Tailored fractional vortex beams for incoherent imaging and deconvolution

Imaging under spatially incoherent illumination remains a key challenge due to resolution loss from diffraction-limited point-spread functions (PSFs). We investigate engineered PSFs generated by two fractional vortex phase masks, the anomalous multiramp phase plate, and the elliptical fractional vortex phase plate, applied here for the first time, to our knowledge, in incoherent imaging. These phase domain-coded apertures introduce controllable phase discontinuities, singularity distributions, and anisotropic diffraction features, enabling flexible PSF shaping through fractional topological charge, ramp geometry, and ellipticity. We analyze how parameter variations transform PSF structures, from compact spiral lobes to extended asymmetric patterns, and discuss their implications for spatial encoding, directional selectivity, and depth discrimination. To overcome the reconstruction challenges posed by such PSFs, we propose a frequency regularized nonlinear reconstruction (FR-NLR) algorithm that incorporates spectral priors for enhanced stability. Quantitative and qualitative evaluations show that FR-NLR consistently outperforms the nonlinear reconstruction (NLR), Lucy-Richardson-Rosen algorithm, and Wiener deconvolution, achieving compact, high-fidelity, robust, and scan-free incoherent imaging.