PET Scanner: Coincidence Detection

PET Scanner

Tracer activity 40 dps

Coincidence window 6 ns

Positron range blur 2 mm

True coincidences

Random coincidences

Decays emitted

Random fraction

How it works

A PET tracer molecule decays by β⁺ (positron) emission. The positron travels a short distance through tissue, loses energy, then annihilates with an electron — converting their rest mass into two 511 keV gamma photons flying in (almost) exactly opposite directions. A ring of detector crystals surrounds the patient; whenever two crystals fire within a short electronic "coincidence window," the scanner assumes both photons came from one annihilation and draws a straight line — the line of response (LOR) — connecting the two hits. No single LOR tells you where along it the decay happened, but summing thousands of LORs by backprojection makes them overlap most densely where the tracer actually is, and the image emerges.

R_random ≈ 2·τ·S₁·S₂     (τ = coincidence window, Sᵢ = singles rate)
image(x) += Σ 1{ LOR passes near x }   (simple backprojection)

Tracer activity — decays per second. More activity fills in the image faster, but random coincidences grow with the square of activity, so a very hot source gets noisier, not just brighter.
Coincidence window — how long the electronics wait for a second hit before giving up. A wider window catches more true pairs but also lets far more unrelated single photons masquerade as a pair — random coincidences scale linearly with it.
Positron range blur — the positron doesn't annihilate exactly where it was emitted; it drifts a little first. This is a hard physical floor on PET resolution no amount of better electronics can remove.
Random coincidences (red flashes) add straight lines with no relation to the source position — watch them fog the reconstructed image as activity and window increase.

Real-world relevance: this true/random tradeoff is exactly why clinical PET scanners use short (nanosecond-scale) coincidence windows and correct measured counts for an estimated random rate before reconstructing the final image.

Tracer hotspot True coincidence Random coincidence Reconstructed image

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