Theoretical limits on errors and acquisition rates in localizing switchable fluorophores - PubMed (original) (raw)

Theoretical limits on errors and acquisition rates in localizing switchable fluorophores

Alexander R Small. Biophys J. 2009 Jan.

Abstract

A variety of recent imaging techniques are able to beat the diffraction limit in fluorescence microcopy by activating and localizing subsets of the fluorescent molecules in the specimen, and repeating this process until all of the molecules have been imaged. In these techniques there is a tradeoff between speed (activating more molecules per imaging cycle) and error rates (activating more molecules risks producing overlapping images that hide information on molecular positions), and so intelligent image processing approaches are needed to identify and reject overlapping images. We introduce here a formalism for defining error rates, derive a general relationship between error rates, image acquisition rates, and the performance characteristics of the image processing algorithms, and show that there is a minimum acquisition time irrespective of algorithm performance. We also consider algorithms that can infer molecular positions from images of overlapping blurs, and derive the dependence of the minimum acquisition time on algorithm performance.

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Figures

Figure 1

Figure 1

Concept of a rejection algorithm. Open and solid circles represent activated and dark molecules. When diffraction-blurred images of two molecules don't overlap, or when only one molecule is activated, the image is accepted with probability _f_1. When blurs from two activated molecules overlap, the algorithm rejects the image with probability _f_2.

Figure 2

Figure 2

Relationship between number of activation cycles required for a given error rate E and rejection algorithm performance characteristics _f_1 and _f_2.

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References

    1. Abbe E. Contributions to the theory of the microscope and microscopic perception. Archiv. Fur Mikroskopische Anatomic. 1873;9:413–468.
    1. Hell S.W. Far-field optical nanoscopy. Science. 2007;316:1153–1158. - PubMed
    1. Lagerholm B.C., Averett L., Weinreb G.E., Jacobson K., Thompson N.L. Analysis method for measuring submicroscopic distances with blinking quantum dots. Biophys. J. 2006;91:3050–3060. - PMC - PubMed
    1. Lidke K., Rieger B., Jovin T., Heintzmann R. Superresolution by localization of quantum dots using blinking statistics. Opt. Express. 2005;13:7052–7062. - PubMed
    1. Betzig E., Patterson G.H., Sougrat R., Lindwasser O.W., Olenych S. Imaging intracellular fluorescent proteins at nanometer resolution. Science. 2006;313:1642–1645. - PubMed

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