Optical Sciences

Biomolecules and nanostructures

The Optical Sciences group studies the interaction of light and matter. Our current focus is on detection and sensing/imaging with an emphasis on the development of integrated photonics. We are part of Twente University's Department of Science and Technology and member of the MESA+ institute.

 

Accurate and unbiased estimation of power-law exponents from single-emitter blinking data

(full pdf)

Jacob P. Hoogenboom, Wouter K. den Otter, and Herman L. Offerhaus
Journal of Chemical Physics
vol 125 issue 20 p204713-1 - 204713-12 nov 28 2006

Single emitter blinking with a power-law distribution for the on and off times has been observed on a variety of systems including semiconductor nanocrystals, conjugated polymers, fluorescent proteins, and organic fluorophores. The origin of this behavior is still under debate. Reliable estimation of power exponents from experimental data is crucial in validating the various models under consideration. We derive a maximum likelihood estimator for power-law distributed data and analyze its accuracy as a function of data set size and power exponent both analytically and numerically. Results are compared to least-squares fitting of the double logarithmically transformed probability density. We demonstrate that least-squares fitting introduces a severe bias in the estimation result and that the maximum likelihood procedure is superior in retrieving the correct exponent and reducing the statistical error. For a data set as small as 50 data points, the error margins of the maximum likelihood estimator are already below 7%, giving the possibility to quantify blinking behavior when data set size is limited, e.g., due to photobleaching. © 2006 American Institute of Physics.
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