Poisson photon contrast benchmark ($\Delta N/N\propto N^{-1/2}$)

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.