= Poisson photon contrast benchmark
{title2=$\Delta N/N\propto N^{-1/2}$}
For a known-background Poisson measurement with mean $N$, the <standard deviation> is $\sqrt N$. A small added mean $\Delta N$ has approximate <signal-to-noise ratio> $\Delta N/\sqrt N$ when background counting noise dominates. A fixed criterion $z$ therefore gives $\Delta N\approx z\sqrt N$ and fractional contrast $z/\sqrt N$. This is a stated observation model, not a universal human threshold or a two-alternative comparison formula.
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