  Standard deviation measurements of intensity profiles of stationary single
fluorescent molecules are useful for studying axial localization, molecular
orientation, and a fluorescence imaging system's spatial resolution. Here we
report on the analysis of the precision of standard deviation measurements of
intensity profiles of single fluorescent molecules imaged using an EMCCD
camera. We have developed an analytical expression for the standard deviation
measurement error of a single image which is a function of the total number of
detected photons, the background photon noise, and the camera pixel size. The
theoretical results agree well with the experimental, simulation, and numerical
integration results. Using this expression, we show that single-molecule
standard deviation measurements offer nanometer precision for a large range of
experimental parameters.
