Position estimation of fluorescent probes in a confocal microscope

Measurements of fluorescence intensity from an isolated fluorescing probe in a confocal microscope can be viewed as range-only measurements of the position of that probe. We present an analytical algorithm for determining its position from a collection of measurements taken at different locations in the plane. This algorithm, fluoroBancroft, is inspired by the Bancroft algorithm in GPS. We investigate the performance of the algorithm through simulation and compare it to the standard technique of fitting the data to a Gaussian profile. Our results indicate that the fluoroBancroft algorithm is more accurate than the fitting procedure when only a few measurements are used. Moreover the technique is typically two orders of magnitude faster in terms of computation time. These preliminary results indicate the fluoroBancroft algorithm holds promise for use in a real-time closed-loop controller to track the motion of single fluorescent probes.