Bias and Precision of the fluoroBancroft Algorithm for Single Particle Localization in Fluorescence Microscopy

The fluoroBancroft (FB) algorithm is an analytical solution to the position estimation problem in single molecule fluorescence microscopy. In this paper we derive a theoretical description of the bias and precision of the estimator for three dimensional estimation based on a stack of charge-coupled device (CCD) images and illustrate the results through realistic simulations. The results indicate that the algorithm exhibits a small bias that is driven primarily by modeling error and is dependent on the location of the source particle relative to the set of pixels used for estimation. In the shot noise limited case, the precision scales approximately as the inverse square root of the number of photons detected and as the inverse of the number of photons detected in the background noise limited case. The results are compared through simulation to the maximum-likelihood (ML) estimator based on the theoretical point spread function and found to have a similar performance. In general, the ML estimate had lower bias and variance, though at the lowest signal-to-noise ratio (SNR), FB outperformed ML. The FB algorithm executes approximately three to four orders-of-magnitude faster than the ML estimator and is well-suited for applications in which real-time results are needed.