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Introduction
Stretched Exponential or the Kohlrausch-Williams-Watts function takes the form:
I(t) = I0exp[(−t/τ) β ] (1.46)
where the exponent β or ‘heterogeneity’ parameter is related to the distribution of
decay times, taking values from 0 to 1. For a single exponential decay, β would
be equal to 1. The stretched exponential model has been applied to complex sys-
tems such as the generation of lifetime maps (FLIM) of biological tissue. It can be
shown that superior signal-to-noise ratios of FLIM images can be obtained using
the stretched exponential model although for complex materials a multi-exponential
model was needed to reduce the noise adequately for image analysis [61, 62].
1.2.8 Experimental methods used to record lifetimes in the
Time and Frequency Domains
The principle TD method used to determine fluorescence lifetimes is Time-Correlated
Single Photon Counting (TCSPC) [63, 64]. This technique exploits the concept that
the time-dependent probability distribution for emission of a single photon after an
excitation event yields the actual intensity versus time distribution of all the photons
emitted as a result of the excitation. By statistically sampling the random emission
of photons following a large number of excitation events, a probability distribution
is constructed [63].
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