Spectral Relaxation Imaging Microscopy II: Complex Dynamics

The dynamics of condensed matter can be measured by the time-dependent Stokes shift of a suitable fluorescent probe. The time-dependent spectral correlation function is typically described by one or more spectral relaxation correlation times, which, in liquid solvents, characterize the timescales of the dipolar relaxation processes around the excited-state probe. The phasor plot provides a powerful approach to represent and analyze time and frequency-domain data acquired as images, thus providing a spatial map of spectral dynamics in a complex structure such as a living cell. Measurements of the phase and modulation at two emission wavelength channels were shown to be sufficient to extract a single excited-state lifetime and a single spectral relaxation correlation time, supplying estimates of the mean rate of excited-state depopulation and the mean rate of spectral shift. In the present contribution, two more issues were addressed. First, the provision of analytic formulae allowing extraction of the initial generalized polarization and the relaxed generalized polarization, which characterize the fluorescence spectrum of the unrelaxed state and the fully relaxed state. Second, improved methods of model discrimination and model parameter extraction for more complex spectral relaxation phenomena. The analysis workflow was illustrated with examples from the literature.