Background correction measurement errors

One important case deserves special mention. In some spectrographs, notably the Philips Autrometer (9.7), the comparison of standard with unknown is done as follows. The time At required for a preset number of counts to be given by the standard is established. The unknown is then counted for the same interval. Time is measured with such high precision that this measurement does not contribute to the over-all error. But At for the standard is subject to the fluctuation defined by Equation 10-4. The result of the comparison is therefore subject to the counting error of Equation 10-14 if no background correction is made, or to a similar counting error that is modified to allow for the background correction. 

Phase correction in contrast to the theoretical expectation, the measured interferogram is typically not symmetric about the centerburst (.v = 0). This is a consequence of experimental errors, e.g., frequency-dependent optical and electronic phase delays. One remedy is to measure a small part of the interferogram doublesided. Since the phase is a weak function of the wavenumber, one can easily interpolate the low resolution phase function and use the result later for phase correction. If there is considerable background absorption, phase errors may falsify the intensities of bands in the difference spectra. To avoid such phase errors for difference spectroscopy, the background absorbance should therefore be less than one. 

Figure 19 is also an example of the background shift errors encountered with ICP-AES. The three emission (100 uL) pulses were measured with a PMT at 257.6 nm. Without the benefit of background correction the calcium concomitant caused an error of 52%, in the determination of the Mn in the Ca interfered solution. With the SIT, where an entire spectral window was simultaneously recorded for the Mn + Ca solutions, background subtraction was possible and resulted in a mere 3% error in the Mn measurement. This error is within the 1-3% sampling precision obtained with 100 uL samples. 

Au and Pt compounds. The Tougaard method gave approximately 3% RSD from theory, which is of the order of the expected uncertainty due to the effects of instrumental stability and the errors in the ratio of photoionization cross-sections258. Additional considerations for background correction were made from reflection electron energy-loss spectroscopy (REELS) measurements at different take-off angles259. 

Final measurements e.g. calibration errors, spectral interferences, peak overlap, baseline and background corrections)... 

A more complicated background is seen in Fig. 7.38. The Cd 214.438 nm emission line is overlapped by a nearby broad A1 emission line, so the background intensity is not the same on both sides of the Cd peak. If Cd were to be measured in an aluminum alloy, this asymmetrical background would result in a positive error. When the background emission intensity is asymmetrical, two background correction points are needed, one on either side of the emission peak, as shown in Fig. 7.39. The computer software uses the two chosen points to draw a new baseline for the peak and automatically corrects for the background emission. 

The three different data sets produce extreme differences In the temperature factors (Table VIII). This difference Is not characteristic of just the SRRC program, as a similar range for cellulose Is In the literature. The temperature factor (B) Is Important because It Indicates systematic error In the Lp correction or other aspect of data gathering and reduction, for at least two of the data sets. Negative temperature factors, as found In the WS data, typically Indicate either that additional atoms, such as water molecules, are needed In the structure, or, when that Is known to be Incorrect, that there Is a flaw In some overall aspect of Intensity measurement, such as background correction. 

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 ... 

As in the case of lead the atomic line does not overlap with any molecular structure, no improvement in the LOD is obtained by the use of least-squares BC. However, it should be mentioned that additional noise, and even measurement errors, could be introduced in LS A AS when deuterium background correction is used in this case. 

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