Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 103, Issue 12, Pages 4457-4462Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.0508047103
Keywords
Cramer-Rao lower bound; photon statistics; Fisher information matrix; fluorescence microscopy
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Funding
- NIAID NIH HHS [R01 AI 50747, R01 AI050747] Funding Source: Medline
- NIGMS NIH HHS [GM 071048, R01 GM071048] Funding Source: Medline
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Rayleigh's criterion is extensively used in optical microscopy for determining the resolution of microscopes. This criterion imposes a resolution limit that has long been held as an impediment for studying nanoscale biological phenomenon through an optical microscope. However, it is well known that Rayleigh's criterion is based on intuitive notions. For example, Rayleigh's criterion is formulated in a deterministic setting that neglects the photon statistics of the acquired data. Hence it does not take into account the number of detected photons, which, in turn, raises concern over the use of Rayleigh's criterion in photon-counting techniques such as single-molecule microscopy. Here, we re-examine the resolution problem by adopting a stochastic framework and present a resolution measure that overcomes the limitations of Rayleigh's criterion. This resolution measure predicts that the resolution of optical microscopes is not limited and that it can be improved by increasing the number of detected photons. Experimental verification of the resolution measure is carried out by imaging single-molecule pairs with different distances of separation. The resolution measure provides a quantitative tool for designing and evaluating single-molecule experiments that probe biomolecular interactions.
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