Analytic plenoptic camera diffraction model and radial distortion analysis due to vignetting

Using a mathematical approach, this paper presents a generalization of semi-analytical expressions for the point spread function (PSF) of plenoptic cameras. The model is applicable in the standard regime of the scalar diffraction theory while the extension to arbitrary main lens transmission functions generalizes a priori formalism. The accuracy and applicability of the model is well verified against the exact Rayleigh-Sommerfeld diffraction integral and a rigorous proof of convergence for the PSF series expression is made. Since vignetting can never be fully eliminated, it is critical to inspect the image degradation it poses through distortions. For what we believe is the first time, diffractive distortions in the diffraction-limited plenoptic camera are closely examined and demonstrated to exceed those that would otherwise be estimated by a geometrical optics formalism, further justifying the necessity of an approach based on wave optics. Microlenses subject to the edge diffraction effects of the main lens vignetting are shown to translate into radial distortions of increasing severity and instability with defocus. The distortions due to vignetting are found to be typically bound by the radius of the geometrical defocus in the image plane, while objects confined to the depth of field give rise to merely subpixel distortions.