Fluorescence lifetime imaging or FLIM is a powerful tool for producing images based on the variation in the fluorescence decay characteristics of a fluorescent sample. It can be used as an imaging technique in confocal microscopy and other microscope systems.

The lifetime of the fluorophore signal, rather than its intensity, is used to create the image in FLIM. This has the advantage of minimizing the effect of photon scattering in thick layers of sample. FLIM is very useful for biomedical tissue imaging, allowing to probe greater tissue depths than conventional fluorescence microscopy.

## Contents

A fluorophore which is excited by a photon will drop to the ground state with a certain probability based on the decay rates through a number of different (radiative and/or nonradiative) decay pathways. To observe fluorescence, one of these pathways must be by spontaneous emission of a photon. In the ensemble description, the fluorescence emitted will decay with time according to

$-t/\tau$

where

$1}{\tau$ .

In the above, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): t is time, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \tau is the fluorescence lifetime, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): F_0 is the initial fluorescence at Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): t=0 , and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): k_i are the rates for each decay pathway, at least one of which must be the fluorescence decay rate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): k_f . More importantly, the lifetime, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \tau , is independent of the initial intensity of the emitted light. This can be utilized for making non-intensity based measurements in chemical sensing.

## Measurement and processing

Fluorescence lifetime imaging yields images with the intensity of each pixel determined by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \tau , which allows one to view contrast between materials with different fluorescence decay rates (even if those materials fluoresce at the exact same wavelength), and also produces images which show changes in other decay pathways, such as in FRET imaging.

### Pulsed illumination

Fluorescence lifetimes can be determined in the time domain by using a pulsed source. Time-correlated single photon counting (TCSPC) is usually employed because variations in source intensity and photoelectron amplitudes are ignored, the time resolution can be upwards of 4 ps, and the data obeys Poisson statistics (useful in determining goodness of fit during reconvolution).

When a population of fluorophores is excited by an ultrashort or delta pulse of light, the time-resolved fluorescence will decay exponentially as described above. However, if the excitation pulse or detection response is wide, the measured fluorescence, M(t), will not be purely exponential. The instrumental response function, IRF(t) will be convolved or blended with the decay function, F(t).

$M}(t) = {IRF}(t) \otimes {F$

The decay function (and corresponding lifetimes) cannot be recovered by direct deconvolution using Fourier transforms because division by zero will produce errors and noise will be amplified. However, the instrumental response of the source, detector, and electronics can be measured, usually from scattered excitation light. The IRF can then be convoluted with a trial decay function to produce a calculated fluorescence, which can be compared to the measured fluorescence. The parameters for the trial decay function can be varied until the calculated and measured fluorescence curves fit well. This process is known as reconvolution or reiterative convolution, and can be performed quickly by several software packages.

### Phase modulation

Alternatively, fluorescence lifetimes can be determined in the frequency domain by a phase-modulated method. The intensity of a cw source is modulated at high frequencey, by an AOM for example, which will modulate the fluorescence. Since the excited state has a lifetime, the fluorescence will be delayed with respect to the excitation signal, and the lifetime can be determined from the phase shift. Also, y-components to the excitation and fluorescence sine waves will be modulated, and lifetime can be determined from the modulation ratio of these y-components. Hence, 2 values for the lifetime can be determined from the phase-modulation method.