page_title: Phasor approach to fluorescence lifetime and spectral imaging
section_title: Spectral phasor
hierarchical_section_title: Phasor approach to fluorescence lifetime and spectral imaging / Spectral phasor
caption_attribution_description: English: Spectral Phasor - Behavior of the phasor for different spectral widths.
context_page_description: Phasor approach refers to a method which is used for vectorial representation of sinusoidal waves like alternative currents and voltages or electromagnetic waves. The amplitude and the phase of the waveform is transformed into a vector where the phase is translated to the angle between the phasor vector and X axis and the amplitude is translated to vector length or magnitude.
  In this concept the representation and the analysis becomes very simple and the addition of two wave forms is realized by their vectorial summation.
  In Fluorescence lifetime and spectral imaging, phasor can be used to visualize the spectra and decay curves. In this method the Fourier transformation of the spectrum or decay curve is calculated and the resulted complex number is plotted on a 2D plot where the X axis represents the Real component and the Y axis represents the Imaginary component. This facilitate the analysis since each spectrum and decay is transformed into a unique position on the phasor plot which depends on its spectral width or emission maximum or to its average lifetime.
context_section_description: Similar to temporal phasor the Fourier transformation of spectra can be used to make phasor. Considering a Gaussian spectrum with zero spectral width and changing the emission maximum from channel zero to K the phasor rotates on a circle from small angles to larger angles. This corresponds to shift theorem of Fourier transformation. Changing the spectral width from zero to infinity moves the phasor toward center. This means that the phasor for background signal which can be considered as a spectrum with infinite spectral width is located at center of phasor with coordinate of (0,0).
caption: Behavior of the phasor for different spectral widths.
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