Counting statistics background subtraction

Figure 5.24(B) shows a line profile extracted from the map of Figure 5.24(A) by averaging over 30 pixels parallel to the boundary direction corresponding to an actual distance of about 20 nm. The analytical resolution was 4 nm, and the error bars (95% confidence) were calculated from the total Cu X-ray peak intensities (after background subtraction) associated with each data point in the profile (the error associated with A1 counting statistics was assumed to be negligible). It is clear that these mapping parameters are not suitable for measurement of large numbers of boundaries, since typically only one boundary can be included in the field of view.

For trace analysis, counting rates are low and peak-to-background ratios are generally poor. This means that the dominant error in trace analysis is normally due to counting statistics. Since peak-to-background ratios are low, it becomes important to measure and subtract the background contribution accurately. 

In this chapter, I will examine the statistical nature of radioactivity counting. Statistics is unavoidably mathematical in nature and many equations will emerge from the discussion. However, only as much general statistical mathematics wiU be introduced as is necessary to understand the relevant matters. I wiU go on to discuss the statistical aspects of peak area measurement, background subtraction, choosing optimum counting parameters and the often superficially understood critical limits and minimum detectable activity. I end with an examination of some special counting situations. 

Counts The maximum total spectrum input count rate should be kept below 3,000 cps. An alternative criterion is that the dead time should be kept below 30 %. Use smaller spot size or C2 aperture to reduce input count. Only peaks that are statistically significant should be considered for identification. The minimum intensity of a peak after background subtraction should be three times the standard deviation of the background at the peak position. 

After incubation, the spontaneous his - his + reversions found on background Plate C are subtracted from the colony count on Test Plate B. If a statistically significant number of colonies remain (i.e., net revertants ), the POM sample contains one or more chemicals that are promutagens. Sam-... 

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