Maximum-likelihood criterion and single-molecule detection

The maximum-likelihood criterion is shown to be a powerful method for analyzing fluorescence-detection data with small signal-to-noise ratios. A probability study of the maximum-likelihood criterion for a supposed single-molecule detection experiment is presented that takes into account the photokinetics of the molecule to be detected, its diffusion, and the laser-beam geometry. Furthermore, the efficiency of time-integrated and time-correlated single-photon counting methods are studied and compared.