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Fluorescence is photon emission following photon absorption by matter: an excited state releases some of its energy as light. A fluorophore can therefore mark where something is, while its fluorescence emission spectrum and fluorescence lifetime report different aspects of its environment. Fluorescein is one example; FRET exploits a competing route for excitation energy rather than requiring a second emitted photon.

The usual molecular sequence is excitation, relaxation, then emission, as in the Jablonski diagram. The emitted photon commonly has lower energy and longer wavelength, giving a Stokes shift; the exceptions are discussed below.^[ref]

A fluorescence emission filter transmits the chosen emitted wavelength band while rejecting excitation leakage. Finite rejection, overlap of the fluorescence emission spectrum with excitation, and the photodetector's wavelength-dependent response can all affect the count. A darker filtered image alone does not establish a changed fluorescence lifetime or increased photobleaching.

A fluorescence emission spectrum resolves emitted photons by wavelength at fixed excitation settings. Subtract a matched sample-container and solvent background, and correct the wavelength-dependent throughput and photodetector sensitivity when estimating the emitted distribution. A camera image through one fluorescence emission filter instead measures a weighted band integral, not a whole fluorescence emission spectrum. A fluorescence lifetime resolves delay after excitation; its horizontal axis is time, not wavelength.

A fluorescence instrument response is the distribution of recorded delays for an effectively prompt optical signal. Finite excitation-pulse width and timing variation in the photodetector and electronics contribute. With a normalized response $R$, intrinsic fluorescent photon rate $I$, and background rate $B$, the expected trace isFit a candidate decay after this convolution with the measured response; treating the broadened leading edge as the intrinsic decay can bias fluorescence lifetime. The accessible technical note describes measuring prompt scattered excitation with a nonfluorescent scattering sample.^[ref]

For the constant-rate model in fluorescence quantum yield, fluorescence lifetime is the mean residence time in the emitting excited state and the $1/e$ timescale of its exponential decay. The detected fluorescent photon rate after an ideal instantaneous pulse is $I(t)=\eta k_{\mathrm{r}}{N}_0{e}^{-t/\tau }$ for $t\ge 0$. Its amplitude and its decay timescale are separate quantities.

For a stipulated example, rates $(k_{\mathrm{r}},k_{\mathrm{nr}})=(0.05,0.20){\mathrm{ns}}^{-1}$ give $\tau =4\mathrm{ns}$ and $\Phi =0.20$. Rates $(0.20,0.05){\mathrm{ns}}^{-1}$ give the same $\tau$ but $\Phi =0.80$. Conversely, doubling $N_0$ doubles the ideal amplitude without changing $\tau$. Equal fluorescence lifetimes need not imply equal brightness or equal fluorescence quantum yields.

Different environments can supply several populations, giving $I(t)={\sum }_j{A}_j{e}^{-t/{\tau }_j}$ rather than one exponential decay. A fitted single timescale then depends on the selected model and detection band. FRET donor lifetime uses the change in a donor's decay when transfer introduces an additional loss route; the FRET branch develops that interpretation.

A fluorescence microscope maps photon emission to an image. Excitation light passes through a fluorescence excitation filter and reflects from a wavelength-selective beam splitter into the objective optical lens. Returning fluorescence passes through that beam splitter and a fluorescence emission filter to the photodetector. Rejecting excitation makes faint emission visible.^[ref]

An ordinary image records emission-band counts at each pixel. Adding pulse-delay measurements gives a fluorescence lifetime map; scanning emission wavelength gives spectral information instead. Confocal microscopy adds spatial rejection and confocal optical sectioning, as developed in its own branch. An unlabeled specimen under the same illumination reveals intrinsic fluorescence and excitation leakage; excitation-blocked frames reveal detector background. A blank cannot perfectly predict background in a differently prepared specimen.

A useful plot must keep three different times separate: source emission $t_e$, atomic absorption or re-emission $t$, and return reception $t_R$. For the cloud centroid,Let $q=f_0/f<1$. Resonant excitation requires $q{D}_{\mathrm{in}}(t)=1$. Since $D_{\mathrm{in}}$ decreases from $\gamma (1+\beta )$ to $\gamma (1-\beta )$, its zero-width resonance first becomes possible atAt equality the line centre is reached only at infinite approach distance, where illumination vanishes. A finite source start time further limits how closely that ideal threshold is approached. For $\beta >{\beta }_{\min }$ the line-centre event satisfiesThere is a second useful critical speed,for which excitation is centred on closest approach, $t_{\ast }=0$. For ${\beta }_{\min }<\beta <{\beta }_{\perp }$ it occurs on approach; for $\beta >{\beta }_{\perp }$ it occurs after closest approach. Even a receding ultra-relativistic atom can see the incident light blueshifted because $\gamma$ is large.

A photon emitted toward the origin near the atomic rest-frame frequency $f$ has return Doppler factorThe sign differs from that in $D_{\mathrm{in}}$ because the returning ray travels in the opposite direction. The returning line centre decreases from $\gamma (1+\beta )f$ on early approach to $\gamma (1-\beta )f$ on late recession, and is $f/\gamma$ at closest-approach emission. The origin receives that closest-approach radiation at $t_R=L/c$, not at zero. Prompt re-emission at exact resonance would giveIt is above $f_0$ below ${\beta }_{\perp }$, equal at ${\beta }_{\perp }$, and below $f_0$ above it. A finite fluorescence lifetime shifts emission later along the orbit and therefore usually toward a lower return frequency.

The following plots adopt a compact, optically thin cloud, weak excitation, isotropic incoherent spontaneous emission in the atomic rest frame, and negligible velocity dispersion. They show an intensity envelope as the observable amplitude; its rms electric-field amplitude is proportional to the square root of this intensity. An incoherent fluorescence signal has no fixed optical phase. The four rows include a nonrelativistic speed, both critical speeds, and an ultra-relativistic speed. All rows share one intensity normalization, so off-resonant signals remain visibly weak.

A model for fluorescence from a uniformly moving cloud generating the plotted envelopes iswhere $\mathcal{L}(\Delta )=[1+4{\Delta }^2/{\Gamma }^2{]}^{-1}$ is a Lorentz line shape of full width $\Gamma$. The factor $1-\beta s$ is the incident photon-flux correction per source-frame time. The population is an exponential memory of earlier absorption events, not an instantaneous resonance indicator. For a detector of fixed small area at the origin, its received bolometric intensity scales asTwo powers of $D_{\mathrm{out}}$ come from aberration of light, one from photon energy, and one from arrival-rate compression. Finite lifetime is dilated to $\gamma \tau$ in the source frame; over an interval with slowly changing geometry its observed decay time is $\tau /D_{\mathrm{out}}$. Thus approach can compress and amplify a pulse, while recession stretches and redshifts it. Illumination and collection each supply an inverse-square geometric factor in the prompt weak-excitation limit. Strong forward beaming can even make a detuned approaching precursor brighter than the later line-centre feature, as in the ultra-relativistic row; the intensity maximum need not occur at exact resonance.

Absolute amplitude and a unique detailed spectral line profile cannot be inferred from $f,\tau ,v$ alone: cloud size, atom number, source power, optical depth, angular emission pattern and saturation were not specified. Finite cloud size convolves these point-centroid curves with additional delays. The plots describe incoherent, frequency-redistributed emission near $f$; a coherent Rayleigh scattering component would instead retain the driving frequency in the atom frame and add a different spectral component. These qualifications do not change the kinematic resonance thresholds or return-time relations.

Photobleaching is an irreversible loss of fluorescent capacity caused by illumination. It changes the number of active fluorophores over experimental time; fluorescence lifetime concerns the delay after an individual excitation. Reversible dark states and ordinary return to the ground state are different processes.

In a stipulated population-loss model, let $T$ denote elapsed illumination time and $t$ denote delay after a pulse. If active population declines as $e^{-k_{\mathrm{b}}T}$ while surviving fluorophores retain the same decay rates, then $I(t;T)=A_0{e}^{-k_{\mathrm{b}}T}{e}^{-t/\tau }$. Brightness falls while $\tau$ stays fixed. This example does not assert that all bleaching follows exponential decay: chemical changes and selective loss from a mixture can also change the observed decay shape. The existing FRET photobleaching controls illustrate why deliberate bleaching requires careful interpretation.

TCSPC accumulates a histogram of detected photon delays relative to repeated excitation pulses. Each cycle supplies a timing reference; many cycles provide the decay distribution. The fluorescence instrument response broadens that distribution. In conventional first-event acquisition, losing later photons in a cycle preferentially preserves early arrivals: this pile-up can falsely shorten the inferred fluorescence lifetime. Keep detection probability per cycle low and check stability when the illumination is attenuated.^[ref]