Signal to noise in sparse aperture imaging

We have performed numerical experiments that mapped out the relationship between fill fraction (f) and exposure time (t), and worked out quantitative and qualitative explanations for why the exposure time scales the way it does with fill fraction. These experiments indicate that the relationship t∝f^-3 holds only if the aperture is scaled properly as the fill fraction decreases. In particular, the number of apertures must increase roughly as the inverse of the fill fraction. This work provides useful insight into what the tradeoffs are between types of sparse apertures