Probabilistic view of the luminescence phasor plot and description of the universal semicircle as the sum of two spiraling curves

作者：Berberan Santos Mario N^*

来源：Journal of Mathematical Chemistry, 2015, 53(5): 1207-1219.

DOI：10.1007/s10910-015-0481-y

• Luminescence decay
• Relaxation function
• Characteristic function
• Fourier transform
• Spiral

Luminescence decay functions describe the time dependence of the intensity of radiation emitted by electronically excited species. Decay phasor plots (plots of the Fourier sine transform vs. the Fourier cosine transform, for one or several angular frequencies) are being increasingly used in fluorescence, namely in lifetime imaging microscopy. In this work it is shown that the universal semicircle, locus of all exponential decay functions, can be viewed as the weighted sum of two spiraling phasors, one corresponding to a truncated exponential and the other to a shifted exponential. The geometric details of this recomposition are discussed. With area normalization, the decay functions form a subset in the universe of one-sided probability density functions, the same being valid for the phasor plots, which are parametric plots of the respective characteristic functions.

• 出版日期2015-5