Accuracy of single molecule localization using electron-multiplying charge-coupled device cameras

The electron-multiplying charge-coupled device (EMCCD) is an important technology for imaging under extremely low light conditions. Whereas a weak signal acquired under low light conditions can be overwhelmed by the readout noise of a conventional charge-coupled device (CCD), it is amplified in the case of an EMCCD such that the readout noise becomes insignificant. The EMCCD is therefore a commonly used image detector in applications such as single molecule microscopy. However, despite its wide use, there has been a lack of rigorous analyses to determine how accurately parameters of interest (e.g., location of a single molecule) can be estimated from an image it produces. Here, we model the EMCCD's stochastic multiplication of electrons as a geometrically multiplied branching process, and develop the theory for calculating the Fisher information for estimating parameters from an EMCCD image. A ``noise coefficient'' is also introduced which enables the comparison of a CCD and an EMCCD in terms of the best accuracy with which parameters can be estimated from the images they produce.