Observed time dependence of fluorescence

3 Observed time dependence of fluorescence 2.3.1 Introduction to convolution integral 

In Section 2.1 we stated that the fluorescence intensity due to a population of exdted-state molecules decreases exponentially with time following their 

L(ti) is the hei t and At the width of the excitation pulse s 6-fimction component at time t/. F(t) (the intrinsic fluorescence decay) is given by equation 1 and its argument t - t accounts fijr the fiict that the elapsed time varies between when the different subpopulations are created (at times t, ) and when the fluorescence intensity is measured. The (relative) height of L at t( appropriately scales the magnitude of the resulting fluorescence response. The effect of convolving an exponential decay with an excitation pulse of finite width will be seen in Section 2.6.4, where we describe the analysis of pulsed-excitation data. A fuller discussion of the convolution integral may be found in (9).  

The phase shift and demodulation both depend on the fluorescence lifetimes and amplitudes and on the modulation frequency u according to (10) 

by measuring the phase shift 0 and the demodulation m, one can determine the fluorescence decay times (t) and amplitudes (a). Such measurements are typically made sequentially over as broad a fiequency range as possible in order to minimize the error in the extracted parameters, and to enable one to distinguish between different multi-exponential fluorescence decays (see 

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