Time-correlated single-photon counting (TCSPC)

Time-correlated single-photon counting (TCSPC) records how light emission evolves after a short excitation pulse by detecting at most one photon per pulse and measuring its delay with picosecond precision. Repeated over millions of pulses, the delays build a histogram whose shape is the decay curve. It is the standard method for fluorescence lifetimes in the 50 ps to 100 ns range, and it is also used for photon-correlation measurements, time-of-flight ranging and time-resolved photoluminescence of semiconductors. With a fast detector the instrument response function (IRF) is typically 20–50 ps FWHM, and deconvolution resolves lifetimes well below that.

How the measurement works

A pulsed laser, usually a gain-switched pulsed diode at 1–80 MHz or a mode-locked laser near 80 MHz, excites the sample. A reference signal marks each pulse. The emitted light is attenuated until a single-photon detector registers a photon on only a small fraction of pulses. A timing circuit, historically a time-to-amplitude converter and now more often a time-to-digital converter, measures the interval between the reference and the photon, and the interval is added to one of several thousand histogram bins. Spreading 4096 bins over a 50 ns window gives 12.2 ps per bin. Because the timing circuit is busy after each event, most systems run in reverse start-stop mode: the photon starts the clock and the next laser pulse stops it, so the circuit is triggered only on the rare pulses that produce a count.

Detector choices are described in their own entries. A thin-junction single-photon avalanche diode or a microchannel-plate photomultiplier tube gives an IRF of a few tens of picoseconds; a conventional dynode PMT gives roughly 150–300 ps; superconducting nanowire detectors (SNSPD) reach below 20 ps in the near infrared. The detector's timing jitter usually dominates the IRF, with the laser pulse width and electronics adding in quadrature.

Pile-up and the count-rate rule

The detector and electronics can register only the first photon after each pulse, so when more than one photon arrives in a period the early ones are over-counted and the histogram is distorted toward short times. The standard rule keeps the detection rate at 1–5 % of the excitation rate. The fraction of detecting pulses that actually contained two or more photons follows from Poisson photon statistics: at a 1 % detection probability it is 0.50 %, and at 5 % it is 2.5 %. At 20 MHz excitation, the 1 % rule allows 200,000 counts per second. Faster multi-stop electronics relax the limit, but the detector's own dead time still applies.

Photon budget and lifetime precision

For a single-exponential decay with negligible background, the relative standard deviation of the fitted lifetime is close to

$$\frac{\sigma_\tau}{\tau} \approx \frac{1}{\sqrt{N}},$$

where $N$ is the number of photons in the histogram. A 1 % lifetime therefore needs about 10,000 counts, which takes 50 ms at 200,000 counts per second. Multi-exponential fits, background and a broad IRF all raise the requirement, often by one to two orders of magnitude for resolving two components with similar lifetimes.

The repetition period must also exceed the decay. For a dye with a 4 ns lifetime at 80 MHz (12.5 ns period), 4.4 % of the emission is still arriving when the next pulse fires and wraps into the start of the histogram. At 20 MHz (50 ns period) the residue is below 10⁻⁵. A working guideline is a period of at least five lifetimes.

Where it is used

Fluorescence lifetime imaging (FLIM) combines TCSPC with a scanning confocal microscope, storing a histogram per pixel to map lifetime changes caused by binding, pH or energy transfer. Carrier lifetimes in semiconductors and quantum wells are measured the same way from time-resolved photoluminescence. With two detectors and no laser reference, the same electronics record the second-order correlation $g^{(2)}(\tau)$ used to show single-photon emission. Timing photons returned from a pulsed source also gives single-photon lidar, where 10 ps corresponds to 3.0 mm of optical path, or 1.5 mm of range.

Pitfalls

A slow diffusion tail in some silicon SPADs and afterpulsing in PMTs and SPADs add features that can be mistaken for a second lifetime component; measuring the IRF with a scattering sample at the excitation wavelength exposes them. The IRF of many detectors shifts with photon wavelength, so an IRF recorded at the laser wavelength can be displaced by tens of picoseconds relative to red-shifted emission. Scattered excitation light leaking through the filters adds a sharp peak at time zero.

Common questions

Why count only one photon per pulse?

The timing channel records the first detected photon of each cycle. If several photons often arrive, the recorded times are biased toward the earliest ones and the measured decay comes out too fast; keeping the probability of detection per pulse low makes the histogram an unbiased estimate of the emission profile.

Can TCSPC measure lifetimes shorter than the instrument response?

Yes, by iterative reconvolution: a model decay is convolved with the measured IRF and fitted to the data. Lifetimes of roughly a tenth of the IRF width can be recovered when the count is high and the IRF is measured carefully.

References: D. V. O'Connor and D. Phillips, Time-Correlated Single Photon Counting (Academic Press, 1984); W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Springer, 2005); J. R. Lakowicz, Principles of Fluorescence Spectroscopy, 3rd ed. (Springer, 2006).