Focusing analysis of the pinhole photon sieve: individual far-field model

Recently, a new class of diffractive optical element called a photon sieve, which consists of a great number of pinholes, was developed for the focusing and imaging of soft x rays. In terms of the closed-form formula for the far field of individual pinholes and the linear superposition principle, we present a simple yet accurate analytical model for the focusing of the pinhole photon sieve. This model is applicable to arbitrary paraxial illumination with arbitrary complex amplitude distribution at the photon sieve plane. We check the validity range of this model by comparing it with the exact Fresnel diffraction integral. Some special problems, such as the individual quasi-far-field correction for very large pinholes and the related phase shift induced by this correction, are also discussed.