How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?

Single molecule fluorescence microscopy is a relatively novel technique that is used, for example, to study the behavior of individual biomolecules in cells. Since a single molecule can move in all three dimensions in a cellular environment, the three dimensional tracking of single molecules can provide valuable insights into cellular processes. It is therefore of importance to know the accuracy with which the location of a single molecule can be determined with a fluorescence microscope. We study this performance limit of a fluorescence microscope from a statistical point of view by deriving the Fisher information matrix for the estimation problem of the location of the single molecule. In this way we obtain a lower bound on the standard deviation of any reasonable (unbiased) estimation method of the location parameters. This lower bound provides a fundamental limit on the accuracy with which a single molecule can be localized using a fluorescence microscope and is given in terms of such quantities as the photon detection rate of the single molecule, the acquisition time, the numerical aperture of the objective lens etc. We also present results that show how factors such as noise sources, detector size and pixelation deteriorate the fundamental limit of the localization accuracy. The present results can be used to evaluate and optimize experimental setups in order to carry out three dimensional single molecule tracking experiments and provide guidelines for experimental design.