SPECTROSCOPY, IMAGING, OTHER TECHNIQUES |
Calculation of photon count number distributions via
Master equations
Kaupo Palo 1, Ülo Mets 1, Vello Loorits 1 and Peet Kask 1*
1 Evotec Technologies GmbH
* To whom correspondence should be addressed. E-mail: peet.kask{at}evotec-technologies.com.
Submitted on May 11, 2005
Revised on June 24, 2005
Accepted on 7 December 2005
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Abstract |
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Fitting of photon count number histograms is a way of analysis of fluorescence intensity fluctuations, a successor to fluorescence correlation spectroscopy. First versions of the theory for calculating photon count number distributions have assumed constant emission intensity by a molecule during a counting time interval. For a long time a question has remained unanswered: to what extent is this assumption violated in experiments. Here we present a theory of photon count number distributions that takes account of intensity fluctuations during a counting time interval. Theoretical count number distributions are calculated via a numerical solution of Master equations (ME), which is a set of differential equations describing diffusion, singlet-triplet transitions and photon emission. After-pulsing and dead time corrections are also included. The ME-theory is tested by fitting a series of photon count number histograms corresponding to different lengths of the counting time interval. Compared to the first version of FIMDA theory introduced in 2000, the fit quality is significantly improved. It is discussed how a theory of photon count number distributions, which assumes constant emission intensity during a counting time interval, may also yield a good fit quality. We argue that the spatial brightness distribution used in calculations of the fit curve is not the "true" spatial brightness distribution. Instead, a number of dynamic processes, which cause fluorescence intensity fluctuations, are indirectly taken into account via the adjustment parameters.
Key Words:
FCS, FIDA, FIMDA, Master equations, PAID, PCH
