Relative random counting error

Consequently, the relative random error in the net peak intensity is equal to the relative random error in the net peak counts. 

The relative variance in the calculated true counts expressed by Eqs. (4.135) and (4.136) is plotted in Fig. (4.54) as a function of the normalized input rate. Clearly, existence of deadtime increases the random error in estimat-... 

The effect of deadtime on the random error leads to the question of whether there is a counting rate that provides the best precision in estimating the true counting rate at the detector. The relative precision in the calculated true counting rate arising from the random error is given by Eqs. (4.137) and (4.138) and is plotted in Fig. (4.55). 

In any measurement process where a given level of accuracy is required, throughput is determined by the amount of real time required to obtain the desired level of measurement accuracy. For an ideal livetime clock the relative precision caused by the random error in estimating the true counting rate at the detector for a specified amount of real time t has been shown to be [43]... 

Basically this is the fixed and variable source method used in Sec. 4.6.3 to measure the deadtime. A number of drawbacks are encountered with this technique in addition to those outlined in Sec. 4.6.3. Only a limited number of counts are permitted in the reference line. The relative statistical precision in the reference line can become the limiting random error in measuring elements with high concentrations. Extreme care must be exercised to avoid the errors in measuring the net counts above background in the reference line caused by changing backgrounds and other types of spectral interferences. 

A normal electronic pulser (a fixed interval pulser) does not give pulses randomly distributed with respect to time, therefore it is important that the pulser does not contribute significantly to the total spectrum. To this end, the ratio of the injected pulses to the total number of pulses should not exceed 0.1 if dead-time losses are to be corrected without error.This restriction arises because injected pulses cannot interact with each other but only with detector pulses however, detector pulses can interact with each other such that more detector pulses are lost than injected pulses. The difference becomes negligible if the injected pulses do not significantly alter the overall count rate. The whole effect can be avoided if a random-interval pulse generator is used when accurate correction can be made over a much wider range of count rates and relative pulse rates. 

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