Intensity correction function

Early powder diffraction experiments relied mostly on the Debye-Scherrer experiment to record a diffractogram. A broad film strip set into a cylindrical chamber produced the first known two-dimensional powder diffraction data. In contrast to modern methods the thin equatorial strip was the only part of interest and intensities merely optically and qualitatively analysed. This changed drastically with the use of electronic scintillation counters. Intensities were no longer a matter of quality but quantity. Inevitably the introduction of intensity correction functions long known to the single-crystal metier, i.e. Lorentz and polarization corrections (see Section 14.3), made their way into the field of powder diffraction. 

Most interpretations of orientation texture data are based on the assumption that the specimen is a sphere. A spherical specimen shape is not easily achieved for the kinds of materials we are dealing with and departures from sphericity interfere with the calculation of orientation functions (8). We expect to address this problem by calculating empirical correction functions that can be applied to specimen shapes that closely simulate the ones we use. This problem must be attacked using numerical integration in 3 dimensions, which is a computer-intensive activity. 

The intensity calculation is based on the knowledge of qKpr), the primary X-ray intensity distribution function as a function of mass depth pz (Fig. 8.9). Some experimental calculations of (iKp ) have been conducted using the tracer method proposed by Castaing. These measurements have only covered a limited number of experimental situations but have enabled adjustment of the parameters used in simulations by the Monte Carlo method or matrix effect correction models using a parameterisation of the function [Pg.164]

Figure 4.17 Example for the one parameter asymmetry correction. Top a symme trical ML curve with the correction function added k= 0.8). This is an odd function that does not change either the integral intensity or the peak height. Moreover the 1st derivate of the correction is zero at the central part. Thereby, also the peak position is kept unchanged. Middle The sum of both curves yields an asymmetrical peak. The minimum of the 2nd derivative is slightly shifted to the narrow slope. Bottom Application of the asymmetrical profile (in total five parameters) on the Si(lll) reflection from Figure 4.14.

In particular, the therapy of severely ill patients with deficiencies of one or several vital systems is based on the surveillance of the important body functions. In addition, the correct function of the medical equipment used and the connections to the patient need to be monitored because a malfunction of devices assisting vital body functions may be fatal for the patient. During intensive care, for continuously monitored parameters automatic alarm systems are used which signal a deviation from preset alarm limits by visual and/or audible alarms and which automatically start a recorder to record selected parameters during the alarm situation. 

The NMR peak area from an adsorbate saturating the solid can be measured as a function of temperature. As the frozen adsorbate is solid, nuclei in this phase will have very short spin-spin relaxation times. Hence, signal from the frozen adsorbate can easily be eliminated by using a spin-echo pulse sequence, or by increasing the specified dead-time after the excitation pulse. This means that the relative amount of liquid present in the pores can be measured by variable-temperature NMR methods. An intensity correction to allow for the change in the Boltzmann equilibrium population of energy levels with temperature is also required ... 

Our report is the first to present intensity corrections of the Raman spectra on cis -rich HOPA [1], deduced from the optical functions measured on the same sample. 

FT-Raman spectra were carried out using Perkin-Elmer spectrometer equipped with Nd YAG laser source. Spectra were accumulated from 64 scans at a resolution of 4cm. An optical bench alignment was performed before each Raman measurements to ensure that e spectrometer was fine-tuned and the detector signal maximized. FT-IR spectra were recorded using Perkin-Elmer spectrometer equipped with diamante crystal for attenuated total reflection (ATR). The FT-IR or Raman spectra were smoothed and their baselines were corrected using the automatic smooth and the automatic baseline correct functions of the built-in software of the spectrophotometer. Then, the intensities of the interested peaks were measured. 

Some research groups prefer to add a correction function based on an assumed molecular model to the intensity in equation (39) before the integration. In this way the result may become close to a true radial distribution function if none of the functions gtj(s) varies too much with s (see, for example, refs. 9g and 22). 

Two types of errors usually happen at this stage (1) systematic error, which influences all measurements within one microarray chip with similar effect — this error may be corrected by estimation and (2) random error that cannot be explained or corrected, which is typically laiown as noise. Such errors are totally stochastic and have different influence on different probes. (Tibshirani et al., 2005) Typically, the pre-processing stage contains three steps background correction, normalization and summarization. For the widely used Affymetrix chips, many Bioconductor routines are available in R for pre-processing. These require creation of an AffyBatch object based on raw Affymetrix data (in a. cel file). The first step is the background adjustment. In this step, one tends to subtract the control intensity from the treatment, to denoise the intensity. However, direct subtraction of uncertain quantities can increase the level of noise and possibly result in negative intensity values for certain spots. Various methods to circumvent these problems are available as metitod parameters in the bg, correct function in R ... 

If you must search ATR spectra against non-ATR libraries there is help. Some FTIR software packages contain an ATR Correction function. This function adjusts the relative intensities in an ATR spectrum so it looks more like a spectrum measured using a transmission experiment the net effect is to make the peaks at higher wavennmber bigger than they were in the original ATR spectrum. A comparison of the ATR spectrum and ATR corrected spectrum of sucrose is seen in Figure 4.51. 

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