Nonparaxial analysis of high-numerical-aperture photon sieves

Recently, a new class of diffractive optical element called a photon sieve, which consists of a great number of pinholes whose positions and radii are properly chosen, was developed for the focusing and imaging of soft X-rays. In the initial work, the concept of Fresnel zone and the numerical calculation of Fresnel-Kirchhoff diffraction integral was used for the analysis and design. More recently, we developed the paraxially individual far-field model for the focusing analysis of low-numerical-aperture (low-NA) photon sieves. Here, we extend this model to the nonparaxial case of high-NA photon sieves working in the soft X-ray region, for which the paraxial Fresnel diffraction formula is invalid.