One flash produces many different waiting times
A laser pulse raises a population of emitters into an excited state. They subsequently release photons at different times. In the simplest single-exponential specimen, lifetime is the mean waiting time. An individual photon may emerge much earlier or much later than that mean. The lifetime describes the distribution of many events.
The instrument takes an excitation pulse as a timing reference. A photon reaches the detector, which sends an electrical pulse to the timing electronics. The electronics stores the delay from the reference. Repeat the excitation, collect another event, and continue. Group arrivals with similar delays into bins and a decay curve appears.
Early bins generally contain more photons than later ones. An exponential decay means that the remaining excited population falls by the same fraction in each equal time interval. The arrival of one photon gives little guidance about the mean. Many sparse observations reveal the shape of the waiting-time distribution.
Sources: [2]
The stopwatch adds a timing spread of its own
Real laser pulses have a finite width. A detector also takes slightly different times to turn successive photons into electrical signals. Even a reference that responds almost immediately produces a small spread of recorded delays. This prompt peak is the instrument response: it measures timing blur from the source, optical path and detection electronics together.
A measured fluorescence peak therefore mixes the specimen wait with that instrumental blur. The analysis measures a prompt reference, applies its spread to each proposed decay, and compares the resulting curves with the observed counts. Adding contributions from the possible response delays in this way is called convolution.
Imagine each recorded arrival as a specimen waiting time plus an additional random instrumental delay. The combined peak width cannot simply be shortened by cutting off a fixed section with a ruler. If the specimen decay is much shorter than the response, finite photon statistics can hide the small differences between possible lifetimes.
Repeated excitation introduces another timing relation. A photon left over from an earlier excitation may arrive after the next reference pulse. Its recorded delay then falls in a later cycle, folding part of a long tail toward the beginning of the histogram. A lower repetition rate separates decays more clearly. A suitable periodic model can also include earlier-cycle contributions when the reference clock and total cycle count are retained.
Brighter light can make the apparent decay faster
Increasing brightness seems an obvious way to collect a decay curve sooner. Some counting arrangements, however, retain only the first photon in an excitation cycle. If several arrive, an early photon occupies the available timing opportunity and later photons disappear from the record. Additional photons then enter the histogram in unequal proportions.
This first-photon preference is called pile-up distortion. The front of the curve becomes relatively too high and its tail too low, making the specimen appear to decay faster. The detector itself also needs time to recover after a detection. During this dead time, arriving photons may produce no usable electrical pulse. Recovery can extend into subsequent excitation cycles.
Conventional low-rate measurements therefore leave most excitation cycles empty. Many repetitions supply sparse events with much less selection bias. Modern timing hardware has different recovery and multiple-event capabilities, so usable rates depend on the particular system. Retaining timestamps, prompt and background measurements, and the complete number of reference cycles makes the sampling process available for examination.