= Poisson photon counting
{c}
{title2=$\sigma_N=\sqrt{\langle N\rangle}$}
For independent <photon> detections with a fixed mean rate, counts in a fixed exposure have a <Poisson distribution>, so the <variance> equals the mean. Multiplying by a representative <photon energy> gives $\sigma_E=h\nu\sqrt N$. A source-only signal-to-noise threshold $q$ therefore needs an expected $N=q^2$ <photons>. Background, detector noise, variable illumination and <photon> correlations can invalidate that source-only formula.
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