Poisson-based detection limit and signal confidence intervals for few total counts

An alternative to the accepted method for calculating detection limits is presented that avoids difficulties often encountered with few total counts. In particular, excessive false positives and large relative uncertainty in the signal determination are prevented. The usually accepted method did not fully incorporate Poisson statistics in the derivation of detection limits. The alternate method defines detection at the same relative uncertainty for all magnitudes of total counts and includes the uncertainty of the signal counts. A method of determining confidence intervals for the signal in the presence of background is also proposed. Use of the confidence interval method to determine the mode or most probable value is particularly useful at few total counts because negative signal results are avoided.