An ideal Fresnel Zone Plate that is extended to infinity would focus light to a d-function like spot (top row).
The focal spot produced by a real Fresnel zone plate is surrounded by rings of intensity (secondary maxima) that blur the images obtained in X-ray microscopy and scanning spectroscopy. For a zone plate each ring contributes equally to the amplitude at the focus. This contribution drops abruptly to zero beyond the outermost ring which leads to strong intensity oscillations in the diffration pattern (middle row).
With a photon sieve the number of pinholes per ring can be readily adjusted to yield a smooth transition which minimizes the secondary maxima (bottom row). This provides sharper images. Note that diffraction intensities are plotted on a log scale (right column).