Resolving power of a hybrid zone-plate/gradient-index lens system

Following the Rayleigh criterion for resolution, we analyze the resolving power of a hybrid optical structure composed of a zone plate and a gradient-index lens at focal planes inside and outside the lens in terms of the type and number of zones of the zone plate. The Fraunhofer approximation can be invoked to study the irradiance at the Fourier planes inside the lens. In all other cases, the Fresnel diffraction integral must be used, although the resolution defined by the Rayleigh criterion still holds. We compare the limit of resolution for the hybrid structure with the resolution of a lens with the same aperture diameter as a function of the number of zones, stating that both coincide for a large number of zones. Finally, we present irradiance profiles with both approximations at various planes inside the lens and compare the results with those obtained by the use of zone plates in free space.