Physics:Detection efficiency

The probability of detecting an event if it has taken place. The event might be e.g. a collision process involving several particles, or simply the passage of one single particle through one single counter.

The detection efficiency is a function of the variables that describe the event, but depending on definition may also include the effects of other events, e.g. by dead time in the detector or its electronics caused by a previous event. If these variables are not completely specified, i.e. if some or all of them are random variables, then the interesting quantity is the expectation value of the detection efficiency. This expectation value is again often called the detection efficiency, although a more precise name would be average detection efficiency . cross-section is to be measured, one must correct for the average detection efficiency, which is often also called the acceptance.

If the detection of the event depends upon several independent necessary conditions, then the total detection efficiency for one given event is the product of independent efficiencies. The same factorization is not necessarily valid for the corresponding average detection efficiencies, due to possible correlations.

The detection efficiency of a single counter or of a complex detector can be measured either in a test experiment or from the final data sample, if there is redundant information. To measure the efficiency of one counter, one needs a sample of events for which the detection does not depend on that counter. If in n out of N events the counter produces a signal, then

is an unbiased estimator for the efficiency , with variance

The probability of obtaining in a measurement n events out of N, given , is estimated from a Poisson distribution with mean (see Bock98).  also Counter Efficiency also Counter Efficiency, Trigger Efficiency.