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.