Archaic focusing properties of Fresnel zone plates

Results published previously [ J. Opt. Soc. Am.57, 610 ( 1967)] concerning the focusing properties of Fresnel zone plates were obtained by implicitly invoking the Fraunhofer approximation. A comparison of these results with those derived from Fresnel diffraction theory shows that the focusing properties of Fresnel zone plates predicted by Fraunhofer diffraction theory are incorrect except for resolution defined by the Rayleigh criterion.