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International Journal of Optics
Volume 2009, Article ID 896208, 6 pages
Research Article

Bayesian Estimation of the Axial Position in Astigmatism-Based Three-Dimensional Particle Tracking

Joseph Henry Laboratory of Physics, Lewis-Sigler Institute for Integrative Genomics, Princeton University, 150 Carl Icahn Laboratory, Princeton, NJ 08544, USA

Received 28 October 2008; Accepted 23 January 2009

Academic Editor: Jianan Qu

Copyright © 2009 Joshua W. Shaevitz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Accurate estimation of the axial position of a molecule using a single lateral image remains a challenge in fluorescent single particle tracking. Here, a principled algorithm for the Bayesian estimation of the axial position of a molecule in three-dimensional astigmatism-based particle tracking is proposed. This technique uses the data from a calibration image set to derive the position without assuming a functional form for the abberated defocusing curve. Using a calibration image set from forty 57 nm beads, the axial position is calculated, and the error associated with position estimation is discussed. This method is compared to previously published algorithms.