeric fibres is determined is to be improved, it is essential both to increase the accuracy of intensity measurement, and to quantify its errors. 

The purpose of this Chapter is to acquaint the chemist and biochemist with some of the possibilities of studying details of molecular motion in crystals by analyses of X-ray diffraction data. Dunitz, Schomaker, and Trueblood remarked Nowadays, with improvements in the precision and accuracy of intensity measurement, it has become possible to detect quite subtle effects arising from the motion of molecules, and portions of molecules, in crystals. ... 

In powder diffraction, x-ray photons or neutrons (in x-ray and neutron diffraction experiments, respectively) are registered by the detector as random events. The measured intensity is directly proportional to the number of counts and therefore, the accuracy of intensity measurements is governed by statistics. Even though below we will refer to x-ray diffraction and photons, all conclusions remain identical when neutron diffraction and neutron count is considered. 

The expected isomorphous amplitude difference is 18.8%. Hence an accuracy of intensity measurement of 5% for Fp or F h is adequate for isomorphous-based phasing, whereas 1% or better is needed, ideally, for non-optimised anomalous dispersion-based phasing for the example quoted. 

Accuracy of intensity measurement Inadequate too many corrections required Better than Laue Standard method but extinction correction necessary Best photographic method Very accurate few corrections but of limited applicability Fairly good... 

Since both p and 1 can be varied in experimental conditions, the theorem (1.62) provides a convenient way of determining the true absorption coefficient A. The entire derivation of Wilson and Wells [11] will be presented since important considerations associated with the accuracy of intensity measurements emerge at different stages of proving the themem. The difference (A-B) is examined... 

A similar situation arises regarding the intensity measurement precision and accuracy of calibration. Again from the S/N point of view we can often measure spectral intensities to 1 part in 10. However the linearity of the response between 0 and 100% transmission is by no means known to this precision. There are many factors affecting the accuracy of intensity measurement. A fundamental problem relates to the geometrical optical properties of the sample the most severe... 

Physical properties are those that do not involve changing the identity of a substance. Chemical properties are those that involve changing the identity of a substance. Extensive properties depend on the mass of the sample intensive properties do not. The precision of a measurement controls the number of significant figures that are justified by the procedure the accuracy of a measurement is its closeness to the true value. 

It is not true that an increase in the resolving power always simultaneously leads to an increase in the accuracy of mass measurement. As soon as the resolving power allows peaks separation it is useless to increase it more as the signal intensity will decrease with subsequent decrease in accuracy of measurements. 

Isotopic mass spectrometry is used to establish 813C values. The sample is burned to C02 and the intensities of the ion peaks of m/z 44, 45, and 46 are measured. Then correction to eliminate the influence of 170 isotope is achieved. If using sector magnetic instrument and three detectors (for each mass) the standard deviation of the results will be better than 0.001%. The high accuracy of the measurements allows valuable results to be obtained. The ancient Europeans and Americans may be distinguished by the analysis of their remnants. The reason involves the fact that wheat constituted the basic food ration in Europe, while com played the same role in America. The difference in the isotopic composition of these plants forms several units of 813C scale [34],... 

The resulting spectra from El usually contain a number of fragments, providing extensive structural information about the analyte. A disadvantage of the observed fragmentation is eventually occurring isobaric overlay from different compounds in the analysis of sample mixtures, which often requires a separation step prior to the MS analysis. For this purpose the coupling of a GC with the ion source of the mass spectrometer via capillary inlet is a well established technique. Volatiles can be selectively introduced into El mass spectrometers via pervaporation membranes. The principle and application of this technique, called membrane introduction (MI) MS was recently reviewed [45]. The accuracy of intensity ratio measurements by El MS is about 0.1 -0.5% [4,8]. 

Fig. 8. The relative uncertainty in the measured intensity of various detectors as a function of the exposure level. A solid straight line indicates an ideal detector. A dashed line indicates a pulse-counting detector of 10 % efficiency. O and indicate the IP system for MoKa and CuKp, respectively. A and A indicate Kodak DEF-5 X-ray film for MoKa and CuKp, respectively. The munber of X-ray photons required to obtain a certain accuracy in intensity measurements can be compared...

Variations in lamp intensity and electronic output between the measurements of the reference and the sample result in instrument drift. The lamp intensity is a function of the age of the lamp, temperature fluctuation, and wavelength of the measurement. These changes can lead to errors in the value of the measurements, especially over an extended period of time. The resulting error in the measurement may be positive or negative. The stability test checks the ability of the instrument to maintain a steady state over time so that the effect of the drift on the accuracy of the measurements is insignificant. 

For many films exposed in the region of density <2.5, the optical density of a diffraction spot is often proportional to exposure and inversely proportional to the log Q of transmission coefficient. Thus, accuracy of reflection measurements tended to be reasonably uniform over the full range of density. The technique proved usable in estimating diffraction data on patterns on low background and reflections of moderate intensity, generally of photographic density < 1.0 and has been found to yield an error of 15-20% (14). 

For a single beam interferometer, the light intensity around the quarter wave point (where the accuracy of the measurement is high) is given by [9]... 

Figure 6 represents typical plots of the spin-echo intensity in PFG NMR experiments. Comparing the slopes of these representations with those of standard liquids, one obtains the mean self-diffusivities, which are found to decrease with increasing sorbate concentration (5,12,16,59,60). It appears from Fig. 6 that within the accuracy of the measurement no deviation from a single exponential decrease may be observed. A comparison of the experimental spin-echo attenuation (Fig. 6) with the results of numerical calcula-... 

A concentration value expressed as a percentage weight of the element in the sample, corresponding to the net intensity measured on the sample, is read off from the calibration line. The accuracy of the measurement is generally better than 1%. 

Regardless of the selection of the scan mode (see sections 3.6.8 and 3.6.9), the intensity recorded at each Bragg angle is measured during a certain period of time - counting time - which is one of the multiple user-specified parameters in the data acquisition process. As clearly seen in Figure 3.47, the importance of the counting time parameter is difficult to overestimate since it directly influences the accuracy of the measured diffracted intensity, and the overall quality of diffraction data. 

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