Counting Statistics and Minimum Detection Limit

The measurement of peak intensity from an X-ray peak is illustrated through Fig. 1.21, where the counts/channel are plotted on log-scale. The peak is generally described by the Gaussian distribution, which is represented as  

The two parameters p. and correspond to the mean and variance (square of the standard deviation) of the distribution. The resolution (FWHM) is interpreted in terms of a as  

The error in the measurement of the area (counts under the peak) depends on the limits. For example area lying between (p-0.68a) and ( o,- -0.68a) has 50% probability or measured with 50% confidence, area lying between (p-a) and (p + a) has 68% probability or measured with 68.3% confidence, area lying between (p-1.65a) and (p+ 1.65a) has 90% probability or measured with 90% confidence while area lying between (p-2a) and (p+3a) has 95.5% probability and area lying between (p- 3a) and (p- -3a) has 99.7% probability. 

The background (under the peak) is estimated by integrating nB/2 channels symmetrically on either side of the peak. If Nb are the background counts 

The figure of merit = (Jp/p). A high value of Fm corresponds to a small statistical error. 

---