Abstract

One of the ongoing challenges in single particle fluorescence microscopy resides in estimating the axial position of particles with sub-resolution precision. Due to the complexity of the diffraction patterns generated by such particles, the standard fitting methods used to estimate a particle's lateral position are not applicable. A new approach for axial localization is proposed: it consists of a maximum-likelihood estimator based on a theoretical image formation model that incorporates noise. The fundamental theoretical limits on localization are studied, using Cramér-Rao bounds. These indicate that the proposed approach can be used to localize particles with nanometer-scale precision. Using phantom data generated according to the image formation model, it is then shown that the precision of the proposed estimator reaches the fundamental limits. Moreover, the approach is tested on experimental data, and sub-resolution localization at the 10 nm scale is demonstrated.

© 2005 Optical Society of America

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Applied Optics

P. Török and R. Varga, "Electromagnetic diffraction of light focused through a stratified medium," Applied Optics 36(11), 2305-2312 (1997).

Biophys J.

V. Levi, Q. Ruan, and E. Gratton, "3-D Particle Tracking in a Two-Photon Microscope: Application to the study of molecular dynamics in cells," Biophys J. 88, 2919-2928 (2005).
[CrossRef]

M. K. Cheezum,W. F.Walker, andW. H. Guilford, "Quantitative Comparison of Algorithms for Tracking Single Fluorescent Particles," Biophys J. 81, 2378-2388 (2001).

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise Nanometer Localization Analysis for Individual Fluorescent Probes," Biophys J. 82, 2775-2783 (2002).

R. J. Ober, S. Ram, and S.Ward, "Localization Accuracy in Single-Molecule Microscopy," Biophys J. 86, 1185-1200 (2004).

H. P. Kao and A. S. Verkman, "Tracking of Single Fluorescent Particles in Three Dimensions: Use of Cylindrical Optics to Encode Particle Position," Biophys J. 67, 1291-1300 (1994).

Chem. Phys. Lett.

A. Van Oijen, J. K¨ohler, J. Schmidt, M.M¨uller, and G. Brakenhoff, "3-Dimensional super-resolution by spectrally selective imaging," Chem. Phys. Lett. 292, 183-187 (1998).
[CrossRef]

ISBI 2004

N. Subotic, D. Van De Ville, and M. Unser, "On the Feasibility of Axial Tracking of a Fluorescent Nano-Particle Using a Defocusing Model," in Proceedings of the Second IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI’04), pp. 1231-1234 (Arlington VA, USA, 2004).

J. Microsc.

A. Egner and S. W. Hell, "Equivalence of the Huygens-Fresnel and Debye approach for the calculation of high aperture point-spread functions in the presence of refractive index mismatch," J. Microsc. 193, 244-249 (1999).
[CrossRef]

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index," J. Microsc. 169, 391-405 (1993).

M. G. L. Gustafsson, D. A. Agard, and J.W. Sedat, "I5M: 3D widefield light microscopy with better than 100nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef]

J. Opt. Soc. Am

S. F. Gibson and F. Lanni, "Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy," J. Opt. Soc. Am. A 8(10), 1601-1613 (1991).

J. Opt. Soc. Am. A

Opt. Commun.

O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy," Opt. Commun. 216, 55-63 (2002).
[CrossRef]

S. Hell and E. H. K. Stelzer, "Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation," Opt. Commun. 93, 277-282 (1992).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

N. Bobroff, "Position measurement with a resolution and noise-limited instrument," Rev. Sci. Instrum. 57, 1152-1157 (1986).
[CrossRef]

Single Molecules

U. Kubitscheck, "Single Protein Molecules Visualized and Tracked in the interior of Eukaryotic Cells," Single Molecules 3, 267-274 (2002).
[CrossRef]

Other

In practice, the number of possible optical sections is constrained by the exposure time, the dynamics of the biological process under study, and photobleaching of the fluorescent labels.

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

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