Signal-to-noise ratio of Singer product apertures

Formulae for the signal-to-noise ratio (SNR) of Singer product apertures are derived, allowing optimal Singer product apertures to be identified, and the CPU time required to decode them is quantified. This allows a systematic comparison to be made of the performance of Singer product apertures against both conventionally wrapped Singer apertures, and also conventional product apertures such as square uniformly redundant arrays. For very large images, equivalently for images at very high resolution, the SNR of Singer product apertures is asymptotically as good as the best conventional apertures, but Singer product apertures decode faster than any conventional aperture by at least a factor of ten for image sizes up to several megapixels. These theoretical predictions are verified using numerical simulations, demonstrating that coded aperture video is for the first time a realistic possibility.