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Introduction
Figure 1.19: Phase and Modulation data for the fluorophore HPTS and the associated
least squares fitting line from a one decay term fit. Experimental details:
λex=405 nm,λem=465 to 500 nm, number of frequencies = 25, from 1 to
120 MHz). Results: τ= 5.4 ± 0.1 ns, χ2 R = 0.5.
Q =
∞
0
I(t) cos(ωt)dt
∞
0
I(t)dt
(1.32)
For a multi-exponential decay, the transforms are related to the pre-exponential
factors and lifetimes by [52, 56]:
P =
i
Q =
i
αiωτ 2 i
1 + ω 2 τ 2 i
αiτi
1 + ω 2 τ 2 i
/
i
/
i
αiτi
αiτi
(1.33)
(1.34)
These transforms are related to the experimental parameters, i.e. phase and
demodulation by:
φ = tan −1 (P/Q) (1.35)
34