Annular Fresnel zone aperture: a single-parameter mask family for lensless imaging

We introduce the annular Fresnel zone aperture (AFZA), a single-parameter analytical extension of the classical Fresnel zone aperture (FZA) for amplitude-mask lensless imaging. AFZA replaces the squared-radius phase r² in the FZA transmittance with a radially shifted (r-αR)², giving a closed-form, binary, rotationally symmetric mask family that retains the analytic forward model and TV-ADMM reconstruction backbone of FZA, with α=0 recovering FZA exactly. The single coefficient α raises area-averaged photon throughput and redistributes modulation transfer toward low-to-mid spatial frequencies while preserving the band-averaged full-band MTF within ±4%. In the physical USAF experiment at α=0.10 and r₁=0.32 mm, PSNR increases from 15.79 dB to 16.87 dB and SSIM from 0.777 to 0.873 under an identical 100-iteration ADMM budget. Fourteen chrome-on-glass masks were fabricated across two mask scales: one FZA and seven AFZAs at r₁=0.32 mm and one FZA and five AFZAs at r₁=0.56 mm.