A Fresnel zone plate, used as a coded aperture, offers a great advantage in geometric collection efficiency over a conventional pinhole or collimator. We present a detailed analysis of the signal-to-noise ratio (SNR) of a quantum-limited zone plate camera. The magnitude and spatial distribution of the noise field and its dependence on the source distribution and the characteristics of the optical processing system are derived. It is shown that the largest SNR advantage occurs for a point source, while for very large, uniform sources there may be a slight net disadvantage to using a zone plate. It is also shown that optical processing does not give the highest possible SNR.
H. H. Barrett and G. D. DeMeester, "Quantum Noise in Fresnel Zone Plate Imaging," Appl. Opt. 13, 1100-1109 (1974)