Sean Andersson
Department of Aerospace and Mechanical Engineering
Boston University
Estimation and control in confocal microscopy
In recent years, single particle tracking techniques in optical microscopy have become an important tool in the study of single molecules. To date, most methods rely on wide-field microscopy with ultra-fast video cameras. In two dimensions, video-rate bandwidth with spatial resolution as high as 5 nanometers can be achieved. However, many biological systems are inherently three dimensional and the two-dimensional projection of the motion of the molecule is often inadequate to understand the associated dynamic phenomena. Efforts to track single particles in three spatial dimensions typically rely on imaging the sample at different axial positions and analyzing the resulting stack of images. This approach suffers from poor temporal resolution and has a limited range in the axial direction. These difficulties present an opportunity for systems and control theory to have an impact on the study of molecular systems. In this talk we discuss some of the challenges and the role that control theory can play. We will also present a novel estimator for determining, with sub-diffraction-limit resolution, the position of a single molecule. This estimator is based on the Bancroft algorithm, a closed-form solution to the localization problem in the global positioning system. The new algorithm, called fluoroBancroft, is computationally efficient and can therefore be used in a real-time closed-loop particle tracking system.