## Time gated Phasor

Phasor approach is powerful technique for visualization and analysis of lifetime images. Here we show the application of this approach to different gate settings (number of time gates, total measurement window...

### Introduction

Phasor approach is a graphical method which has been used for representation
of alternative currents and electromagnetic waves which simplifies their analysis
by converting them into a vector. In Fluorescence lifetime imaging, the decay curves
are transformed into a vector where the magnitude and the phase of the vector correspond
to the lifetime of the decay curve.

Assuming an exponential decay curve with lifetime of τ :

The Fourier transformation is represented by:

This is a complex function where plotting the imaginary part versus real part for
lifetimes ranging from zero to infinity will make a semicircle :

As demonstrated in the figure above, by varying the lifetime from zero to infinity
the phasor point moves along a semicircle in the counter clock wise direction from
coordinate (1,0) to (0,0). The lifetimes can be estimated by measuring the phase
or the amplitude of the phasor shown by pink vector. For measurements with a discrete
number of time bins of equal width, like time gating and TCSPC, equation for reference
semicircle R can be rewritten as(Fereidouni et al.):

Where *T* is the total time window and *K* is the number of time gates.
ωis the first harmonic frequency and is defined by: 2π/T. Figure below
shows the modified semicircle for different number of time gates.

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## Links

- Wikipedia

An article on phasor approach - ImageJ

Open source Image processing -
Molecular Biophysics Utrecht

Biophysics Utrecht - Blablab

Understanding Matter, One Molecule At A Time - BioImaging
Utrecht

Website Builder Software & Tools - SimFCS

Globals Software for Spectroscopy and Images

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