Spiral adaptive Fresnel lens: wave optics

We recently introduced adaptive Fresnel lenses (AFLs) based on complementary cylindrical lenses "bent into" spirals. Here, we start to investigate the wave optics of such components. We calculate typical point-spread functions and investigate diffraction effects in the case of narrow windings. We design a modification that results in the phase profile for light that passes through corresponding windings being that of a parabolic lens, exactly, but only in the case of infinitesimally thin phase components. Our findings contribute to the improvement and understanding of spiral AFLs.