Photon limit of an eclipse difference spectrum

For a fractional feature amplitude $d$, equal independent in- and out-of-eclipse samples with $N_{\gamma }$ stellar photons each have fractional difference noise approximately $\sqrt{2/N_{\gamma }}$. The ideal significance is $d\sqrt{N_{\gamma }/2}$. Correlated systematics, stellar variability and unequal exposure budgets change this result.