= Photon counting
<Photon counting> registers discrete detector events and their times. A <beam splitter> sends the selected <light> to two <photodetectors>; a <coincidence circuit> or time-recording system compares the outputs. With a vacuum input at the unused <optical port>, splitter fractions $R,T$ and independent <quantum efficiencies> $\eta_1,\eta_2$, a selected input <photon> reaches the two recorded channels with probabilities $p_1=R\eta_1$ and $p_2=T\eta_2$. Conditional on input occupation $N$, each pair of distinct <photons> contributes $p_1p_2$ to the cross-channel pair moment. Therefore
$$
\langle K_1\rangle=p_1\mu,\qquad
\langle K_2\rangle=p_2\mu,\qquad
\langle K_1K_2\rangle=p_1p_2\langle N(N-1)\rangle.
$$
Their normalized ratio recovers $g^{(2)}(0)$. This assumes number-resolving counts, or sufficiently dilute gates for threshold detectors to approximate them. One <photon> cannot create both channel counts in this ideal model.
\Image[/photon-coincidence-readout.png]
{title=Functional two-detector photon-correlation measurement and its normalization}
{description=Original schematic: optical selection and a beam splitter feed independent detectors; all cross-channel time differences populate a histogram. A single photon produces at most one ideal detection. The empty splitter input is vacuum.}
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