The detection limit is the answer to the question - what is the
minimum number of counts we can be confident of detecting in a given
Suppose measure a weakly active sample, obtaining a count C. A
measurement of background gives B. So the count due to the sample
itself, S = C - B.
At the detection limit the average value of S: <S> = LD.
The plot shows the distribution P(S) of repeated measurements. They are
distributed about LD with a standard deviation sD.
If the critical limit is LC, the detection limit LD =
Lc + ksD = k2 + 2LC.
LD depends on background
B and your choice of k.
The fractional area of P(S) above LC gives the probability that any
measurement of this source will be significantly above background,
i.e. not consistent with zero.
The area gives us our confidence level, which depends on our
choice of k.