Signal-to-noise ratio in coded aperture imaging

We present a derivation of the signal-to-noise ratio (SNR) of a cyclic difference set (CDS) based coded mask which is simpler than that given in the literature, and which applies to any distribution of flux against the mask, not just Poisson statistics as is currently the case. We also present a derivation of a formula for the ratio of the SNR of a coded mask to that of an optimal mask which again is simpler and which applies to any open fraction, not just half open. This formula, which applies also in the presence of background noise, shows that Singer masks with just three different open fractions are sufficient to capture 95% of the optimal SNR in all cases, compared to 70% for half open masks. By distinguishing between three kinds of attenuation inherent to a coded mask imaging system, we also explain why, for extended sources, lowering the open fraction of CDS based masks can improve performance, while for several classes of non-CDS based masks the opposite is true.