Polar plot representation of time-resolved fluorescence

Measuring changes in a molecule's fluorescence emission is a common technique to study complex biological systems such as cells and tissues. Although the steady-state fluorescence intensity is frequently used, measuring the average amount of time that a molecule spends in the excited state (the fluorescence lifetime) reveals more detailed information about its local environment. The lifetime is measured in the time domain by detecting directly the decay of fluorescence following excitation by short pulse of light. The lifetime can also be measured in the frequency domain by recording the phase and amplitude of oscillation in the emitted fluorescence of the sample in response to repetitively modulated excitation light. In either the time or frequency domain, the analysis of data to extract lifetimes can be computationally intensive. For example, a variety of iterative fitting algorithms already exist to determine lifetimes from samples that contain multiple fluorescing species. However, recently a method of analysis referred to as the polar plot (or phasor plot) is a graphical tool that projects the time-dependent features of the sample's fluorescence in either the time or frequency domain into the Cartesian plane to characterize the sample's lifetime. The coordinate transformations of the polar plot require only the raw data, and hence, there are no uncertainties from extensive corrections or time-consuming fitting in this analysis. In this chapter, the history and mathematical background of the polar plot will be presented along with examples that highlight how it can be used in both cuvette-based and imaging applications.